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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★ Calculate the gradient of a straight line
2★ Calculate a rate of change between 2 points
3★ Calculate a rate of change at a point
4★ Analysing the meaning of the rate of change
5★ Contextualised rates of change

Find a instanteous rate of change

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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 function given the equation and domain
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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1★ Convert between exponential form to logarithmic form
2★ Evaluate an logarithmic form
3★ Write logarithmic operations as a single logarithmic expression
4★ Solve logarithmic equations
5★ Given logarithmic approximations, find a related logarithmic operation calculation
6★ Change the base

Understand and evaluate logarithms

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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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$1★ Calculate the range for a simple list of postive integers 2★ Calculate the range for positive and negative numbers 3★ Calculate the range for fractions or decimals 4★ Calculate the range real life problems 5★ Problem solve with the range 6★ Compare 2 sets of data$

Calculate the range from a list

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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?

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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 plot
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 pictogram (involving frequencies that require only whole diagrams)
5★ Draw a pictogram (involving frequencies that require half a diagram)
6★ Given a pictogram, find the percentage who answered a category

Construct a pictogram

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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

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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

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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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Roman numerals

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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★ Order integers
2★ Compare 2 calculations
3★ Write an inequality in words
4★ Identify the correct inequality for a given set
5★ Write the set of values that satisfy a given inequality
6★ Find approximations or changes in

Understand and correctly use symbols

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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 does 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★ Calculate 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

Generate Qu

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

Generate Qu

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

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 departure 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★ Convert from degrees to radians
2★ Convert from radians to degrees
3★ Comparison between radians and degrees
4★ Use of a calculator with trigonometry functions
5★ Calculating arc and area of sectors

Convert between degrees and radians

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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 reflection 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

Generate Qu

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

Generate Qu

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

Generate Qu

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

Generate Qu

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

Generate Qu

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

Generate Qu

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)

Generate Qu

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

Generate Qu

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

Generate Qu

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

Generate Qu

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

Generate Qu

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

Leave your answer in exact form

Generate Qu

Vectors

Generate Qu

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

Generate Qu

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

Generate Qu

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

Generate Qu

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

Generate Qu

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★ Calculate 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)

Best buys

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Currency conversion

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Direct proportion

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Inverse proportion

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OPEN MAIN MENU

Search tool:

Write my own on a blank board

Blank Board

Algebra vocabulary and understanding

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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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Find a instanteous rate of change

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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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Understand and evaluate logarithms

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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 the range from a list

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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 pictogram

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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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Roman numerals

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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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Understand and correctly use symbols

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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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Convert between degrees and radians

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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

Generate Qu

Divide a quantity into a given ratio

Generate Qu

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

Generate Qu

OPEN MAIN MENU

Search tool:

Write my own on a blank board

Blank Board

Algebra vocabulary and understanding

Generate Qu

Algebraic proof

Generate Qu

Simplify an expression

Generate Qu

Algebraic fractions

Generate Qu

Change the subject

Generate Qu

Identify coordinates in all 4 quadrants

Generate Qu

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

Generate Qu

Find y = mx + c from a graph

Generate Qu

Rearranging into the form y = mx + c

Generate Qu

Using and exploring y = mx + c

Generate Qu

Find the equation of a parallel line

Generate Qu

Find the equation of a perpendicular line

Generate Qu

Find a instanteous rate of change

Generate Qu

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)

Generate Qu

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

Generate Qu

Solve linear equations (unknown both sides)

Generate Qu

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

Generate Qu

Solve linear inequalities

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Graphical inequalities

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Solve quadratic inequalities

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Recognise common sequences

Generate Qu

Understand linear sequences

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Understand geometric sequences

Generate Qu

Algebraic sequences

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Understand quadratic sequences

Generate Qu

Solve linear simultaneous equations

Generate Qu

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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Understand and evaluate logarithms

Generate Qu

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 the range from a list

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Calculate averages from a list

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Calculate quartiles from a list

Generate Qu

Which average should you use?

Generate Qu

Calculate the mode/mean from a frequency table

Generate Qu

Calculate the median/IQR from a frequency table

Generate Qu

Stem and leaf diagrams

Generate Qu

Draw/Interpret a frequency polygon

Generate Qu

Draw/Interpret cumulative frequency

Generate Qu

Draw/Interpret a box plot

Generate Qu

Draw/Interpret a bar chart

Generate Qu

Draw/Interpret a composite bar chart

Generate Qu

Draw/Interpret a histogram

Generate Qu

Construct a pictogram

Generate Qu

Construct a pie chart

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Interpret a pie chart

Generate Qu

Draw/Interpret a scatter graph

Generate Qu

PMCC and regression line

KS5/STATS

Generate Qu

Standard deviation

KS5/STATS

Generate Qu

Normal distribution

KS5/STATS

Generate Qu

Confidence intervals

KS5/STATS

Generate Qu

Facebook maths

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Place value

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Roman numerals

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Times tables

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Commutative, associative and distributive laws

Generate Qu

Related calculations

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Factors and multiples

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Prime factors

Generate Qu

Order of operations

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Interpret fractions

Generate Qu

Equivalent fractions

Generate Qu

Reciprocals of numbers

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Add or subtract fractions

Generate Qu

Write one number as a fraction of another

Generate Qu

Fraction of an amount (part i)

Generate Qu

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

Fraction of an amount (part ii)

Generate Qu

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

Multiply or divide fractions

Generate Qu

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

Generate Qu

Understand and correctly use symbols

Generate Qu

Efficient use of a calculator

Generate Qu

Operate with integers (+ and -)

Generate Qu

Operate with integers (x and ÷)

Generate Qu

Column multiplication

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Short division

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Product rule for counting

Generate Qu

Operate with decimals (+ and -)

Generate Qu

Operate with decimals (x and ÷)

Generate Qu

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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Convert between degrees and radians

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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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