GCSE Mathematics

Revision Checklist

Stage 1
Stage 2
Stage 3
Class dates
Other info

This is a list of objectives that should have been achieved after studying each chapter of the book. Additional objectives added to ensure full coverage of the syllabus will be covered in class. Objectives that are covered in the book but aren't required for your syllabus are shown in this colour. You can use this list as a revision checklist.

The syllabus for this course is available from the AQA website http://www.aqa.org.uk/qual/gcse/math_b.html

Stage 1


  • Calculate the perimeter of simple shapes, including those with missing side lengths.
  • Calculate the circumference of a circle when given the radius or diameter
  • Calculate the radius or diameter of a circle when given the circumference
  • Calculate the length of arcs of circles
  • Calculate the perimeter of shapes involving curved sections

Fact Sheet 1: Fractions, Decimals and Percentages

  • Cancel fractions, form equivalent fractions, order fractions
  • Convert between improper fractions and mixed numbers
  • Enter, manipulate and use fractions with a calculator
  • Convert between fractions, decimals and percentages and order by size.
  • Writing a number as a fraction or percentage of another

Number 1

  • Solve problems using fractions, decimals and percentages
  • Use non-calculator methods for calculating
  • Make estimates by approximating numbers to 1 significant figure
  • Add and subtract fractions without a calculator


  • Use correct vocabulary
  • Identify probabilities on a probability scale
  • List all possible outcomes for an event using a systematic method
  • List all possible outcomes for a combination of events, again using a systematic method
  • Use a probability space / two-way table
  • Calculate probabilities using equally likely outcomes
  • Know the meaning of mutually exclusive
  • Know that the sum of probabilities of mutually exclusive events is 1
  • know that the prob of event not occurring is 1 - prob of event occurring
  • Use the "or" rule for mutually exclusive events
  • Use relative frequency to estimate probabilities
  • Use relative frequency to calculate the expected number of a particular outcome
  • Estimate probabilities using suitable methods: equally likely outcomes, relative frequency, historical evidence

Fact Sheet 2: The language and Shorthand of Algebra

  • Understand and use correct vocabulary for algebra
  • Use negative numbers with the four operations, add, subtract, multiply and divide
  • Input negative numbers in to a calculator
  • Understand the shorthand notation used with algebra

Algebra 1

  • Form algebraic expressions from a given situation
  • Simplify algebraic expressions by collecting like terms
  • Substitute numbers into expressions and evaluate
  • Construct formulae
  • Substitute numbers into formula
  • Construct equations
  • Solve linear equations where the unknown is on one side

Fact Sheet 3: The language of geometry

  • Measure and draw angles
  • Identify types of angles
  • Know and work with the different labelling conventions for angles
  • Perpendicular and parallel lines
  • Know the names of polygons
  • Label the type of angle in a polygon - interior and exterior
  • Be able to label and use the properties of special triangles and special quadrilaterals

Geometry 1

  • Angle facts on straight lines and at a point
    • Angles on a straight line add up to 180 degrees
    • Angles at a point add up to 360 degrees
    • Vertically opposite angles are equal
  • Angle facts on parallel lines
    • F-angles - Corresponding angles
    • Z-angles - Alternate angels are equal
    • C-angles - Interior angles on parallel lines add up to 180 degrees
  • Triangles and quadrilaterals
    • The interior angles of a triangle add up to 180 degrees
    • An exterior angle of a triangle is equal to the sum of the interior opposite angles
    • The interior angles of a quadrilateral add up to 360 degrees
  • Construct accurate diagrams using a rule and compass

Fact Sheet 4: The language of graphs

check with revision checklist
  • Construct axes suitable for drawing a graph, ie consistent scale, large enough, etc
  • Know that the independent variable is usually the horizontal axis and the dependant variable the vertical axis
  • Plot co-ordinates in all quadrants, know where the origin is and give its co-ordinates
  • Calculate the mid-point of two points (given as co-ordinates)
  • Recognise the general shapes of graphs of linear, quadratic, cubic an reciprocal functions

Linear graphs 1

  • Know that a graph represents the relationship between two variables
  • Make a table of values
  • Draw a line graph by plotting 3 suitable points
  • Know the equations of graphs of horizontal and vertical lines and be able to plot them
  • Use graphs in practical situations, eg. currency conversion

Area and volume 1

  • Know that area is a measure of surface
  • Know that area is measured in square units
  • Know that measurements must be in the same units before calculating area
  • Calculate the area of a rectangle and square
  • Calculate the area of composite by breaking them into regular shapes
  • Calculate side length of a square when area is known, and an unknown side length of a rectangle when the area and one side length is known
  • Calculate the area of a triangle
  • Calculate the area of a circle
  • Calculate the area of a sector
  • Know that the volume of a solid shape is the amount of space it occupies
  • Calculate the volume of a cube and cuboid
  • Calculate the surface area of a cuboid
  • Draw the net of a solid shape
  • Represent a solid object on isometric paper when given a net or orthographic views

Transformations 1

  • Know and use accurately the terminology object, image, map, displacement, congruent
  • Translation
    • Know the properties of a translation. (position changes, what properties stay the same (are invariant), object and image are congruent)
    • Describe a translation using a column vector
    • Perform a translation
  • Reflection
    • Describe the preserved properties of a reflection
    • Know the properties of a reflection
    • Perform a reflection
    • Describe fully a reflection
  • Rotation
    • Describe the preserved properties of a rotation
    • Know the properties of a rotation
    • Perform a rotation
    • Describe fully a rotation
  • Enlargement
    • Describe the preserved properties of an enlargement
    • Know the properties of an enlargement
    • Perform an enlargement
    • Describe fully an enlargement

Fact Sheet 5: The language of data handling

  • Know that data can be classified into descriptive and numerical and numerical data are either discrete of continuous
  • Identify methods for collecting data
  • Construct and evaluate questionnaires for collecting data
  • Use a variety of methods for displaying data including frequency tables, bar charts, comparative bar charts, histograms, line graphs, pie charts, histograms

Data handling

  • Draw statistical diagrams including bar charts, histograms, pie charts and line graphs
  • Interpret statistical diagrams
  • Calculate the three averages: mean, median, mode
  • Know properties of each average
  • Range
  • Use statistical measures (mean, median, mode, range) to compare data sets
  • Know that a scatter diagram can be used to compare bivariate data
  • Plot a scatter diagram
  • Draw a line of best fit
  • Use terminology positive / negative correlation

Stage 2

Fact Sheet 6: The language of Number

  • Define integer, multiple, common multiple, lowest common multiple, factor, common factor, highest common factor, prime number, prime factor.
  • Use square and square root keys on a calculator, cube and cube root
  • Understand the meaning of square / cube root as the reverse of squaring / cubing and as the number multiplied by itself 2/4 times to obtain the number started with
  • Use index numbers for repeated multiplication
  • Decompose a number into a product of its primes
  • Use the reciprocal function

Number 2

  • use square and cube numbers in problems
  • Round to significant figures
  • Form equivalent ratios and cancel ratios to their lowest form
  • Write ratios in the form 1:x, x:1
  • Share out a quantity in a given ratio (Proportional division)
  • Find a missing amount in a ratio: Multiple, Unitary, Algebraic methods
  • Direct proportion and relate it to a graph with no intercept
  • Calculate the scale factor of enlargement
  • Use ratios in enlargements and map scales

Algebra 2

  • Expand brackets
  • Evaluate formula containing brackets
  • Solve linear equations with unknowns on both sides
  • Solve linear equations requiring prior removal of brackets
  • Represent inequalities on a number line
  • Solve linear inequalities (inc. multiplying or dividing by a negative number)

Geometry 2

  • Use three figure bearings to describe location, find the bearing of A from B, plot a point B on a given distance and bearing from a point A
  • Constructions using a ruler (unmarked) and compass
    • Perpendicular bisector of a straight line
    • Bisector of an angle
    • Parallel line
    • the perpendicular from a point to a line
  • Loci - mark out the locus of
    • a point that is a constant distance from a fixed point
    • a point that is equidistant from two fixed points
    • a point that is equidistant from two intersecting straight lines
    • combinations of the above rules

Data Handling 2

  • Know and use the formula for the mean of raw data
  • Calculate the mean for data given in a frequency table
  • Estimate the mean of grouped data
  • Find mid-interval values for discrete and continuous data (pg 244, Crawshaw)
  • Construct a frequency polygon for data with equal class intervals
  • Identify a modal class

Algebra 3

  • Find the HCF of an algebraic expression
  • Factorise an expression by taking the HCF outside of a bracket. Check by multiplying out the bracket.
  • Substitute into a formula (involving powers and square roots) and evaluate
  • Rearrange formulae, including formulae involving squares and square roots including cases where the subject occurs twice or where a power of the subject occurs
  • Linear sequences

Area and Volume 2

  • Calculate the area of a parallelogram
  • Calculate the area of a trapezium
  • Know that prisms have a constant cross section
  • Calculate the volume of a prism
  • Calculate the volume of a cylinder
  • Calculate the surface area of solids

Transformations 2

  • Find the centre and angle of rotation by construction methods when necessary.
  • Compound transformations - perform a compound transformation, define a compound transformation and determine whether the effect of a compound transformation can be obtained from a single transformation. (use the yr9 end of year exam question i wrote for this)

Pythagoras' Rule

  • Recall Pythagoras' theorem and know that it only applies to right-angled triangles
  • Identify right angled triangles using Pythagoras' theorem
  • Find the length of the hypotenuse
  • Find the length of one of the shorter sides
  • Use Pythagoras' theorem to 'problem type' questions
  • Be able to spot right-angled triangles in diagrams, in particular half of isosceles triangles, angle in a semi circle, rhombus)
  • Calculate the distance between two points (given as co-ordinates)

Linear Graphs 2

  • Calculate the gradient of straight line segments
  • Know that parallel lines have the same gradient
  • Know the the gradient is the rate of change of one variable with respect to another. (Go up m units for every 1 unit across)
  • Speed, distance and time. - Compound measures
  • Use the gradient-intercept form of the equation of a line
  • Know that line graphs represent a linear relationship between two numbers
  • Know the effect of scale changes on the overall look of a linear graph
  • Draw graphs of straight lines without plotting three values (use y=mx+c or cover-up method)
  • Sketch graphs given in y=mx+c form (and rearrange to y=mx+c if necessary)
  • Recognise a linear relationship from a table
  • determine the solution of a linear equation from a graph - ie where it cross the x-axis
  • given the co-ordinates of two points, determine the euqation of the line passing through them

Simultaneous Linear equations

  • Solve simultaneous linear equations graphically
  • Solve using substitution
  • Solve using elimination, including where both equations need to be multiplied


  • Know that the trigonometric functions give the ratios of side length of triangles
  • Label hypotenuse, opposite and adjacent
  • Recall the trig formulae / definitions
  • Use a calculator to find the values of the trig ratios
  • Use trig ratios to find missing lengths (in right angled triangles)
  • Use trig ratios to find missing angles
  • Be able to spot right-angled triangles in diagrams, in particular half of isosceles triangles, angle in a semi circle, rhombus)
  • use trig to solve 'problem' questions

Quadratics 1

  • Multiply out two brackets, and recognise (a+b)2 as a question of this type
  • Draw graphs of quadratic equations
  • Solve quadratic (and other)equations using graphs
  • Solve quadratic equations using trial and improvement to a given number of (n) decimal places and know how to terminate correctly (either halve interval differing by 1 in the nth decimal place or by determine closest)

Geometry 3

  • Calculate the sum of the interior angles of a polygon by splitting into triangles
  • Calculate the interior angle of a regular polygon
  • Know that the exterior angles of a polygon sum to 360 degrees (the book has a justification, maybe give proof too)
  • Hence calculate the exterior angle of an n-sided regular polygon
  • Identify lines of symmetry of regular polygons and know the an n-sided regular polygon has n lines of symmetry
  • Identify rotational symmetries and know that an n-sided regular polygon has rotational symmetry of order n
  • Tessellations determine whether shapes can tessellate by considering the interior angles at a vertex

Stage 3

Number 3

  • Simplify and evaluate indices for numbers and algebra. Use a calculator to calculate powers of numbers. Including negative powers
  • Standard form: write large and small numbers in standard form
  • Standard form on a calculator
  • Calculate Percentages - profit / loss
  • Percentage error
  • Increase / decrease by a percentage
  • Compound percentages
  • Reverse percentages
  • Multiplying and dividing fractions (change mixed numbers to improper fractions)

Data handling 3

  • Calculate the probability of combined events using or and and rules
  • Draw and use tree diagrams to calculate the probabilities of combined events
  • Calculate the median for and odd or even number of pieces of data.
  • Estimate quartiles from a cf diagram
  • Find the upper and lower quartile values
  • Construct a box plot and compare box plots
  • Interquartile range. Know that it gives the range of the middle 50% of the values
  • Cumulative frequency
  • Compare two cumulative frequency distributions

Quadratics 2

  • Factorise quadratics of the type x2+bx+c
  • Solve quadratic equations of the type x2+bx+c=0 by factorising, including where rearrangement is required first
  • Factorise difference of two squares and recognise the pattern x2-a2
  • Quadratic sequences - generate terms of, find nth term of, construct formula for nth term of one

Further shape and space

  • Dimension analysis - determine whether a given expression could represent a length, area, volume, none,
  • Similar shapes - identify by using properties of, find missing length and angles
  • Similar triangles - know the properties of, use properties in questions, find missing lengths in,
  • Solve mixed problems requiring the use of Pythagoras' theorem, trigonometry and similar shapes

Algebra 4

  • Solve quadratic inequalities
  • Represent inequalities in two variables as regions on a graph. Linear programming.
  • Solve cubic equations by trial and improvement
  • Draw cubic and reciprocal graphs
  • Sketch standard graphs
  • Use graphs to model real life graphs

You must also be able to:

stem and leaf (extracted from syllabus but not covered in the book or at least not listed in the above objectives) non-calculator methods understand how errors are compounded in certain calculations present and interpret solutions in the context of the original problem understand the difference between a practical demonstration and a proof know the meaning of and use the words ‘equation’, ‘formula’, ‘identity’ and ‘expression’ change the subject of a formula, including cases where the subject occurs twice distinguish between practical demonstrations and proofs distinguish between lines and line segments; use parallel lines, alternate angles and corresponding angles, understand the consequent properties of parallelograms and a proof that the angle sum of a triangle is 180 degrees; understand a proof that the exterior angle of a triangle is equal to the sum of the interior angles at the other two vertices recall the definition of a circle and the meaning of related terms, including centre, radius, chord, diameter, circumference, tangent, arc, sector and segment; understand that the tangent at any point on a circle is perpendicular to the radius at that point; understand and use the fact that tangents from an external point are equal in length; explain why the perpendicular from the centre to a chord bisects the chord; understand that inscribed regular polygons can be constructed by equal division of a circle; use the facts that the angle subtended by an arc at the centre of a circle is twice the angle subtended at any point on the circumference, the angle subtended at the circumference by a semicircle is a right angle, that angles in the same segment are equal, and that opposite angles of a cyclic quadrilateral sum to 180 degrees understand and use vector notation recognise that measurements given to the nearest whole unit may be inaccurate by up to one half in either direction distinguish between fractions with denominators that have only prime factors of 2 and 5 (which are represented by terminating decimals), and other fractions (which are represented by recurring decimals) understand and use unit fractions as multiplicative inverses [for example, by thinking of multiplication by 1/5 as division by 5; or multiplication by 6/7 as multiplication by 6 followed by division by 7 (or vice versa)], multiply and divide a given fraction by an integer, by a unit fraction and by a general fraction understand the multiplicative nature of percentages as operators [for example, a 15% increase in value Y, followed by a 15% decrease is calculated as 1.15 × 0.85 × Y] recall integer squares from 2 × 2 to 15 × 15 and the corresponding square roots, the cubes of 2, 3, 4, 5 and 10 develop a range of strategies for mental calculation recognisning that, in many cases, only a fraction can express the exact answer (add this to the fractions objs) use surds and pi in exact calculations, without a calculator use calculators effectively and efficiently; know how to enter complex calculations; use an extended range of function keys, including trigonometrical and statistical functions relevant across this programme of study know not to round during the intermediate steps of a calculation check and estimate answers to problems; select and justify appropriate degrees of accuracy for answers to problems; recognise limitations on the accuracy of data and measurements box plots moving averages use statistical functions on a calculator know that zero correlation does not necessarily imply "no relationship" but merely "no linear relationship" understand the increasing sample size will generally lead to better estimate s of probabilities and population parameters interpret a wide range of graphs and diagrams and draw conclusions; identify seasonality and trends in time series look at data to find patterns and exceptions
The Lessons

Number 1
Algebra 1
Geometry 1
Linear Graphs 1
Area and Volume 1
Transformations 1
Data Handling
Number 2
Algebra 2
Geometry 2
Data Handling 2
Algebra 3
Area and Volume 2
Transformations 2
Pythagoras' Theorem
Linear Graphs 2
Simultaneous Equations
Quadratics 1
Geometry 3
Number 3
Data Handling 3
Quadratics 2
Furhter Shape and Space
Algebra 4
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© 2003 Andrew Martin
Last updated:27thSeptember 2003