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1★ What is it? (term, expression, equation, formula or identity?)
2★ Is it an equation or an identity?
3★ Product of two brackets equating coefficients (quadratics)
4★ Equating coefficients (inc. factorising)
5★ Equating coefficients (inc. completing the square)
6★ Equating coefficients (inc. completing the square) - harder

Algebra vocabulary and understanding

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1★ Provide a counterexample to disprove a statement
2★ Show a simple identity by expanding a linear expression is true
3★ Show that an identity involving a product of two linear expressions is true
4★ Show that an expression is even, odd, multiple of or factor of a number
5★ Show that a harder expression is a even, odd, multiple of or factor of a number

Algebraic proof

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1★ Single variable addition and subtraction
2★ Addition and subtraction of multiples of a single variable
3★ Multiplying and dividing terms
4★ Collecting two or more variables
5★ Collecting two or more variables inc powers
6★ Find the perimeter of a shape with linear expressions as the lengths of the sides

Simplify an expression

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$1★ Simplify 2★ Add or subtract fractions 3★ Simplify a fraction by factorising 4★ Multiply or divide 5★ Add or subtract fractions with linear denominator expressions 6★ Solve algebraic fractional equations (integer solutions)$

Algebraic fractions

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$1★ Rearrange in 1 step 2★ Rearrange in 2 steps 3★ Rearrange a formula involving a fraction 4★ Rearrange a formula involving powers or roots 5★ Rearrange common formula 6★ Rearrange a formula where the subject appears more than once$

Change the subject

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1★ First quadrant only
2★ First and second quadrant only
3★ Third and fourth quadrants only
4★ All quadrants
5★ Identify a coordinate to complete a shape
6★ Find the midpoint of a line between 2 points

Identify coordinates in all 4 quadrants

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1★ State the equation from a graph
2★ Sketch the graph from the equation (integer intercepts)
3★ Sketch the graph from the equation (decimal intercepts)
4★ Where does x = a and y = b meet?
5★ Does the point lie on the line?

Find and use y = a, x = a and y = x

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1★ Find the y-intercept
2★ Calculate the gradient where Δx is 1
3★ Calculate a positive gradient where Δx is not 1
4★ Calculate a negative gradient where Δx is not 1
5★ Finding gradient from a graph
6★ Finding y=mx+c from a graph

Find y = mx + c from a graph

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1★ Interpret the gradient or y-intercept from y = mx + c
2★ Rearrange ax + by = c into the form y = mx + c and interpret the gradient or y-intercept (integer values only)
3★ Rearrange ax + by = c into y = mx + c and interpret the gradient or y-intercept

Rearranging into the form y = mx + c

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1★ Complete a table of coordinate pairs (find y coordinates)
2★ Complete a table of coordinate pairs (find x or y coordinates)
3★ Find the y-intercept given the gradient and a coordinate
4★ State the equation of a line given the gradient and a coordinate
5★ Calculate the gradient given 2 coordinates
6★ State the equation of a line given 2 coordinate pairs

Using and exploring y = mx + c

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1★ Given coordinates for two lines, determine if they are parallel
2★ Write down the equation of a line parallel to y=mx+c
3★ Given 2 linear equations, determine if they are parallel
4★ Write the linear equation of a line parallel to y=mx+c that passes through (a,b)
5★ Given the equation of a line and the horizontal distance between this and a parallel line, find the equation of the parallel line

Find the equation of a parallel line

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1★ Write the perpendicular gradient to a given gradient
2★ Given two pairs of coordinates from two straight lines, determine if they are perpendicular
3★ Write down a linear equation that is perpendicular to y=mx+c
4★ Given 2 linear equations, prove they are perpendicular to eachother
5★ Given 2 linear equations, determine if they are perpendicular
6★ Write the linear equation of a line perpendicular to y=mx+c that passes through (a,b)

Find the equation of a perpendicular line

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1★ Write the perpendicular gradient to a given gradient
2★ State the gradient of a tangent given the gradient of the radius
3★ Find the equation of the tangent given the equation of the radius and coordinates of tangent intersection with the radius on the circumference of the circle
4★ Find the equation of the tangent given equation of circle and coordinates of the intersection with the tangent and the radius on the circumference of the circle
5★ Find the equation of the tangent given the equation of the circle and the x-coordinate of the intersection with the tangent and the radius on the circumference of the circle
6★ Problem solving - e.g. find the area bounded by the axes and the tangent to a circle

Equation of a tangent to a circle

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1★ Use a graph to solve when x=a and y=b
2★ Use a graph to solve when x=a/y=b and y=mx+c
3★ Use a graph to solve when y=ax+b and y=cx+d
4★ Use a graph to show why there no solution to two linear equations - they are parallel
5★ Use a graph to solve when a quadratic and linear equation

Graphical solutions of equations

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1★ Complete a table of coordinate pairs for simple quadratics y=x^2 or cubics y=x^3
2★ Complete a table of coordinate pairs for quadratics y=x^2+bx+c or cubics y=x^3 + bx^2 + d
3★ Draw a quadratic y=ax^2+c or cubic y=ax^3 + cx function
4★ Given a quadratic and cubic, identify the equation from a given graph
5★ Given a quadratic or cubic graph, find x or y estimates from the graph

Quadratic and cubic functions

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Equation of a circle

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1★ Draw a speed-time graph for a given scenario
2★ Calculate the area under a speed-time graph (given that the graph is trapezium or rectangular in shape)
3★ Calculate the y-axis scale given a speed-time graph and the area under the graph
4★ Estimate the area under a graph (quadratic)
5★ Given a curve, determine if the estimate for the area under the curve is an under or over estimate
6★ Given a curve, calculate the area under the curve when it includes calculating negative areas (dependent on context)

Area under a graph

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1★ Complete a table of coordinate pairs given a domain of values
2★ Draw an reciprocal function given the equation and domain
3★ Given a reciprocal and exponential function, identify the equation of a given graph
4★ Given a reciprocal graph, find x or y estimates from the graph
5★ Identify asymptotes of a reciprocal function given its graph

Reciprocal functions

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1★ Complete a table of coordinate pairs given a domain of values
2★ Draw an exponential functio given the equation and domainn
3★ Given a reciprocal and exponential function, identify the equation of a given graph
4★ Given an exponential graph, find x or y estimates from the graph
5★ Use a graph to solve exponential equations in the form a^x=b

Exponential functions

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1★ Given a trigonometry graph, identify whether it is the sin, cos and tan graph
2★ Identify specific coordinates on a sin, cos or tan graph
3★ Sketch y=sinx, y=cosx or y=tanx for a given domain
4★ Using the graph of y=sinx, y=cosx or y=tanx and 1 solution to a given equation for the same function, find another solution using the graph
5★ Given a solution to sinx=a, cosx=a or tanx=a, find another solution without the aid of a graph

Trigonometry graphs

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1★ Solve a 1 step equation by reversing the addition or subtraction of a constant
2★ Solve a 1 step equation by reversing a multiplication or division of a constant
3★ Solve a 2 step equation in the form ax+b=c where x has a positive coefficient
4★ Solve a 2 step equation in the form ax+b=c where x has a negative coefficient
5★ Solve a linear equation in the form a(x+b)=c
6★ Problem solving

Solve linear equations (unknown on 1 side, int ans)

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Solve linear equations (unknown on 1 side, dec ans)

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1★ Solve a linear equation with the unknown on both sides in the form ax=bx+c
2★ Solve a linear equation with unknowns on both sides in the form ax+b=cx+d where x has positive coefficients
3★ Solve a linear equation with unknowns on both sides in the form ax+b=cx+d where x has negative coefficients
4★ Solve a linear equation with unknowns on both sides in the form a(x+b)=cx+d
5★ Solve a 'I think of a number' problem where the unknown number appears on both sides of a linear equation
6★ Problem solving, e.g. opposite sides of a rectangle are given as linear expressions and need to solve for an unknown

Solve linear equations (unknown both sides)

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$1★ Solve linear equation in the form a(x+b)=c 2★ Solve an equation involving the collection of like terms when finding the sum or difference of two linear expressions involving brackets 3★ Solve a linear equation in the form a(bx+c)=dx+e 4★ Solve a linear equation in the form a(bx+c)=dx+e where the multiplier of the bracket is a unit fraction 5★ Solve a linear equation involving the expansion of brackets on both sides of the equals sign 6★ Solve a linear equation involving multiple expansion of brackets$

Solve linear equations with brackets

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$1★ Solve a linear rational equation in the form ax/b=c 2★ Solve a linear rational equation in the form (ax+b)/c=d 3★ Solve a linear rational equation in the form (ax+b)/(cx+d)=e 4★ Solve a linear equation with fractional expressions on each side of the equals 5★ Solve a linear rational equation where you have the sum or difference of two fractional expressions 6★ Solve a rational equation involving the sum or difference of two linear equations, that leads to solving a quadratic equation$

Solve rational equations

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1★ Expand a(x+b)
2★ Expand a(bx+c)
3★ Expand x(x+a)
4★ Expand ax(bx+c)
5★ Expand the sum or difference of two linear brackets and simplify
6★ Given a linear identity in the form a(bx+c)=dx+e, identify unknown values where 1 letter is not given on each side

Expand over a single bracket

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1★ Expand (x + a)(x + b)
2★ Expand (x±a)(x±b)
3★ Expand (x+a)(x-a)
4★ Expand (ax±b)(cx±d)
5★ Expand the product of 2 quadratic or cubic expressions
6★ Expand the product of 3 linear expressions

Expand 2 or more binomials

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1★ Factorise linear expression ax±b
2★ Factorise a quadratic expression ax^2±bx
3★ Factorise a quadratic expression ax^2±bx with a expression common factor
4★ Can a quadratic in the form ax^2±bx be factorised?
5★ Problem solving, e.g. find the sides of a rectangle given a quadratic that represents the area
6★ Fully factorise a linear expression by combining a sum of 2 terms where 1 is partially factorised

Factorise a simple expression

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1★ Factorise a quadratic resulting in (x + a)(x + b)
2★ Factorise a quadratic resulting in (x + a)(x - b)
3★ Factorise a quadratic resulting in (x - a)(x - b)
4★ Factorise a quadratic resulting in (x + a)(x - a)
5★ Factorise a quadratic resulting in (ax + b)(x + c)
6★ Factorise a quadratic resulting in (ax + b)(c - dx) or (ax + b)(cx + d)

Factorise a quadratic expression

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1★ Solve a quadratic resulting in (x + a)(x + b)
2★ Solve a quadratic resulting in (x + a)(x - b)
3★ Solve a quadratic resulting in (x - a)(x - b)
4★ Solve a quadratic resulting in (x + a)(x - a)
5★ Solve a quadratic resulting in (ax + b)(x + c)
6★ Solve a quadratic resulting in (ax + b)(c - dx) or (ax + b)(cx + d)

Solve a quadratic by factorising

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$1★ Solve like a quadratic x^(2n)±bx^n+c where n>1 2★ Solving like a quadatic involving a rearrangement e.g. x^(2n)=bx^n+c where n>1 3★ Solve like a quadratic involving fractional powers e.g. x^(1/n)+bx^(1/2n)=c 4★ Solve like a quadratic involving variable as a power 5★ Solve like a quadratic involving trigonometric equations$

Solving quadratics in disguise

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1★ Completing the square (x+a)^2+b where b>0
2★ Completing the square (x+a)^2+b where b<0
3★ Completing the square of x^2+bn+c where b is divisible by 2
4★ Completing the square x^2+bn+c where b is not divisible by 2
5★ Find the minimum point of a quadratic function by completing the square
6★ Identify the translation of a function given it is based on f(x)=x^2

Complete the square

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1★ Solve by completing the square given part of the working
2★ Solve by completing the square given part of the working
3★ Solve by completing the square of x^2+bn+c where b is divisible by 2
4★ Solve by completing the square of x^2+bn+c where b is not divisible by 2
5★ Solve by completing the square ax^2+bx+c where a>0
6★ Solve by completing the square ax^2+bx+c

Solve a quadratic by completing the square

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1★ Substituting positive numbers into the quadratic formula
2★ Substituting any numbers into the quadratic formula
3★ Given that numbers were correctly substituted into the quadratic formula state the quadratic equation
4★ Use of the discriminant to show how many roots a quadratic has
5★ Solve a quadratic using the quadratic formula

Solve a quadratic by using the formula

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1★ Describe a quadratic graph transformation in words
2★ Describe the effect of a transformation on a single point on a quadratic function
3★ Given f(x)=x^2, state the equation of a transformation of f(x)
4★ Given the transformed function of f(x)=x^2, draw it alongside f(x)
5★ Describe the effect of a transformation on a single point on a trig graph
6★ Draw/Identify a trig graph transformation

Graph transformations

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1★ Substitute an input value into a single operation function machine
2★ Substitute an input value into a 2 operation function machine
3★ Find the input value of a 2 operation function machine given the output
4★ Calculate the missing operation in a 2 operation function machine given the input and output values
5★ Write an expression to represent the output of a 2 operation function machine given the input is x
6★ Calculate the missing operation of a 2 operation function machine given the input is x and the output is in the form ax+b

Use simple function machines

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1★ Identify the range of f(x)=ax given the domain
2★ Find the corresponding domain or range values given f(x)=ax
3★ Find the range of f(x)=ax+b
4★ Find the corresponding domain or range values given f(x)=ax+b
5★ Find the domain of f(x)=ax+b given a range in set notation
6★ Find the values of f(x) for which is it is undefined

Identify domain and range

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1★ Find gf(x) or fg(x) for a given value knowing that f(x)=ax and g(x)=x+b
2★ Find gf(x) or fg(x) for a given value knowing that f(x)=ax+b and g(x)=cx+d
3★ Find gf(x) or fg(x) for a given value knowing that f(x)=ax+b and g(x)=x^2+c
4★ Find fg(x) for a given value knowing that f(x)=ax^2+bx+c and g(x)=dx+e
5★ Problem solving e.g. find fg(x)=gf(x) where f(x)=x^2+bx+c and g(x)=x+d

Use composite functions

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1★ Given a1 and a(n+1)=ba(n)+c, find a2
2★ Given a1 and a(n+1)=ba(n)+c, find a3 or a4
3★ Real world problem where an iterative formula and a0 is given
4★ Given x0 and an iterative formula derived from a rearranged cubic, find x3
5★ Show that a cubic equation can be rearranged to a given iterative form
6★ Show that a cubic equation as a solution between a given ratio

Iterations

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$1★ Rearrange a function involving only 1 operation (addition, subtraction, multiplication or division) 2★ Rearrange a function involving 2 operations 3★ Rearrange a function that is fractional 4★ Rearrange a function involving powers 5★ Rearrange a quadratic function that first involves completing the square$

Inverse functions

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1★ Interpreting a not equal to representation from a number line
2★ Interpreting an equal to representation from a number line
3★ Interpret any inequality from a number line
4★ Represent a given inequality on a number line
5★ Interpret a compound inequality from a number line
6★ Represent a compound inequality on a number line

Read/Represent inequalities on a number line

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1★ Solve a 1 step inequality by reversing the addition or subtraction of a constant
2★ Solve a 1 step inequality by reversing the multiplication or division of a constant
3★ Solve a 2 step inequality where x has a positive coefficient
4★ Solve a 1 step inequality where x has a negative coefficient
5★ Solve a 2 step inequality where x has a negative coefficient
6★ Solve a compound inequality in the form of a<bx+c<d

Solve linear inequalities

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1★ Identify the single linear inequality from a graph in the form x<a, x>b, y<c, y>d, x≤e, x≥f, y≤g or y≥h
2★ Sketch the single linear inequality on a graph in the form x<a, x>b, y<c, y>d, x≤e, x≥f, y≤g or y≥h
3★ Given a graph, identify the 4 inequalities that bound a rectangular region using x<a, x>b, y<c, y>d, x≤e, x≥f, y≤g or y≥h
4★ Identify the 3 inequalities that bound a given region including y-x>a
5★ State the coordinates of points that satisfy a given region bounded by 3 inequalities

Graphical inequalities

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1★ Graphically solve a quadratic inequality in the form x^2±a<0 or x^2±a>0
2★ Graphically solve a quadratic inequality in the form x^2±a≤0 or x^2±a≥0
3★ Solve a quadratic inequality x^2±a<0, x^2±a>0, x^2±a≤0 or x^2±a≥0
4★ Solve a quadratic inequality x^2±bx±c<0, x^2±bx±c>0, x^2±bx±c≤0 or x^2±bx±c≥0
5★ Solve a quadratic inequality ax^2±bx±c<0, ax^2±bx±c>0, ax^2±bx±c≤0 or ax^2±bx±c≥0
6★ Solve a quadratic inequality (where a is not 1) that first involves a rearrangement

Solve quadratic inequalities

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$1★ Continue an arithmetic sequence for the next two terms 2★ Continue a geometric sequence for the next two terms 3★ Continue a square or triangular sequence for the next two terms 4★ Continue a Fibonacci sequence for the next two terms 5★ Continue a periodic sequence for the next two terms 6★ Continue a fractional sequence for the next two terms where the numerators and denominators each follow a linear sequence$

Recognise common sequences

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1★ Continue a linear sequence for the next two terms
2★ Given the first and last term in a small linear sequence, find the missing middle values
3★ Write the first 4 terms of a linear sequence given the nth term rule
4★ Find the nth term rule for a linear sequence
5★ Given a number and the first 4 terms of a linear sequence, determine if the number is part of the sequence
6★ Given 2nd and 4th term of a linear sequence find 100th term

Understand linear sequences

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1★ Determine if a given sequence is geometric, if not, state the name of the sequence family
2★ Find the next 2 terms of a geometric sequence (integer common ratio)
3★ Find the next 2 terms of a geometric sequence (decimal common ratio)
4★ Given the first term and common ratio, find the first 3 terms of a geometric sequence
5★ Given an algebraic term to term rule and the first term, find a specific term in a geometric sequence
6★ Problem solving, e.g. given the 2nd and 4th term of a geometric sequence, find the 10th term

Understand geometric sequences

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1★ Continue an algebraic sequence that is based on an arithmetic or Fibonacci sequence
2★ Continue an algebraic sequence that is based on a geometric sequence
3★ Show that the sixth term of an algebraic sequence is a given expression
4★ Find the nth term of an arithmetic algebraic sequence
5★ Given the value of 2 terms and the first 3 terms of an arithmetic algebraic sequence, find the unknowns in the sequence

Algebraic sequences

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1★ Continue a quadratic sequence for the next two terms
2★ Write the first 4 terms a quadratic sequence given the nth term rule in the form of n^2+bn+c
3★ Find the nth term rule of a quadratic sequence based on an^2
4★ Find the nth term rule of a quadratic sequence based on n^2+bn+c
5★ Find the nth term rule of a quadratic sequence based on an^2+bn+c
6★ Use the nth term rule of a quadratic sequence based on an^2+bn+c to find a specific term

Understand quadratic sequences

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1★ Solve 2 simultaneous equations where a term in each equation has a common coefficient
2★ Solve 2 simultaneous equations where a term in each equation has a common term but a different sign
3★ Solve 2 simultaneous equations where all coefficients are different
4★ Solve a word problem that involves the creation and solving of 2 simultaneous equations
5★ Solve 2 simultaneous equations that first involves rearranging one or both of the 2 given equations
6★ Form and solve 2 simultaneous equations in other Maths topics

Solve linear simultaneous equations

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1★ Simultaneously solve a quadratic in the form of y=x^2 and a linear equation in the form y=ax+b
2★ Simultaneously solve a quadratic in the form of y=x^2±bx±c and a linear equation in the form y=ax+b
3★ Simultaneously solve a reciprocal equation in the form of xy=±c and a linear equation in the form y=ax+b
4★ Simultaneously solve a circle equation in the form of x^2+y^2=c and a linear equation in the form x+y=c (integer answers only)
5★ Simultaneously solve a circle equation in the form of x^2+y^2=c and a linear equation in the form x+y=c

Solve non linear simultaneous equations

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1★ Substitute a positive value into an expression that includes only 1 operation
2★ Substitute a positive value into an expression that includes 2 operations
3★ Substitute negative values into an expression involving 2 variables
4★ Substitute values into a simple quadratic expression
5★ Substitute values into common formulae
6★ Substitute values into a linear function f(x)

Substitute into expressions/formula

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1★ Create a simple expression in the form x±a or ax based on a word problem
2★ Create an expression to represent a word problem based I think of a number
3★ Create a rational expression to represent a word problem based I think of a number
4★ Create an expression based on a word problem, e.g. find the sum of 3 algebraic ages
5★ Form and solve an equation with unknowns on both sides
6★ Create a formula to represent the perimeter of a shape

Form expressions and equations

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Data handling cycle

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1★ Find a stratified sample
2★ Find the total frequency given the stratified sample

Calculate a stratified sample

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1★ Find an easy estimate of the population
2★ Find an estimate of a population
3★ Find the estimate of a population given the percentage with tags
4★ Critically analyse the sampling technique

Capture recapture

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$1★ Create a simple two-way table from images 2★ Find totals from a two-way table 3★ Complete missing values in a two-way table 4★ Calculate probabilities or fractions of amount from a two-way table 5★ Given a word problem, create and interpret a two-way table 6★ Multi-skill problem solving by creating and interpreting a two-way table, including ratios or percentages$

Two-way tables

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1★ Calculate the mode
2★ Calculate the median (odd number of values)
3★ Calculate the median (even number of values)
4★ Calculate the mean
5★ Calculate a missing value given the mean and the other values
6★ Write 4 numbers with a given mean, mode, median and range

Calculate averages from a list

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1★ Calculate IQR (easy ordered list)
2★ Calculate IQR (unordered list with easy quartiles)
3★ Calculate IQR (unordered list with half position values)
4★ Calculate IQR (unordered list of decimals)
5★ IQR from a stem and leaf diagram
6★ Given the IQR and range find unknown values in a list of data

Calculate quartiles from a list

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1★ Which average gives the best or worst result?
2★ State advantages or disadvantages of a specific type of average
3★ Given a data set, decide which average is best to use to represent the data

Which average should you use?

Generate Qu

1★ Calculate the mode from a frequency table
2★ Calculate the total score from a frequency table
3★ Calculate the mean from a frequency table
4★ Calculate an estimate of the mean from a grouped frequency table
5★ Calculate a missing score given the mean from a frequency table
6★ Calculate a missing frequency given the mean from a frequency table

Calculate the mode/mean from a frequency table

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1★ Calculate the median from a frequency table
2★ Identify the interval that contains the median from a grouped frequency table
3★ Use linear interpolation to find the median (always the midpoint of the interval) from a grouped frequency table
4★ Use linear interpolation to find the median (never the midpoint of the interval) from a grouped frequency table
5★ Find the interquartile range from a grouped frequency table

Calculate the median/IQR from a frequency table

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$1★ Draw a stem and leaf diagram from an unordered list of data containing integers 2★ Draw a stem and leaf diagram from an unordered list of data containing decimals 3★ Interpret a stem and leaf diagram, e.g. what fraction were under a specific score? 4★ Find averages and range from a stem and leaf diagram 5★ Adding data to a stem and leaf and analysing the effects on statistical measures 6★ Analysing a back to back stem and leaf diagram$

Stem and leaf diagrams

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1★ Draw a frequency polygon from a grouped frequency table
2★ Interpret probabilities of events from a frequency polygon
3★ Interpret the mean from a frequency polygon
4★ Draw comparisons between 2 frequency polygons drawn on the same axes

Draw/Interpret a frequency polygon

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1★ Construct a cumulative frequency table
2★ Construct a cumulative frequency table from a graph
3★ Estimate a median from a cumulative frequency graph
4★ Estimate the interquartile range from a cumulative frequency graph
5★ Estimate the number of people that scored more or less than an amount from a cumulative frequency graph

Draw/Interpret cumulative frequency

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1★ Draw a box plot given 5 point summary
2★ Draw a box plot from a cumulative frequency diagram
3★ Draw a box plot given some information given key statistical measures about a list of data
4★ Analyze a given box plots
5★ Calculate median, inter-quartile range or range from a box plot
6★ Make comparisons between 2 box plots drawn on the same number line

Draw/Interpret a box plot

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1★ Create a tally chart from a list of data
2★ Given a tally chart, interpret key measures from the chart
3★ Draw a bar chart from a frequency table
4★ Interpret least/most common or frequency from a bar chart
5★ Draw a bar chart given a word problem that requires problem solving

Draw/Interpret a bar chart

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1★ Analyse a composite bar chart
2★ Draw a composite bar chart given a two way table
3★ Interpret proportions from a composite bar chart

Draw/Interpret a composite bar chart

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1★ Complete a frequency density column given a grouped frequency table
2★ Complete missing values in a grouped frequency table including frequency density column and frequency values
3★ Estimate how many got greater than a score from a histogram
4★ Estimate how many got greater than a score from a grouped frequency table
5★ Construct a frequency table from a histogram
6★ Given the frequency of one interval represented by a histogram, complete a frequency table to represent all other intervals

Draw/Interpret a histogram

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1★ Given a pictogram, identify least/most common or total (involving frequencies that require only whole diagrams)
2★ Given a pictogram, identify least/most common or total (involving frequencies that require half a diagram)
3★ Given a pictogram, find the frequency of a category or total frequency
4★ Draw a pictograph (involving frequencies that require only whole diagrams)
5★ Draw a pictograph (involving frequencies that require half a diagram)
6★ Given a pictogram, find the percentage who answered a category

Construct a pictograph

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1★ Draw a pie chart (total freq 360 with categories having a frequency that is a factor of 360)
2★ Draw a pie chart (total frequency is 90 or 180)
3★ Draw a pie chart (total frequency is a factor of 360)
4★ Calculate the angles needed to construct a pie chart (total frequency is not a factor of 360)
5★ Draw a pie chart (total frequency is not a factor of 360)
6★ Draw a pie chart where the total frequency is given but the category frequencies are expressions in terms of x

Construct a pie chart

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$1★ Find the mode from a given pie chart 2★ Calculate the fraction represented by a sector on a given pie chart 3★ Given a pie chart and the frequency of a sector, calculate total frequency 4★ Given a pie chart and the percentage represented by 2 sectors and the total, calculate the frequency of a third sector$

Interpret a pie chart

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1★ Plot a scatter diagram from a given table
2★ Describe the correlation represented in a scatter graph
3★ Draw a line of best fit on a given scatter graph
4★ Estimate from a line of best fit on a scatter graph
5★ Identify anomalies from a given scatter graph

Draw/Interpret a scatter graph

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1★ Comment on the correlation shown in a given scatter graph
2★ Find the PMCC from table
3★ Interpret the meaning of the PMCC value in a given context
4★ Calculate the regression line equation from a given table
5★ Interpolate/extrapolate using a regression line equation formed from a given table
6★ Limitations of using a regression line given a scatter graph

PMCC and regression line

KS5/STATS

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Standard deviation

KS5/STATS

Generate Qu

1★ Calculate the z-score given a value, µ and the standard deviation
2★ Find P(X < ?) where Z > 0
3★ Find P(X < ?) or P(X > ?) where Z < 0
4★ Find P(a < X < b)
5★ Find X where Y% are less than X
6★ Find µ given P(X < x)

Normal distribution

KS5/STATS

Generate Qu

1★ Use standard error of the mean to find the P(Z < ?)
2★ Find a z-score given a percentage confidence interval
3★ Construct a confidence interval given a sample
4★ Construct a confidence interval given a different confidence interval of the same sample

Confidence intervals

KS5/STATS

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1★ A look repetitive question involving the same number but different operations that focuses on the use of BIDMAS
2★ Solving simultaneous equations but depicted as fruit
3★ Order of operation circles

Facebook maths

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Place value

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Times tables

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1★ Commutative law involving only addition or multiplication
2★ Commutative law involving a combination of addition and multiplication
3★ Associative law
4★ Distributive law
5★ Identify which number law is being shown
6★ Evaluate calculations based on the use of the number laws

Commutative, associative and distributive laws

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1★ Given a calculation, evaluate a simple rearrangement of the same calculation
2★ Given a calculation, evaluate a rearrangement of the same calculation with the numbers having been changed by multiplying or dividing by positive powers of 10
3★ Given a calculation, evaluate a rearrangement of the same calculation with a number having been multiplied or divided by a negative power of 10
4★ Given a calculation, evaluate a rearrangement of the same calculation with both numbers having been multiplied or divided by a negative power of 10

Related calculations

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1★ Write down all the factors of a number
2★ Write down the first 5 multiples of a number
3★ Find a common factor of 2 numbers
4★ Find the HCF or LCM of 2 numbers
5★ Find the HCF or LCM of 3 numbers
6★ Find a second number given 1 number and their LCM

Factors and multiples

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Prime factors

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$1★ Evaluate a simple calculation involving a combination of addition, subtraction, multiplication or division 2★ Evaluate a calculation involving brackets 3★ Evaluate a calculation involving brackets and powers 4★ Find the value of a multi-step calculation involving the application of all parts of BIDMAS 5★ Find the value of a fractional calculation with steps to evaluate in both the numerator and denominator 6★ Insert brackets into a calculation to make it true$

Order of operations

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$1★ Identify the unit fraction from a given diagram 2★ Shade a unit fraction of a diagram 3★ Read simple fractions from a diagram 4★ Represent simple fractions on a diagram 5★ Understanding equivalences from shaded rows or columns of a diagram 6★ Read a given diagram as a mixed number$

Interpret fractions

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$1★ Simplify a fraction given the denominator of the simplified fraction 2★ Simplify a fraction 3★ Compare 2 fractions using an equals or inequalities 4★ Would you rather have this ... or this ...? 5★ Find half way between 2 fractions 6★ Convert to and from a mixed number$

Equivalent fractions

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$1★ Given an integer, provide the reciprocal so the product equals 1 2★ Reciprocal of integers 3★ Reciprocal of fractions 4★ Reciprocal of decimals < 1 5★ Reciprocal of fractions or decimals > 1 6★ Equivalent fraction fill in the blank reciprocals$

Reciprocals of numbers

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$1★ What fraction is needed to complete a diagram? 2★ Two fractions with common denominators 3★ Two fractions with different denominators 4★ Combination of adding and subtracting 3 fractions 5★ Mixed numbers 6★ Simple algebraic fractions$

Add or subtract fractions

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$1★ Write the amount shaded as a fraction of the total 2★ Write one number as a fraction of another 3★ Understanding complements when finding a fraction of an amount 4★ Write one measurement as a fraction of another when they are given with different units 5★ Given a total and the quantities of two of the three items in the total, write the third as fraction of the total 6★ Equivalent fraction problem$

Write one number as a fraction of another

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$1★ Multiply a fraction by an integer 2★ Multiply a fraction by a fraction 3★ Find a fraction of an amount 4★ Which of two fraction of amounts statements is larger? 5★ Word problem involving expenditure 6★ Fraction of one amount is equal to fraction of unknown, find the unknown$

Fraction of an amount (part i)

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$1★ Unit fraction of an amount 2★ Non-unit fraction of an amount 3★ Mixed number of an amount 4★ Increase or decrease by a fraction 5★ Word problems 6★ Fraction between 2 numbers$

Fraction of an amount (part ii)

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$1★ Given an integer, provide the reciprocal so the product equals 1 2★ Integer by a fraction 3★ 2 fractions 4★ 3 fractions 5★ Mixed numbers 6★ Simple algebraic fractions$

Multiply or divide fractions

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$1★ Convert between common FDP 2★ Convert between FDP 3★ Are 2 numbers written in different number formats (FDP) equal? 4★ Order FDP 5★ Convert a recurring decimal to a fraction where the recurring digit is the first decimal place 6★ Convert a recurring decimal to a fraction (harder)$

FDP conversion

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$1★ Order positive integers 2★ Order positives and negatives 3★ Order decimals 4★ Order FDP 5★ Order fractions 6★ Order numbers written in standard form$

Order numbers

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$1★ Calculator familiarisation - identify what function a button has on a calculator 2★ Enter BIDMAS related calculations on a calculator 3★ Identify whether a number is prime on a calculator 4★ Evaluate a given expression by substituting in both positive and negative values 5★ Evaluate a calculation invovling standard form on a calculator 6★ Perform fraction calculations on a calculator$

Efficient use of a calculator

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1★ Numbers bonds to 10 or 100
2★ Alternative vocabulary for addition or subtraction
3★ 1 digit integer ± 1 digit integer
4★ 2 digit integer ± 2 digit integer
5★ 3 digit integer ± 2 digit integer
6★ Directed number calculations

Operate with integers (+ and -)

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1★ Times tables
2★ Alternate vocabulary to multiplication or division
3★ 2 digit integer x÷ 1 digit integer
4★ 3 digit integer x÷ 2 digit integer
5★ Directed numbers calculations

Operate with integers (x and ÷)

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1★ 2 digit integer x 1 digit integer
2★ 2 digit integer x 2 digit integer
3★ 3 digit integer x 2 digit integer
4★ Identify the last digit of a multiplication answer
5★ Fill in the missing number of 3 digit integer x 2 digit integer calculation given all the working
6★ 3 digit integer x 3 digit integer

Column multiplication

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Short division

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Product rule for counting

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1★ Decimal (1dp) ± integer
2★ Integer ± decimal (1dp)
3★ Decimal (1dp) ± decimal (1dp) both less than 1
4★ Decimal (1dp) ± decimal (1dp) both more than 1
5★ Decimal ± Decimal (2 or more dp)
6★ Recurring decimal ± decimal

Operate with decimals (+ and -)

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1★ Decimal (1dp) multiplied by a power of 10
2★ Decimal (1dp) divided by a power of 10
3★ Decimal (1dp) x÷ integer
4★ Decimal x÷ decimal (both 1 or 2 dp)
5★ Decimal x÷ decimal (2 or more dp)
6★ Contextualised use of x÷ with decimals

Operate with decimals (x and ÷)

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1★ Given a shopping list of prices, calculate the cost of buying 1 each of two items
2★ Given a shopping list of prices, calculate the cost of buying multiple items
3★ Given a shopping list of prices, calculate the cost of buying multiple items with different units of money, e.g. £ and p
4★ Given a shopping list, calculate the change due from making a multi item purchase
5★ Given a shopping list, calculate how many can I buy of 1 item?
6★ What proportion of the total cost of purchasing multiple items doe 1 item represent?

Money problems

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1★ How much do I pay each month? (No deposit)
2★ How much do I pay each month? (With deposit)
3★ Given 2 offers from different shops, is it better value to buy now or spread the payments?
4★ Deposit with equal payments and one-off interest

Money problems - payment plans

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1★ Calculating gross pay
2★ Calculating gross pay inc overtime
3★ Calculating the total deductions or net pay
4★ Calculate the monthly tax for a basic rate tax earner given the 20% and personal tax free allowance thresholds
5★ Calculate the monthly tax for a high income earner given the tax free personal allowance, 20% tax and 40% tax thresholds
6★ Calculate National Insurance given annual salary and personal tax free threshold

Pay slips

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1★ Percentage to find is a multiple of 10
2★ Percentage to find is a multiple of 5 (exc multiples of 10)
3★ Percentage to find is a multiple of 1
4★ Calculator use
5★ Percentage to find is a multiple of 0.5
6★ Populate and interpret a two-way table based on percentages of a population

Percentage of an amount

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1★ Recognise that percentage is out of 100
2★ Write one number as a percentage of another (out of 100)
3★ Write one number as a percentage of another (not out of 100)
4★ Find a simple percentage change
5★ Contextualised percentage change
6★ Percentage change from a compound interest problem

Percentage change

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Increase/decrease by a percentage

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1★ What percentage is left after increasing or decreasing a number by a percentage
2★ Effect of using a decimal multiplier on a number
3★ Simple reverse percentage
4★ Reverse percentage based on compound interest/decay

Reverse percentage

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1★ Interest earned after 1 year
2★ Total after n years (where % is an integer)
3★ Total after n years (where % is not integer)
4★ Total after n years (where % is less than 1)
5★ Calculate the interest rate given the total and the number of years
6★ Problem solving

Simple interest

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1★ Effect of using a decimal multiplier on a number
2★ Growth/decay percentage is an integer
3★ Growth/decay percentage is a decimal (1dp)
4★ Find the number of years to exceed a given amount
5★ Find the percentage growth/decay

Calculate growth/decay

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1★ Calculate 9% of a annual salary
2★ Calculate the amount deducted from an annual salary or monthly repayment
3★ Calculate how many months it will take to repay the student loan
4★ Calculate the amount of student loan is left to repay after n years

Student loans

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1★ Compound interest
2★ Calculate AER
3★ Calculate how much would be in an account
4★ Which is better value?
5★ Backwards AER questions

Annual equivalent rate

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1★ Estimate the product of a decimal and integer
2★ Estimate money total
3★ Estimate a decimal divided by a decimal (greater than 1)
4★ Estimate a decimal divided by a decimal (less than 1)
5★ Estimate square roots/cube roots
6★ Estimate the value of longer BIDMAS related calculations

Estimation

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Fermi

KS5

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1★ Truncate to 10, 100 or 1000
2★ Truncate to dp or sf
3★ Error interval when truncated to 10, 100 or 1000
4★ Error interval when truncated to dp or sf
5★ Caculate the error interval relating to a contextualised word problem

Truncation

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1★ Round to the nearest 100
2★ Round to the nearest 10
3★ Round to the nearest integer
4★ Round to 1dp
5★ Round to 2dp
6★ Calculate the bounds/error interval

Basic rules of rounding (inc dp and bounds)

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1★ Integer rounding to 1 significant figure
2★ Integer rounding to 2 significant figures
3★ Decimal rounding to the nearest 1 significant figure
4★ Decimal rounding to the nearest 2 significant figures
5★ Decimal rounding to the nearest 2 significant figures (where 2nd significant figure is 0)
6★ Calculate the bounds/error interval

Round to specific sf (inc bounds)

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1★ Define the bounds/error interval of a number
2★ Bounds of addition and multiplication
3★ Bounds of subtraction and division
4★ Mixture of operations
5★ Compound measure calculations with bounds
6★ Use of bounds in other Mathematical topics

Upper and lower bound calculations

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1★ Given a square grid, count the squares to determine the square number
2★ Knowledge of square numbers up to 225
3★ Knowledge of square roots of numbers up to 225
4★ Combination of operations with squares and roots of numbers
5★ Knowledge of cube numbers up to below 200
6★ Combination of operations with squares, cubes and roots of numbers

Squares, cubes and roots

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1★ 1st index law - multiplying terms
2★ 2nd index law - dividing terms
3★ Mixture of 1st and 2nd index law
4★ 3rd index law - power of power
5★ Harder 3rd index law involving simple algebraic expressions raised to a power
6★ Write a calculation as a single power of a number

Use the laws of indices

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1★ Mixed index laws
2★ Write one number as a power of another
3★ Simplify index laws and write as a single power of a number
4★ Simplify a complex problem and write the answer as a power of a number
5★ Solving equations by equating bases
6★ Solving harder equations by equating bases

Equating bases

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$1★ To the power of -1 2★ To the power of a negative number 3★ To the power of a half or a third 4★ To the power of negative half or third 5★ To the power of a fraction (inc top heavy) 6★ To the power of a negative fraction (inc top heavy)$

Integers with negative/fractional indices

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$1★ Decimal or fraction raised to the power of -1 2★ Decimal or fraction raised to the power of a negative 2 3★ To the power of a half or a third 4★ To the power of negative half or third 5★ To the power of a fraction (inc top heavy) 6★ To the power of a negative fraction (inc top heavy)$

Decimals/fractions with negative/fractional indices

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1★ Multiplying and dividing by powers of 10
2★ Convert to standard form (numbers greater than 0)
3★ Convert to standard form (numbers less than 0)
4★ Convert from standard form
5★ Convert ax10^b where is a<1 or a>10 into standard form

Conversion of standard form

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1★ Add and subtract numbers written in standard form with common powers of 10
2★ Add and subtract numbers written in standard form with different powers of 10
3★ Add and subtract numbers written in standard form
4★ Multiplying numbers written in standard form
5★ Dividing numbers written in standard form
6★ Combination of operations with numbers written in standard form

Operate in standard form

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1★ Write a surd as the square root of the product of 2 numbers where 1 number is missing
2★ Write a surd as the square root of the product of 2 numbers
3★ Write a surd as a product of two square roots where 1 square root is missing
4★ Write a surd as a product of two square roots
5★ Simplify a surd

Simplify a surd

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1★ Add and subtract common surds
2★ Simplify one surd before adding or subtracting it to another
3★ Multiplication of surds
4★ Division of surds
5★ Combination of operations involving surds
6★ Combination of operations involving the expansion of surds in brackets

Operate with surds

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$1★ Given the root of a number, how would you rationalise it? 2★ Rationalise a unit fraction 3★ Rationalise a simple denominator 4★ Rationalise a denominator where the same surd appears in both the numerator and denominator 5★ Rationalise the denominator using the difference of two squares 6★ Rationalise the denominator using the difference of two squares and a surd in the numerator$

Rationalise the denominator

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1★ Reading a clock face (12hr format) (15mins, 30mins or 45mins past)
2★ Reading a clock face (12hr format)
3★ Converting a pm time into 24hr format
4★ Interpret a bus time table
5★ Calculating a journey time from a bus time table
6★ Given a department time and length of journey, will I be late for an appointment?

Reading time and tables

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1★ Reading a scale with integer increments
2★ Reading a scale with integer increments with labels for every other marker on the scale
3★ Reading a scale with 0.5 increments and labels on the integer markers
4★ Reading a scale with a large gaps between labelled markers
5★ Reading a scale with only 2 values given on the scale
6★ Reading a scale with decimal increments

Reading scales

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1★ Identify the angle type (e.g. acute, obtuse, right-angle or reflex)
2★ Measuring acute/90°/obtuse angles using a protractor
3★ Given that a student has incorrectly interpretted their protractor, identify the number bond to 180°
4★ Measure acute/90°/obtuse angles
5★ Measure a reflex angle
6★ Draw a reflex angle

Measuring/Drawing angles

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1★ Construct a scalene triangle using loci constructions
2★ Construct an equilateral/isosceles triangle using loci constructions
3★ Construct an angle bisector using loci constructions
4★ Construct a perpendicular bisector using loci constructions
5★ Construct a perpendicular line from a point using loci constructions
6★ Real life loci problem solving

Constructions/loci

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1★ Identify the number of cubes needed to make a solid shape
2★ Draw the plan, front and side elevations for a solid shape
3★ Sketch a solid shape on isometric paper given the plan, front and side elevation
4★ Draw the plan, front and side elevations for trickier 3D solids
5★ Sketch a tricky 3D solid given the plan, front and side elevation
6★ Identify a solid shape from a word description of the plan, front and side elevations

Plans and elevations

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1★ Calculate an unknown angle on a straight line
2★ Use the vertically opposite angles property to find an unknown angle
3★ Calculate an angle using the fact that a right angle is 90°
4★ Calculate an unknown angle using the fact angles around a point sum to 360°
5★ Given 3 algebraic expressions to represent angles, solve the equation formed using appropriate angle facts

90°, 180°, and 360° angles

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1★ Name a given triangle
2★ Calculate an unknown angle in a triangle
3★ Calculate an unknown angle in an equilateral triangle
4★ Calculate an unknown angle in a right angle triangle
5★ Calculate an unknown angle in an isosceles triangle
6★ Calculate an unknown angle in 2 adjoining triangles

Angles in triangles

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1★ Name a given quadrilateral
2★ Calculate an unknown angle in a quadrilateral
3★ Calculate an unknown angle in a quadrilateral where one angle is 90°
4★ Calculate an unknown exterior angle given 3 interior angles
5★ Calculate an unknown angle in special quadrilaterals
6★ Given algebraic expressions to represent the angles in a quadrilateral, form an equation and solve it

Angles in quadrilaterals

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Angles on parallel lines

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1★ Find the interior angle sum of a polygon
2★ Find a missing angle in a n-sided polygon given all but 1 angle
3★ Will it regular n-sided polygon tesselate?
4★ Use an exterior angle of a regular n-sided polygon to calculate the number of sides
5★ Use an interior angle of a regular n-sided polygon to calculate the number of sides
6★ Problem solving

Angles in polygons

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1★ Measure an angle
2★ Measure a bearing
3★ Calculate a return bearing from a diagram
4★ Solve a word problem involving the calculation of a return bearing
5★ Given a bearing that has been read incorrectly, calculate the correct bearing
6★ Real life scaled drawings involving the construction of multiple bearings

Bearings

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1★ State the order of rotational symmetry
2★ Rotate a shape about the origin
3★ Describe the transformation about the origin
4★ Rotate a shape about a point
5★ Describe the transformation about a point

Rotations

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1★ State the number of lines of symmetry
2★ Draw the mirror line x=a/y=a mirror for a given reflection
3★ Reflect a given shape in x=a/y=a
4★ Reflect a shape in x=a/y=a
5★ Reflect a shape in given y=x/y=-x
6★ Describe the rotation transformation

Reflections

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1★ Describe a translation in words
2★ Draw a horizontal/vertical translation
3★ Describe a horizontal/vertical translation
4★ Drawing any vector translation
5★ Describe a vector translation
6★ Given the vectors of A to B and B to C, state the vector C to A

Translations

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$1★ Enlarge a shape (without centre of enlargement) 2★ Finding a scale factor given 2 similar shapes (positive or fractional) 3★ Enlarge a shape from a centre of enlargement 4★ Describe an enlargement given 2 similar shapes on a set of axes 5★ Enlarge a shape by a fractional scale factor 6★ Enlarge a shape by a negative scale factor$

Enlargements

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1★ Find the area of an enlarged 2D shape
2★ Find the volume of an enlarged 3D shape
3★ Find the area of the original 2D shape
4★ Find the volume of the original 3D shape
5★ Find a side length given the areas of the original and enlarged shape
6★ Find a side length given the volumes of the original and enlarged 3D shapes

Area/Volume scale factors

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Congruence

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1★ Are two given shapes similar?
2★ Knowing two shapes are similar, find an unknown side length (orientation exercise)
3★ Use a scale factor to find an unknown side
4★ Use a scale factor to find an unknown side (harder)
5★ Use Pythagoras theorem to find an unknown side given 2 similar shapes

Similar shapes

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1★ Given a 2D shape, identify the polygon family
2★ Name a regular shape given its geometrical properties
3★ Given a basic 4 sided shape, name the quadrilateral
4★ Name a quadrilateral given its geometrical properties

Names and properties of polygons

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1★ Calculate the area of a shape by counting squares
2★ Calculate the area of a triangle or rectangle
3★ Calculate the area of a parallelogram
4★ Calculate the area of a trapezium
5★ Calculate the area of a regular hexagon
6★ Given 2 shapes and the fact their areas are equal, calculate a missing length in 1 of the shapes

Area of 2D shapes

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1★ Given the area of a rectangle, calculate an unknown side length
2★ Given the area of a triangle, calculate an unknown side length
3★ Given the area of a parallelogram, calculate an unknown side length
4★ Given the area of a trapezium, calculate an unknown side length
5★ Given 2 shapes and the fact their areas are equal, calculate a missing length in 1 of the shapes
6★ Given that a length is a multiple of another in a basic 2D shape and the area, calculate the unknown length

Reverse area of 2D shapes

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1★ Calculate the area of a rectangle with simple terms to represent the sides
2★ Calculate the area of a rectangle where the sides are expressions
3★ Given an expression to represent the area of a rectangle and 1 integer side, write the expression for the other side
4★ Find the area of a rectangle with expressions for both sides
5★ Find the area of shaded region with a cut out made from rectangles
6★ Calculate the area of simple compound shape with algebraic sides

Algebraic area of 2D shapes

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1★ Calculate the area of a compound shape made from combining 2 rectangles
2★ Calculate the area of a compound shape made from combining 2 triangles
3★ Calculate the area of a compound shape made from combining a triangle and a rectangle
4★ Calculate the area of a compound shape made from combining a triangle and a semi circle
5★ Calculate the shaded area of a compound shape made from removing a rectangle from another rectangle
6★ Calculate the shaded area of a compound shape made from removing a circle from a square

Area of composite shapes

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1★ Calculate the perimeter of a rectangle by counting squares
2★ Calculate the perimeter of a given square, rectangle or triangle
3★ Calculate the perimeter of a simple compound shape made from rectangles
4★ Calculate the perimeter of a rhombus
5★ Form an expression to represent the perimeter of a rectangle with algebraic side lengths
6★ Calculate the perimeter of a half or quarter of a circle

Perimeter of 2D shapes

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1★ Identify which line within a circle is the diameter
2★ Find the radius or diameter given the other
3★ Name the given part of a circle
4★ Draw the named part of a circle

Parts of a circle

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1★ Calculate the circumference given the diameter
2★ Calculate the circumference given the radius
3★ Calculate the diameter given the circumference
4★ Calculate the perimeter of a quarter or half circle
5★ Calculate the perimeter of a sector or the arc length
6★ Calculate the angle of a sector given the perimeter

Circumference of a circle

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Area of a circle

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1★ Calculate an unknown angle using the angles in a semi-circle theorem
2★ Calculate an unknown angle using the angles in the cyclic quadrilateral property
3★ Calculate an unknown angle using the angle at the center is twice the angle on the circumference theorem or angles in the same segment theorem
4★ Calculate an unknown angle using the alternate segment theorem
5★ Calculate an unknown angle using circle theorems that are tricky to spot
6★ Form and solve an equation based on algebraic angles linked by circle theorems

Circle theorems

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1★ Calculate the hypotenuse of a right angled triangle
2★ Calculate a shorter side of a right angled triangle
3★ Use Pythagoras theorem for right angled triangles
4★ Apply Pythagoras theorem in non-right angle triangles
5★ Calculate the distance between 2 coordinates
6★ Apply Pythagoras theorem in 3D

Apply Pythagoras' Theorem

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Apply SOH CAH TOA

Generate Qu

1★ Label the angles and sides of triangle ABC ready to apply the sine or cosine rule
2★ Using the sine rule to find a side or angle
3★ Using the cosine rule to find a side
4★ Using the cosine rule to find an angle
5★ Apply either the sine or cosine rule in a problem
6★ Apply both the sine and cosine rule in a multi-step problem

Sine and cosine rules

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1★ Label the angles and sides of triangle ABC ready to apply the sine or cosine rule
2★ Evaluate the correct use of the formula on a calculator
3★ Calculate the area of a non-right angled triangle using 0.5absinC
4★ Find a side of a non-right angled triangle given the area, the angle and the length of the adjacent side
5★ Find an angle of a non-right angled triangle given the area and two adjacent sides
6★ Apply the area formula to find an unknown value that assists with then using the cosine rule in a multi-step problem

Area of a triangle (trigonometry)

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1★ Reading exact values from either a right-angled triangle or a right-angled isosceles triangle
2★ Recalling exact values of sin, cos or tan
3★ Find the sum of exact sin, cos or tan values
4★ SOH CAH TOA application of exact values
5★ Identify alternate exact values of angles greater than 90
6★ Apply exact values within a cosine rule problem

Trigonometry exact values

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1★ Give the name of a common 3D shape given a diagram or description
2★ Surface area of a cube or cuboid
3★ Surface area of a cylinder or triangular prism
4★ Surface area of a cone or sphere
5★ Calculate a missing length given the surface area of a sphere, cylinder or cuboid

Surface area of 3D shapes

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1★ Give the name of a common 3D shape given a diagram or description
2★ Calculate the volume of a cuboid
3★ Calculate the length of an edge of a cube or of a cuboid given its volume
4★ Calculate the volume of a cylinder or triangular prism
5★ Calculate a missing length in a cylinder or triangular prism given the volume
6★ Calculate the most items you can fit in a container

Volume of 3D shapes

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1★ Give the name of a common 3D shape given a diagram or description
2★ Calculate the volume of a cone or sphere or square based pyramid
3★ Calculate a missing length given the volume of a cone or sphere or square based pyramid
4★ Calculate the volume of a hemi sphere or frustum
5★ Calculate a missing length given the volume of a frustum

Volume of complex 3D shapes

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$1★ Calculate the area or circumference of a circle in terms of pi 2★ Calculate the area or arc length of a sector in terms of pi 3★ Calculate the longest or shortest side using Pythagoras leaving the answer in surd form 4★ Calculate the volume of a cone, sphere or cylinder in terms of pi 5★ Find the sum of exact sin, cos or tan values 6★ Evaluate a value raised to a fractional power leaving the answer in surd form$

Leave your answer in exact form

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Vectors

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1★ Probability vocabluary - impossible, unlikely, even chance, likely, certain
2★ Place likelihood of an event on a number line (0 to 1)
3★ Place the likelihood of events on a number line (0 to 1) that are mutually exclusive events

Probability scale

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List outcomes

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1★ Calculate the probability for a simple single event
2★ Calculate the probability of selecting an item given a list of all outcomes
3★ Calculate the probability of selecting a letter from a given word
4★ Calculate the probability of an event given a simple sample space diagram showing all possible outcomes from 2 events
5★ Calculate the probability of an event from a sample space diagram showing all possible outcomes from 2 events

Calculate simple probabilities

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1★ Create a frequency tree for a single event
2★ Create a frequency tree for 2 events
3★ Create a frequency tree for 2 events involving some arithmetic to complete the tree
4★ Create a frequency tree for 2 events involving problem solving to complete the tree
5★ Calculate the probability of an event by first drawing a frequency tree

Frequency trees

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1★ Calculate the probability of a simple mutually exclusive event
2★ Complete a table of the likelihood of outcomes of a mutually exlusive event with 3 outcomes
3★ Complete a table of the likelihood of outcomes of a mutually exlusive event where 2 of the outcomes are equally likely
4★ Complete a probability tree diagram for a single event
5★ Given the probabilities of a mutually exclusive event as algebraic expressions, form and solve the equation

Mutually exclusive events

Generate Qu

1★ Find the relative frequency where the total is 100
2★ Find the relative frequency where the total is not 100
3★ Find the relative frequency where the total is not given
4★ Use relative frequency to calculate the expected frequency
5★ Complete a table of relative frequencies and expected frequencies of a single event
6★ Use relative frequency from an experiment to estimate the population

Calculate relative/expected frequency

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1★ Calculate a probability given a complete tree diagram for 2 events - AND style questions
2★ Calculate a probability given an incomplete tree diagram for 2 events - AND style questions
3★ Calculate a probability of 2 events - AND style questions
4★ Calulate a probability of 2 events where you can only have 1 of each - OR style questions
5★ Calculate a probability of 2 events for AT LEAST style questions
6★ Calculate a probability of more than 2 events

Probabilities of independent events

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Probabilities of dependent events

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1★ Construct a venn diagram
2★ Calculate simple probabilities from a venn diagram
3★ Calculate union or intersection probabilities from a venn diagram
4★ Calculate union or intersection probabilities from a venn diagram including NOT
5★ Calculate union or intersection probabilities given domains outlined by set notation
6★ Calculate union or intersection probabilities where an equation needs to be formed and solved

Complete and interpret a venn diagram

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1★ Conditional probability from a venn diagram
2★ Conditional probability without a venn diagram but given domains outlined by set notation
3★ Conditional probability of selecting letters from a given word
4★ Calculating a conditional probability given percentages of specific outcomes

Calculate conditional probabilities

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1★ Conversion between metric units of length, mass and volume
2★ Conversion between cm^3 and l
3★ Simple problem solving given measures of different metric units
4★ Conversion between metric units of area
5★ Conversion between metric units of volume
6★ Problem solving with metric units of measure

Conversion of metric units

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1★ Convert between miles and kilometres
2★ Speed/distance/time calculations
3★ Given a conversion ratio, change between metric and imperial units
4★ Problem solving with measures given in metric and imperial units
5★ Multiple conversions of units
6★ Convert between units of area/volume

Conversion of metric and imperial

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1★ Given a conversion ratio, convert a map distance into a real life distance
2★ Conversion between metric units of length
3★ Given a conversion ratio, convert a real life distance into a map distance
4★ Given a scale written in different metric units, write the ratio in its simplest form
5★ Given a distance represented as a measureable line on map and a scale, convert into a real life distance

Map scales

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1★ Convert between different units of time
2★ Speed, distance and time calculations
3★ Density, mass and volume calculations/Pressure, mass and area calculations
4★ Problem solve with compound measures
5★ Problem solve with compound measures involving volume calculation
6★ Convert between different units of compound measure

Compound measures

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Simplify a ratio

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$1★ What fraction of a bar model divided into the ratio a:b is shaded 2★ What fraction of a bar model divided into the ratio a:b:c is shaded) 3★ Given a ratio a:b, what fraction is represented 4★ Given a ratio a:b:c, what fraction is represented 5★ Given a fraction/percentage of a bar model that is shaded, represent this as a ratio 6★ Represent a part of a contextualised ratio problem as fraction$

Interpret ratio as a fraction

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1★ Divide an amount into a:b
2★ Divide an amount into a:b:c
3★ Divide a contextualised amount into the ratio a:b
4★ With an amount of money shared in the ratio a:b, if someone gets this, what does the other get?
5★ With an amount of money shared in the ratio a:b, if the difference is this, how much did they share?
6★ Divide an amount into a given ratio when the problem is linked with other topics in Maths, e.g. angles

Divide a quantity into a given ratio

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$1★ Given an equation of A in terms of B, write the fraction A/B 2★ Given an equation of A in terms of B, write the ratio A:B 3★ Given A:B=C:D, write the equation of A in terms of B, where C and D are positive integers 4★ Given the ratio of 2 pairs of points on a straight line give ratio between each point 5★ Given an equation of A in terms of B, problem solve with multiplicative ratios 6★ Problem solve when multiplicative operations with ratios are applied in other Mathematical topics$

Multiplicative operations with ratios

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1★ Compare 2 offers (same quantities but different prices £)
2★ Compare 2 offers (different quantities and different prices £)
3★ Compare 2 offers (different quantities and different prices £pp)
4★ Compare 2 offers (different units, quantities and prices)
5★ Compare 2 offers (special offer deals)

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Find and use y = a, x = a and y = x

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Find y = mx + c from a graph

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Rearranging into the form y = mx + c

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Find the equation of a parallel line

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Equation of a tangent to a circle

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Graphical solutions of equations

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Quadratic and cubic functions

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Equation of a circle

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Area under a graph

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Reciprocal functions

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Exponential functions

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Trigonometry graphs

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Solve linear equations (unknown on 1 side, int ans)

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Factorise a simple expression

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Complete the square

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Solve a quadratic by completing the square

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Solve quadratic inequalities

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Recognise common sequences

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Understand geometric sequences

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Algebraic sequences

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Solve linear simultaneous equations

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Solve non linear simultaneous equations

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Stem and leaf diagrams

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Draw/Interpret a bar chart

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PMCC and regression line

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Standard deviation

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Place value

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Commutative, associative and distributive laws

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Order of operations

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Reciprocals of numbers

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Add or subtract fractions

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Write one number as a fraction of another

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Fraction of an amount (part i)

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$1★ Unit fraction of an amount 2★ Non-unit fraction of an amount 3★ Mixed number of an amount 4★ Increase or decrease by a fraction 5★ Word problems 6★ Fraction between 2 numbers$

Fraction of an amount (part ii)

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$1★ Given an integer, provide the reciprocal so the product equals 1 2★ Integer by a fraction 3★ 2 fractions 4★ 3 fractions 5★ Mixed numbers 6★ Simple algebraic fractions$

Multiply or divide fractions

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FDP conversion

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$1★ Order positive integers 2★ Order positives and negatives 3★ Order decimals 4★ Order FDP 5★ Order fractions 6★ Order numbers written in standard form$

Order numbers

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Column multiplication

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Short division

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Product rule for counting

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Money problems

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Percentage of an amount

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Percentage change

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Increase/decrease by a percentage

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Reverse percentage

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Simple interest

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Calculate growth/decay

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Student loans

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Annual equivalent rate

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Fermi

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Truncation

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Basic rules of rounding (inc dp and bounds)

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Round to specific sf (inc bounds)

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Upper and lower bound calculations

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Squares, cubes and roots

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Use the laws of indices

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Equating bases

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Integers with negative/fractional indices

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Conversion of standard form

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Simplify a surd

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Reading time and tables

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Constructions/loci

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90°, 180°, and 360° angles

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Rotations

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Area/Volume scale factors

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Congruence

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Names and properties of polygons

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Area of 2D shapes

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Algebraic area of 2D shapes

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Area of composite shapes

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Perimeter of 2D shapes

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Parts of a circle

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Circumference of a circle

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Area of a circle

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Circle theorems

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Apply Pythagoras' Theorem

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Sine and cosine rules

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Area of a triangle (trigonometry)

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Trigonometry exact values

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Surface area of 3D shapes

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Volume of 3D shapes

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Volume of complex 3D shapes

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Leave your answer in exact form

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Vectors

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List outcomes

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Frequency trees

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Calculate relative/expected frequency

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Probabilities of independent events

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Probabilities of dependent events

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Complete and interpret a venn diagram

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Calculate conditional probabilities

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Conversion of metric units

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Conversion of metric and imperial

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Map scales

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Compound measures

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Simplify a ratio

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Interpret ratio as a fraction

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Divide a quantity into a given ratio

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Multiplicative operations with ratios

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Best buys

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Currency conversion

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Direct proportion

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Simplify an expression

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Algebraic fractions

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Change the subject

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Identify coordinates in all 4 quadrants

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Find and use y = a, x = a and y = x

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Find y = mx + c from a graph

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Rearranging into the form y = mx + c

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Using and exploring y = mx + c

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Find the equation of a parallel line

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Find the equation of a perpendicular line

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Equation of a tangent to a circle

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Graphical solutions of equations

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Quadratic and cubic functions

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Equation of a circle

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Area under a graph

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Reciprocal functions

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Exponential functions

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Trigonometry graphs

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Solve linear equations (unknown on 1 side, int ans)

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Solve linear equations (unknown on 1 side, dec ans)

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Solve linear equations (unknown both sides)

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Solve linear equations with brackets

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Solve rational equations

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Expand over a single bracket

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Expand 2 or more binomials

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Factorise a simple expression

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Factorise a quadratic expression

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Solve a quadratic by factorising

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Solving quadratics in disguise

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Complete the square

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Solve a quadratic by completing the square

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Solve a quadratic by using the formula

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Graph transformations

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Use simple function machines

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Identify domain and range

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Use composite functions

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Iterations

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Inverse functions

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Read/Represent inequalities on a number line

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Solve linear inequalities

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Graphical inequalities

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Solve quadratic inequalities

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Recognise common sequences

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Understand linear sequences

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Understand geometric sequences

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Algebraic sequences

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Understand quadratic sequences

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Solve linear simultaneous equations

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Solve non linear simultaneous equations

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Substitute into expressions/formula

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Form expressions and equations

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Data handling cycle

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Calculate a stratified sample

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Capture recapture

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Two-way tables

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Calculate averages from a list

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Calculate quartiles from a list

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Which average should you use?

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Calculate the mode/mean from a frequency table

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Calculate the median/IQR from a frequency table

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Stem and leaf diagrams

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Draw/Interpret a frequency polygon

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Draw/Interpret cumulative frequency

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Draw/Interpret a box plot

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Draw/Interpret a bar chart

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Draw/Interpret a composite bar chart

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Draw/Interpret a histogram

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Construct a pictograph

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Construct a pie chart

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Interpret a pie chart

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Draw/Interpret a scatter graph

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PMCC and regression line

KS5/STATS

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Standard deviation

KS5/STATS

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Normal distribution

KS5/STATS

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Confidence intervals

KS5/STATS

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Facebook maths

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Place value

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Times tables

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Commutative, associative and distributive laws

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Related calculations

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Factors and multiples

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Prime factors

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Order of operations

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Interpret fractions

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Equivalent fractions

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Reciprocals of numbers

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Add or subtract fractions

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Write one number as a fraction of another

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Fraction of an amount (part i)

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$1★ Unit fraction of an amount 2★ Non-unit fraction of an amount 3★ Mixed number of an amount 4★ Increase or decrease by a fraction 5★ Word problems 6★ Fraction between 2 numbers$

Fraction of an amount (part ii)

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$1★ Given an integer, provide the reciprocal so the product equals 1 2★ Integer by a fraction 3★ 2 fractions 4★ 3 fractions 5★ Mixed numbers 6★ Simple algebraic fractions$

Multiply or divide fractions

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FDP conversion

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$1★ Order positive integers 2★ Order positives and negatives 3★ Order decimals 4★ Order FDP 5★ Order fractions 6★ Order numbers written in standard form$

Order numbers

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Efficient use of a calculator

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Operate with integers (+ and -)

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Operate with integers (x and ÷)

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Column multiplication

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Short division

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Product rule for counting

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Operate with decimals (+ and -)

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Operate with decimals (x and ÷)

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Money problems

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Money problems - payment plans

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Pay slips

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Percentage of an amount

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Percentage change

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Increase/decrease by a percentage

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Reverse percentage

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Simple interest

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Calculate growth/decay

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Student loans

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Annual equivalent rate

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Estimation

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Fermi

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Truncation

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Basic rules of rounding (inc dp and bounds)

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Round to specific sf (inc bounds)

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Upper and lower bound calculations

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Squares, cubes and roots

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Use the laws of indices

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Equating bases

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Integers with negative/fractional indices

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Decimals/fractions with negative/fractional indices

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Conversion of standard form

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Operate in standard form

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Simplify a surd

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Operate with surds

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Rationalise the denominator

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Reading time and tables

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Reading scales

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Measuring/Drawing angles

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Constructions/loci

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Plans and elevations

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90°, 180°, and 360° angles

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Angles in triangles

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Angles in quadrilaterals

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Angles on parallel lines

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Angles in polygons

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Bearings

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Rotations

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Reflections

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Translations

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Enlargements

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Area/Volume scale factors

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Congruence

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Similar shapes

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Names and properties of polygons

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Area of 2D shapes

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Reverse area of 2D shapes

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Algebraic area of 2D shapes

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Area of composite shapes

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Perimeter of 2D shapes

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Parts of a circle

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Circumference of a circle

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Area of a circle

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Circle theorems

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Apply Pythagoras' Theorem

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Apply SOH CAH TOA

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Sine and cosine rules

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Area of a triangle (trigonometry)

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Trigonometry exact values

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Surface area of 3D shapes

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Volume of 3D shapes

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Volume of complex 3D shapes

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Leave your answer in exact form

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Vectors

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Probability scale

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List outcomes

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Calculate simple probabilities

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Frequency trees

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Mutually exclusive events

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Calculate relative/expected frequency

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Probabilities of independent events

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Probabilities of dependent events

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Complete and interpret a venn diagram

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Calculate conditional probabilities

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Conversion of metric units

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Conversion of metric and imperial

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Map scales

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Compound measures

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Simplify a ratio

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Interpret ratio as a fraction

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Divide a quantity into a given ratio

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Multiplicative operations with ratios

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Best buys

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Currency conversion

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Direct proportion

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Inverse proportion

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Algebraic proof

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Simplify an expression

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Algebraic fractions

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Change the subject

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Identify coordinates in all 4 quadrants

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Find and use y = a, x = a and y = x

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Find y = mx + c from a graph

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Rearranging into the form y = mx + c

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Using and exploring y = mx + c

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Find the equation of a parallel line

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Find the equation of a perpendicular line

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Equation of a tangent to a circle

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Graphical solutions of equations

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Quadratic and cubic functions

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Equation of a circle

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Area under a graph

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Reciprocal functions

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Exponential functions

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Trigonometry graphs

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Solve linear equations (unknown on 1 side, int ans)

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Solve linear equations (unknown on 1 side, dec ans)

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Solve linear equations (unknown both sides)

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Solve linear equations with brackets

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Solve rational equations

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Expand over a single bracket

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Expand 2 or more binomials

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Factorise a simple expression

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Factorise a quadratic expression

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Solve a quadratic by factorising

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Solving quadratics in disguise

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Complete the square

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Solve a quadratic by completing the square

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Solve a quadratic by using the formula

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Graph transformations

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Use simple function machines

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Identify domain and range

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Use composite functions

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Iterations

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Inverse functions

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Read/Represent inequalities on a number line

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Solve linear inequalities

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Graphical inequalities

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Solve quadratic inequalities

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Recognise common sequences

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Understand linear sequences

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Understand geometric sequences

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Algebraic sequences

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Understand quadratic sequences

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Solve linear simultaneous equations

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Solve non linear simultaneous equations

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Substitute into expressions/formula

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Form expressions and equations

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Data handling cycle

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Calculate a stratified sample

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Capture recapture

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Two-way tables

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Calculate averages from a list

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Calculate quartiles from a list

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Which average should you use?

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Calculate the mode/mean from a frequency table

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Calculate the median/IQR from a frequency table

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Stem and leaf diagrams

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Draw/Interpret a frequency polygon

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Draw/Interpret cumulative frequency

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Draw/Interpret a box plot

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Draw/Interpret a bar chart

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Draw/Interpret a composite bar chart

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Draw/Interpret a histogram

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Construct a pictograph

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Construct a pie chart

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Interpret a pie chart

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Draw/Interpret a scatter graph

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PMCC and regression line

KS5/STATS

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Standard deviation

KS5/STATS

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Normal distribution

KS5/STATS

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Confidence intervals

KS5/STATS

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Facebook maths

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Place value

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Times tables

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Commutative, associative and distributive laws

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Related calculations

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Factors and multiples

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Prime factors

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Order of operations

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Interpret fractions

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Equivalent fractions

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Reciprocals of numbers

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Add or subtract fractions

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Write one number as a fraction of another

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Fraction of an amount (part i)

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$1★ Unit fraction of an amount 2★ Non-unit fraction of an amount 3★ Mixed number of an amount 4★ Increase or decrease by a fraction 5★ Word problems 6★ Fraction between 2 numbers$

Fraction of an amount (part ii)

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$1★ Given an integer, provide the reciprocal so the product equals 1 2★ Integer by a fraction 3★ 2 fractions 4★ 3 fractions 5★ Mixed numbers 6★ Simple algebraic fractions$

Multiply or divide fractions

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FDP conversion

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$1★ Order positive integers 2★ Order positives and negatives 3★ Order decimals 4★ Order FDP 5★ Order fractions 6★ Order numbers written in standard form$

Order numbers

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Efficient use of a calculator

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Operate with integers (+ and -)

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Operate with integers (x and ÷)

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Column multiplication

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Short division

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Product rule for counting

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Operate with decimals (+ and -)

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Operate with decimals (x and ÷)

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Money problems

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Money problems - payment plans

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Pay slips

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Percentage of an amount

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Percentage change

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Increase/decrease by a percentage

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Reverse percentage

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Simple interest

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Calculate growth/decay

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Student loans

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Annual equivalent rate

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Estimation

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Fermi

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Truncation

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Basic rules of rounding (inc dp and bounds)

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Round to specific sf (inc bounds)

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Upper and lower bound calculations

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Squares, cubes and roots

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Use the laws of indices

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Equating bases

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Integers with negative/fractional indices

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Decimals/fractions with negative/fractional indices

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Conversion of standard form

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Operate in standard form

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Simplify a surd

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Operate with surds

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Rationalise the denominator

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Reading time and tables

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Reading scales

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Measuring/Drawing angles

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Constructions/loci

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Plans and elevations

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90°, 180°, and 360° angles

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Angles in triangles

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Angles in quadrilaterals

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Angles on parallel lines

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Angles in polygons

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Bearings

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Rotations

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Reflections

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Translations

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Enlargements

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Area/Volume scale factors

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Congruence

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Similar shapes

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Names and properties of polygons

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Area of 2D shapes

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Reverse area of 2D shapes

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Algebraic area of 2D shapes

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Area of composite shapes

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Perimeter of 2D shapes

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Parts of a circle

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Circumference of a circle

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Area of a circle

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Circle theorems

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Apply Pythagoras' Theorem

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Apply SOH CAH TOA

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Sine and cosine rules

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Area of a triangle (trigonometry)

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Trigonometry exact values

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Surface area of 3D shapes

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Volume of 3D shapes

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Volume of complex 3D shapes

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Leave your answer in exact form

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Vectors

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Probability scale

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List outcomes

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Calculate simple probabilities

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Frequency trees

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Mutually exclusive events

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Calculate relative/expected frequency

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Probabilities of independent events

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Probabilities of dependent events

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Complete and interpret a venn diagram

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Calculate conditional probabilities

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Conversion of metric units

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Conversion of metric and imperial

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Map scales

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Compound measures

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Simplify a ratio

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Interpret ratio as a fraction

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Divide a quantity into a given ratio

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Multiplicative operations with ratios

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Best buys

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Currency conversion

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Direct proportion

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Inverse proportion

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