Edexcel Foundation Maths Exam

What's included in the maths exam?

Ratio 22-28%
Number 22-28%
Algebra 17-23%
Geometry
Statistics

Number

Number 1 Review Questions

You need be able to:

  • Order positive numbers
  • Order negative numbers
  • Order decimal numbers
  • Order fractions
  • Use the symbols =, ≠, <, >, ≤, ≥

You will need to be able to:

  • Add, subtract, multiply and divide whole numbers
  • Add, subtract, multiply and divide fractions (proper and improper)
  • Add, subtract, multiply and divide mixed numbers
  • Add, subtract, multiply and divide negative numbers
  • Add, subtract, multiply and divide decimal numbers

You will need to be able to:

  • Use BIDMAS
  • Use Inverse operations
  • Understand reciprocals

You will need to be able to:

  • Identify and explain prime numbers
  • Identify and explain factors
  • Identify and explain multiples
  • Identify and explain highest common factors
  • Identify and explain lowest common multiple
  • Identify and explain prime factors

You will need to be able to:

  • Systematic listings

You will need to be able to:

  • know square numbers
  • know square roots
  • know cube numbers
  • recognise numbers to the power of 4 and 5

You will need to be able to:

  • Complete calculations with roots
  • Complete calculations with indices

You will need to be able to:

  • Complete calculations with fractions
  • Complete calculations with multiples of π

You will need to be able to:

  • Complete calculations including standard form

You will need to be able to:

  • Recognise and explain terminating and recurring decimals
  • Convert terminating decimals to fractions and vice versa

You will need to be able to:

  • Identify and work with fractions in ratio problems

You will need to be able to:

  • Interpret fractions and percentages as operators

You need to be able to:

  • Use units of mass
  • Use units of length
  • Use units of time
  • Use units of money

You need to be able to:

  • Use estimation and approximation

You need to be able to:

  • Round numbers and measures using decimal places
  • Round numbers and measures using significant figures
  • Identify error intervals due to truncation
  • Identify error intervals due to rounding

You need to be able to:

  • Apply and interpret limits of accuracy

Algebra

You need be able to:

  • Use and interpret algebraic manipulation

You will need to be able to:

  • Substitute numerical values into formulae and expressions

You will need to be able to:

  • Explain the term “expressions”
  • Explain the term “equations”
  • Explain the term “formulae”
  • Explain the term “identities”
  • Explain the term “factors”

You will need to be able to:

  • Simplify expressions
  • Expand a single bracket
  • Expand double brackets
  • Factorise a quadratic expression
  • Factorise using difference of two squares
  • Simply expressions using laws of indices

You will need to be able to:

  • Use mathematical formulae
  • Rearrange formulae to change the subject

You will need to be able to:

  • Explain the difference between an equation and an identity
  • Argue mathematically to show algebraic expressions are equivalent

You will need to be able to:

  • Interpret simple expressions as functions with inputs and outputs

You will need to be able to:

  • work with coordinates in all four quadrants

You will need to be able to:

  • Plot straight line graphs
  • Identify parallel lines
  • Find the equation of a line given one point and gradient
  • Find the equation of the line through two given points

You will need to be able to:

  • Identify and interpret gradients and intercepts of linear functions graphically and algebraically.

You will need to be able to:

  • Identify and interpret roots of quadratic graphs
  • Identify intercepts of quadratic graphs
  • Identify turning points of quadratic graphs
  • Deduce roots graphically

You will need to be able to:

  • Recognise, sketch and interpret quadratic graphs

You need to be able to:

  • Plot and interpret reciprocal graphs
  • Plot and interpret real-life graphs

You need to be able to:

  • Solve linear equations with an unknown on one side
  • Solve linear equations with the unknown on both sides
  • Find approximate solutions using a graph

You need to be able to:

  • Solve quadratic equations using factorising
  • Find approximate solutions using a graph

You need to be able to:

  • Solve two simultaneous equations
  • Find approximate solutions using a graph

You need to be able to:

  • Form expressions and equations
  • Derive simultaneous equations and solve.

You need to be able to:

  • Solve linear inequalities
  • Represent and interpret inequalities on a number line

You need to be able to:

  • generate a term to term rule from a given sequence
  • generate a position to term rule from a given sequence

You need to be able to:

  • Recognise and use sequences of triangular numbers
  • Recognise and use sequences of square numbers
  • Recognise and use sequences of cube numbers
  • Recognise and use Fibonacci sequences
  • Recognise and use simple geometric progressions

You need to be able to:

  • Find expressions to calculate the nth term of linear sequences

Geometry

You need be able to:

  • Understand these terms: points, lines, vertices, edges, planes, parallel lines, perpendicular lines, right angles, polygons, regular polygons
  • Label sides and angles of a triangle
  • Draw diagrams from written descriptions

You will need to be able to:

  • Construct a perpendicular bisector of a line
  • Construct a perpendicular bisector to a given line from a given point
  • Bisect a given angle
  • Solve loci problems
  • Know that the perpendicular distance from a point to a line is the shortest distance to the line.

You will need to be able to:

  • Apply the properties of angles at a point
  • Apply the properties of angles on a straight line
  • Apply the properties of vertically opposite angles
  • Understand and use corresponding angles
  • Understand and use alternate angles
  • Derive and use the sum of angles in a triangle
  • Find the sum of angles in any polygon

You will need to be able to:

  • Derive and apply the properties and definitions of special types of quadrilaterals; including square, rectangle, parallelogram, trapezium, kite, and rhombus.
  • Derive and apply the properties of all types of triangles

You will need to be able to:

  • Use the basic congruence criteria for triangles (SSS, SAS, ASA, RHS)

You will need to be able to:

  • Apply angle facts
  • Apply triangle congruence
  • Apply similarity and properties of quadrilaterals
  • Apply Pythaoras’ theorem
  • Know the base angles of an isosceles triangle are equal
  • Show simple proofs

You will need to be able to:

  • Identify, describe and construct congruent and similar shapes
  • Identify congruent and similar shapes by considering rotation, reflection, translation, and enlargement (including fractional scale factors)

You will need to be able to:

  • Identify and apply circle definitions and properties; centre, radius, chord, diameter, circumference, tangent, arc, sector and segment

You will need to be able to:

  • Solve geometrical problems on coordinate axes

You will need to be able to:

  • Identify properties of the faces, surfaces, edges and vertices of: cubes, cuboids, prisms, cylinders, pyramids, cones and spheres.

You need to be able to:

  • Construct and interpret plans and elevations of 3D shapes

You need to be able to:

  • Use standard units of measures

You need to be able to:

  • Measure line segments and angles in geometric figures
  • Interpret maps
  • Interpret scale drawings
  • Interpret use of bearings

You need to be able to:

  • Know and apply formulae to calculate areas of triangles
  • Know and apply formulae to calculate areas of parallelograms
  • Know and apply formulae to calculate areas of trapezium
  • Know and apply formulae to calculate volume of cuboids
  • Know and apply formulae to calculate volume of prisms
  • Know and apply formulae to calculate volume of cylinders

You need to be able to:

  • Calculate circumference
  • Calculate area of a circle
  • Calculate perimeters of 2d shapes
  • Calculate perimeter of composite shapes
  • Calculate surface area and volume of spheres
  • Calculate surface area and volume of pyramids
  • Calculate surface area and volume of cones
  • Calculate surface area and volume of composite solids

You need to be able to:

  • Calculate arc lengths of circles
  • Calculate angles of sectors
  • Calculate areas of sectors

You need to be able to:

  • Apply the concept of congruence and similarity

You need to be able to:

  • Know the Pythagoras’ theorem
  • Know the trigonometric ratios
  • Use trigonometry to find angles and lengths in right angled triangles

You need to be able to:

  • Know the exact values of Sin 0, 30, 45, 60 and 90 degrees
  • Know the exact values of Cos 0, 30, 45, 60 and 90 degrees
  • Know the exact values of Tan 0, 30, 45, and 60 degrees

You need to be able to:

  • Describe translations as 2D vectors

You need to be able to:

  • Apply addition and subtraction of vectors
  • Calculate multiplication of vectors by a scalar
  • Apply column representations of vectors

Ratio

You need be able to:

  • Change between units (time, length, area, volume, mass).
  • Change between compound units (speed, rates of pay, prices, density, pressure).

You will need to be able to:

  • Use scale factors, scale diagrams and maps

You will need to be able to:

  • Express one quantity as a fraction of another (fraction is less than one)
  • Express one quantity as a fraction of another (fraction is greater than one)

You will need to be able to:

  • Simplify ratios

You will need to be able to:

  • Divide a given quantity by a ratio

You will need to be able to:

  • Express a multiplicative relationship between two quantities as a ratio or a fraction

You will need to be able to:

  • Understand and use proportion as equality of ratios

You will need to be able to:

  • Relate ratios to fractions and to linear functions

You will need to be able to:

  • Interpret percentages and percentage changes as a fraction or a decimal
  • Express one quantity as a percentage of another
  • Compare two quantities using percentages
  • Work with percentages greater than 100%
  • Solve problems involving percentage change
  • Solve problems involving percentage increase/ decrease
  • Calculate simple interest

You will need to be able to:

  • Solve problems involving direct proportion
  • Solve problems involving indirect proportion

You will need to be able to:

  • Calculate speed, rates of pay, unit pricing, density and pressure

You will need to be able to:

  • Compare lengths
  • Compare areas and volumes using ratio notation
  • Recognise and identity similarity including trigonometry ratios
  • Use scale factors

You need to be able to:

  • Understand that X is inversely proportional to Y is equivalent to X is proportional to 1/Y
  • Interpret equations that describe direct and inverse proportion

You need to be able to:

  • Interpret the gradient of a straight line graph as a rate of change
  • Recognise and interpret graphs that illustrate direct and inverse proportion

You need to be able to:

  • Solve problems involving compound interest
  • Solve problems including growth and decay

Probability

You need be able to:

  • Record, describe and analyse the frequency of outcomes of probability experiments using tables and frequency trees

You will need to be able to:

  • Apply ideas of randomness, fairness and equally likely events to calculate expected outcomes of multiple future events.

You will need to be able to:

  • Express one quantity as a fraction of another (fraction is less than one)
  • Express one quantity as a fraction of another (fraction is greater than one)

You will need to be able to:

You will need to be able to:

  • Understand that empirical unbiased samples tend towards theoretical probability distributions, with increasing sample size.

You will need to be able to:

  • Enumerate sets and combinations of sets systematically, using tables, grids, Venn diagrams and tree diagrams.

You will need to be able to:

  • Construct theoretical possibility spaces for single and combined experiments with equally likely outcomes and use these to calculate theoretical probabilities.

You will need to be able to:

  • Calculate the probability of independent and dependent combined events
  • Interpret and use tree diagrams

Statistics

You need be able to:

  • Infer properties of populations or distributions from a sample, while knowing the limitations of sampling.

You will need to be able to:

  • Interpret and construct tables, charts and diagrams including frequency tables, bar charts, pie charts, and pictograms.
  • Interpret and construct vertical line charts for ungrouped discrete numerical data.
  • Interpret and construct tables and line graphs for time series data

You will need to be able to:

  • Interpret, analyse and compare the distributions of data sets involving discrete, continuous or grouped data.
  • Interpret, analyse and compare median, mean, mode and modal class
  • Interpret, analyse and compare range (including consideration of outliers)

You will need to be able to:

  • Apply statistics to describe a population

You will need to be able to:

  • Use and interpret scatter graphs
  • Recognise correlation and know that it does not indicate causation
  • Draw estimated lines of best fit
  • Make predications, interpolate and extrapolate apparent trends while knowing the dangers of so doing.