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1★ What is it? (term, expression, equation or identity?)
2★ Is it an equation or an identity?
3★ 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 to be true
3★ Show that an identity (involving product of brackets) to be true
4★ Show that an expression is even, odd, multiple of or factor of
5★ Show that a harder expression is a even, odd, multiple of or factor of

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★ Shape geometry

Simplify an expression

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$1★ Simplify 2★ Add and subtract 3★ Simplify (inc. factorising) 4★ Multiply or divide 5★ Add or subtract with denominator expressions 6★ Solve algebraic fractional equations (integer solutions)$

Algebraic fractions

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$1★ 1 step operation 2★ 2 step operation 3★ Rearrangement involving fractions 4★ Rearrangement involving powers 5★ Common formulae rearrangement 6★ Subject appears more than once$

Change the subject

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1★ First quadrant
2★ First and second quadrant
3★ Third and fourth quadrants
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★ Find the gradient where Δx is 1
3★ Finding positive gradient
4★ Finding negative gradient
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★ Simple rearrange into the form y = mx + c and interpret
3★ Rearranging from ax + by = c into y = mx + c and interpret

Rearranging into the form y = mx + c

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1★ Complete a table of values (find y)
2★ Complete a table of values (x and y)
3★ Find c given gradient and a point
4★ Find the equation of a line given gradient and point
5★ Find gradient given 2 points
6★ Find the equation of a line given 2 points

Using and exploring y = mx + c

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1★ Given coordinates for two lines, are they parallel?
2★ Write down the gradient of a line parallel to y=mx+c
3★ Given 2 equations of lines, are they parallel?
4★ Write down the equation of a line parallel to y=mx+c and 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 coordinates for two lines, are they perpendicular?
3★ Write down the gradient of a line perpendicular to y=mx+c
4★ Prove 2 lines are perpendicular
5★ Given 2 equations of lines, are they perpendicular?
6★ Write down the equation of a line perpendicular to y=mx+c and passes through (a,b)

Find the equation of a perpendicular line

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1★ Find perpendicular gradients
2★ State the gradient of a tangent
3★ Find the equation of the tangent given the equation of the radius and coordinates of tangent intersection
4★ Find the equation of the tangent given equation of circle and coordinates of the intersection with the tangent
5★ Find the equation of the tangent given the equation of the circle and the x-coordinate of the intersection with the tangent
6★ Problem solving

Equation of a tangent to a circle

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1★ x=a and y=b
2★ x=a/y=b and y=mx+c
3★ y=ax+b and y=cx+d
4★ Why is there no solution?
5★ Quadratic and linear graph

Graphical solutions of equations

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1★ Table of values for simple quadratics or cubics
2★ Table of values for harder quadratics or cubics
3★ Draw a quadratic or cubic function
4★ Identify quadratic and cubic graphs
5★ Estimate values from a graph

Quadratic and cubic functions

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1★ State the radius or centre
2★ Given the centre and radius state the equation
3★ Draw a circle with specific equation
4★ State the equation from a graph
5★ Does it lie on the circle?
6★ Problem solving

Equation of a circle

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Area under a graph

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1★ Table of values
2★ Draw an reciprocal function
3★ Identify reciprocal graphs
4★ Estimate values from a graph
5★ Identify asymptotes

Reciprocal functions

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1★ Table of values
2★ Draw an exponential function
3★ Identify exponential graphs
4★ Estimate values from a graph
5★ Solve exponential equations

Exponential functions

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1★ Identify sin, cos and tan graphs
2★ Identify specific coordinates on a graph
3★ Sketch a graph
4★ Find another solution using a graph
5★ Find another solution without the aid of a graph

Trigonometry graphs

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1★ 1 step equations (add or subtract)
2★ 1 step equations (multiply or divide)
3★ 2 step equations (positive coefficient of x)
4★ 2 step equations (negative coefficient of x)
5★ Linear equation involving brackets
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★ Simple unknown both sides
2★ Positive coefficients
3★ Negative coefficients
4★ Involving brackets
5★ Word problems
6★ Problem solving

Solve linear equations (unknown both sides)

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1★ Linear equation involving brackets
2★ Collecting the sum or difference of two brackets
3★ Unknowns on both sides with brackets
4★ Fractional multiplier
5★ Brackets on both sides
6★ Brackets in brackets

Solve linear equations with brackets

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$1★ Solve a simple rational equation 2★ Solve a rational equation with an expression numerator 3★ Solve a rational equation with an expression numerator and denominator 4★ Solve an equation with fractional expressions on each side of the equals 5★ Solve a rational equation where you have the sum of two fractional expressions 6★ Solve a rational equation involving factorising$

Solve rational equations

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1★ Multiplying a positive or negative by a simple expression
2★ Multiplying a positive or negative number by a harder expression
3★ Multiplying 𝑥 over bracket
4★ Multiplying an expression over a single bracket
5★ Expand the sum of two brackets and simplify
6★ Identify unknowns in an identity

Expand over a single bracket

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1★ Expand with positive terms
2★ Expand with 1 or more negative terms
3★ Difference of two squares
4★ Harder product of 2 expressions
5★ Expanding quadratic/cubic expressions
6★ Product of 3 brackets

Expand 2 or more binomials

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1★ Factorise simple linear expressions
2★ Factorise simple quadratic expression
3★ Factorise simple quadratic expression (factor with coefficient)
4★ Can it be factorised?
5★ Problem solving
6★ Fully factorise by combining a sum of 2 terms

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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$1★ Solve like a quadratic 2★ Solving like a quadatic involving rearrangement 3★ Solve like a quadratic involving fractional powers 4★ Solve like a quadratic involving variable as a power 5★ Solve like a quadratic involving trigonometric equations$

Solving quadratics in disguise

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1★ Completing the square scaffold 1
2★ Completing the square scaffold 2
3★ Completing the square where b is divisible by 2 in quadratic
4★ Completing the square where b is not divisible by 2 in quadratic
5★ Find the minimum point of a function
6★ Graphical translation

Complete the square

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1★ Solve by completing the square scaffold 1
2★ Solve by completing the square scaffold 2
3★ Solve by completing the square where b is divisible by 2 in quadratic
4★ Solve by completing the square where b is not divisible by 2 in quadratic
5★ Harder solve by completing the square
6★ Positive or negative value of a

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 a correctly used formula find the quadratic equation
4★ Use of the discriminant
5★ Solving quadratics by using the quadratic formula

Solve a quadratic by using the formula

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1★ Describe a transformation in words (quadratics)
2★ Effect of a transformation on a single point (quadratics)
3★ Identify the function of a quadratic graph transformation
4★ Draw the function of a quadratic graph transformation
5★ Effect of a transformation on a single point (trig graphs)
6★ Draw/Identify a trig graph transformation

Graph transformations

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1★ 1 step finding output
2★ 2 step finding output
3★ 2 step finding input
4★ 2 step finding a missing operation
5★ 2 step algebraic output
6★ 2 step finding a missing operation given algebraic output

Use simple function machines

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1★ 1 step finding the range
2★ 1 step finding range or domain
3★ 2 step finding the range
4★ 2 step finding range or domain
5★ Find the range given a function
6★ Find restrictions for a given function

Identify domain and range

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1★ Substitute values into simple composite functions
2★ Substitute values into harder composite functions
3★ Substitute values into composite functions involving powers
4★ Algebraically simplify composite functions
5★ Problem solving

Use composite functions

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1★ Find the next term
2★ Find the third or fourth term
3★ Word problem with a given formula
4★ Find a term given a rearrangement
5★ Show that an equation can be rearranged to a given form
6★ Find a solution given a rearrangement and two starting values

Iterations

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$1★ 1 step rearrangement 2★ 2 step rearrangement 3★ Rearrangement involving fractions 4★ Rearrangement involving powers 5★ Rearrangement involving completing the square$

Inverse functions

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1★ Interpreting a not equal to representation
2★ Interpreting an equal to representation
3★ Interpreting a mixture of first 2 tasks
4★ Represent an inequality on a number line
5★ Interpreting a compound inequality
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 (inc add or subtract)
2★ Solve a 1 step inequality (inc multiply or divide)
3★ Solve a 2 step inequality
4★ Solve a simple inequality with a negative coefficient of x
5★ Solve a 2 step inequality with a negative coefficient of x
6★ Solve a compound inequality

Solve linear inequalitities

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1★ Identify the linear inequality from a graph
2★ Sketch the linear inequality
3★ Identify the inequalities that satisfy a given region
4★ Identify the inequalities that satisfy a given region (inc y - x > a)
5★ State the coordinates of points that satisfy the given region

Graphical inequalities

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1★ Graphically solve a quadratic inequality (part i)
2★ Graphically solve a quadratic inequality (part ii)
3★ Solve a simple quadratic inequality
4★ Solve a quadratic inequality (where a is 1)
5★ Solve a quadratic inequality (where a is not 1)
6★ Solve a quadratic inequality (where a is not 1) involving rearrangement

Solve quadratic inequalities

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$1★ Continue for the next two terms for an arithmetic sequence 2★ Continue for the next two terms for a geometric sequence 3★ Continue for the next two terms the square/triangular number sequence 4★ Continue for the next two terms for a Fibonacci sequence 5★ Continue for the next two terms a periodic sequence 6★ Continue for the next two terms a fractional sequence$

Recognise common sequences

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1★ Continue for the next two terms
2★ Find the missing middle two values
3★ Write the first 4 terms given the nth term rule
4★ Find the nth term rule
5★ Is a number part of the sequence?
6★ Given 2nd and 4th term find 100th term

Understand linear sequences

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1★ Is it geometric?
2★ Find the next 2 terms (integer common ratio)
3★ Find the next 2 terms (decimal common ratio)
4★ Given the first term and common ratio, find the first 3 terms
5★ Given an algebraic rule and the first term, find a specific term
6★ Problem solving

Understand geometric sequences

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1★ Continue an arithmetic or Fibonacci sequence
2★ Continue a geometric sequence
3★ Show the sixth term is ...
4★ Find the nth term
5★ Given 2 terms, find the unknowns

Algebraic sequences

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1★ Continue for the next two terms
2★ Write the first 4 terms given the nth term rule
3★ Find the nth term rule (where rule is an^2)
4★ Find the nth term rule (where rule is n^2+bn+c)
5★ Find the nth term rule (where rule is an^2+bn+c)
6★ Use the nth term rule (where rule is an^2+bn+c)

Understand quadratic sequences

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1★ Has a common term with the same coefficient
2★ Has a common term but different signs
3★ All coefficients are different
4★ Word problem
5★ Rearrangement required
6★ Form and solve simultaneous equations

Solve linear simultaneous equations

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1★ A simple quadratic and 1 straight line
2★ A quadratic and a straight line
3★ A reciprocal graph and a straight line
4★ A circle and a straight line (integer answers)
5★ A circle and a straight line (decimal answers)

Solve non linear simultaneous equations

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1★ Substitute positive values into a 1 step expression
2★ Substitute positive values into a 2 step expression
3★ Substitute negative values into an expression
4★ Substitute values into a simple quadratic expression
5★ Substitute values into common formulae
6★ Substitute into a function

Substitute into expressions/formula

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$1★ Create a simple expression 2★ I think of a number (2 step expression) 3★ I think of a number (inc fraction) 4★ Multi step problem 5★ Form and solve an equation with unknowns on both sides 6★ Create a formula to represent the perimeter of a shape$

Form expressions and equations

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Data handling cycle

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

Calculate a stratified sample

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1★ Find an easy estimate of the population
2★ Find the 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
3★ Complete missing values
4★ Calculate probabilities/values from a two way table
5★ Word problems
6★ Multi-skill problem solving

Two-way tables

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

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 the list

Calculate quartiles from a list

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

Which average should you use?

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

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

Calculate the median/IQR from a frequency table

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$1★ Draw a stem and leaf diagram (inc key where data values are integers) 2★ Draw a stem and leaf diagram (inc key where data values are decimals) 3★ Interpret a stem and leaf diagram (how many were over?/What fraction were under?) 4★ Find averages and range from a stem and leaf diagram 5★ Adding data to a stem and leaf and analysing the effects on statistical measures 6★ Analysing back to back stem and leaf$

Stem and leaf diagrams

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1★ Draw a frequency polygon
2★ Interpret frequencies from a frequency polygon
3★ Interpret the mean from a frequency polygon
4★ Draw comparisons between 2 frequency polygons

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 (e.g. IQR)
4★ Analyze proportions represented
5★ Calculate median, inter-quartile range or range from a box plot
6★ Make comparisons between 2 box plots

Draw/Interpret a box plot

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1★ Create a tally chart from a list of data
2★ Interpret a tally chart
3★ Draw a bar chart
4★ Interpret least/most common or frequency from a bar chart
5★ Problem solving

Draw/Interpret a bar chart

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1★ Analyse a composite bar chart
2★ Draw a composite bar chart
3★ Interpret proportions from a composite bar chart

Draw/Interpret a composite bar chart

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1★ Complete a frequency density table
2★ Complete a frequency density table (harder)
3★ Estimate how many got greater than a score from a histogram
4★ Estimate how many got greater than a score from a frequency table
5★ Construct a frequency table from a histogram
6★ Interpret a histogram

Draw/Interpret a histogram

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1★ Identify least/most common or total (easy key)
2★ Identify least/most common or total (tricky key)
3★ Find the frequency of a category or total frequency
4★ Draw a pictograph (easy key)
5★ Draw a pictograph (tricky key)
6★ Find the percentage who answered a category

Construct a pictograph

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1★ Draw a pie chart (total freq 360 with items factors of 360)
2★ Draw a pie chart (total freq 90 or 180)
3★ Draw a pie chart (total freq factor of 360)
4★ Calculate the angles needed to construct a pie chart (random total freq)
5★ Draw a pie chart (random total freq)
6★ Problem solving

Construct a pie chart

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$1★ Find the mode 2★ Calculate the fraction represented by a sector 3★ Frequency of a sector, calculate total frequency 4★ Given the percentage represented by 2 sectors and the total calculate the number in third sector$

Interpret a pie chart

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

Draw/Interpret a scatter graph

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1★ Comment on correlation
2★ Find the PMCC
3★ Interpret the PMCC
4★ Calculate the regression line
5★ Interpolate/extrapolate using a regression line
6★ Limitations of using a regression line

PMCC and regression line

KS5/STATS

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1★ Substitute into formula
2★ Find sd from sample
3★ Find sd from population
4★ Comment on results
5★ Percentage of data within 1 sd
6★ Find sd from a frequency table

Standard deviation

KS5/STATS

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1★ Calculate the z-score
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

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★ Most people will fail this question
2★ Values of fruit
3★ Order of operation circles

Facebook maths

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Place value

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Times tables

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1★ Commutative law (simple)
2★ Commutative law
3★ Associative law
4★ Distributive law
5★ Identify the law
6★ Evaluate calculations

Commutative, associative and distributive laws

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1★ Simple rearrangement
2★ Rearrangement inc positive powers of 10
3★ Rearrangement inc negative powers of 10
4★ Rearrangement inc negative power of 10 (harder)

Related calculations

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1★ Write down all the factors of a number
2★ Write down all the 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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$1★ Simple calculation 2★ Calculation inc brackets 3★ Calculation inc brackets and powers 4★ Calculation inc multisteps 5★ Calculation inc fraction 6★ Insert brackets to make a calculation true$

Order of operations

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$1★ Identify the unit fraction 2★ Shade the unit fraction 3★ Read simple fractions 4★ Represent simple fractions 5★ Understanding shaded rows and columns 6★ Write as a mixed number$

Interpret fractions

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$1★ Simplify a fraction (given simplified denominator) 2★ Simplify a fraction 3★ Compare 2 fractions 4★ Would you rather? Comparing 2 sectors 5★ Find half way between 2 fractions 6★ Convert to and from a mixed number$

Equivalent fractions

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$1★ Product makes 1 2★ Reciprocal of integers 3★ Reciprocal of fractions 4★ Reciprocal of decimals < 1 5★ Reciprocal of numbers > 1 6★ Equivalent fraction fill in the blank reciprocals$

Reciprocals of numbers

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$1★ Complete the whole 2★ Common denominators 3★ Different denominators 4★ Add or subtract 3 fractions 5★ Mixed numbers 6★ Simple algebraic fractions$

Add or subtract fractions

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$1★ Write amount shaded as a fraction of the total 2★ Write one number as a fraction of another 3★ Understanding complements in fraction totals 4★ Different units 5★ Multi-step problems 6★ Equivalent fraction problem$

Write one number as a fraction of another

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$1★ Multiply a fraction by an integer 2★ Multiply a fraction by a fraction 3★ Find a fraction of an amount 4★ Which is larger? 5★ Word problems 6★ Fraction of one amount is equal to fraction of unknown$

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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$1★ Product makes 1 2★ Integer by a fraction 3★ 2 fractions 4★ 3 fractions 5★ Mixed numbers 6★ Simple algebraic fractions$

Multiply or divide fractions

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$1★ Convert between common FDP 2★ Convert between FDP 3★ Are 2 numbers equal? 4★ Order FDP 5★ Convert a recurring decimal to a fraction 6★ Convert a recurring decimal to a fraction (harder)$

FDP conversion

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

Order numbers

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1★ Calculator familiarisation
2★ Simple operations to input
3★ Using special calculator functions
4★ Issues with negative numbers
5★ Standard form on a calculator
6★ Fraction calculations

Efficient use of a calculator

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1★ Numbers bonds
2★ Key vocabulary
3★ U ± U
4★ TU ± TU
5★ HTU ± TU
6★ Directed numbers

Operate with integers (+ and -)

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1★ Times tables
2★ Key vocabulary
3★ TU x÷ U
4★ HTU x÷ TU
5★ Directed numbers

Operate with integers (x and ÷)

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1★ TU x U
2★ TU x TU
3★ HTU x TU
4★ Identify the last digit of a multiplication
5★ Fill in the missing number HTU x TU
6★ HTU x HTU

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
5★ Decimal x÷ decimal (2 or more dp)
6★ Contextualised use of x÷ with decimals

Operate with decimals (x and ÷)

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$1★ Buy 1 each of two items 2★ Buy multiple items 3★ Buy multiple items with different units 4★ Calculating change 5★ How many can I buy? 6★ What fraction of the total cost does it represent?$

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★ Is it better 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★ Income basic rate tax calculation
5★ Income higher rate tax calculation
6★ Calculate National Insurance

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★ Problem solving - two way table

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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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★ Calculator use
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★ 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 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★ Worded 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★ Bounds

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★ Bounds

Round to specific sf (inc bounds)

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1★ Define the bounds of a number
2★ Bounds of addition and multiplication
3★ Bounds of subtraction and division
4★ Mixture of operations
5★ Compound measures with bounds
6★ Use of bounds in other topics

Upper and lower bound calculations

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1★ Counting squares
2★ Square numbers up to 225
3★ Square roots
4★ Operating with squares and roots
5★ Cube numbers
6★ Operating with squares, cubes and roots

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 algebra
6★ Write as a single power of a number

Use the laws of indices

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1★ Mixed index laws
2★ Write as a power of ...
3★ Simplify index laws and write as a power of ...
4★ Simplify a complex problem and write as a power of ...
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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$1★ To the power of -1 2★ To the power of a negative 2 3★ To the power of a half or a third 4★ To the power of negative half or third 5★ To the power of a fraction (inc top heavy) 6★ To the power of a negative fraction (inc top heavy)$

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 an incomplete attempt into standard form

Conversion of standard form

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