Mr Barton's GCSE Maths Quizzes
The following set of free maths quizzes have been designed to use to assess each of the objectives for the new Maths GCSE that students will sit for the first time in June 2017. They are suitable for use with students in Years 7 to 10.
Number - Structure and Calculation N1
Order positive and negative integers, decimals and fractions; use the symbols =, not equals, <, >
Number - Structure and Calculation N2
Apply the four operations, including formal written methods, to integers, decimals and simple fractions (proper and improper), and mixed numbers - all both positive and negative; understand and use place value (eg when working with very large or very small numbers, and when calculating with decimals)
Number - Structure and Calculation N3
Recognise and use relationships between operations, including inverse operations (eg cancellation to simplify calculations and expressions); use conventional notation for priority of operations, including brackets, powers, roots and reciprocals
Number - Structure and Calculation N4
Use the concepts and vocabulary of prime numbers, factors (divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation and the unique factorisation theorem
Number - Structure and Calculation N5
Apply systematic listing strategies. (For Higher only - including the use of product rule for counting)
Number - Structure and Calculation N6
Use positive integer powers and associated real roots (square, cube and higher), recognise powers of 2, 3, 4, 5
Number - Structure and Calculation N6 (Higher Only)
Estimate powers and roots of any given positive number
Number - Structure and Calculation N7
Calculate with roots and with postive integer indices
Number - Structure and Calculation N7 (Higher Only)
Also negative and fractional
Number - Structure and Calculation N8
Calculate exactly with fractions, and multiples of pi
Number - Structure and Calculation N8 (Higher Only)
Also includes calculating exactly with surds, simplify surd expressions involving squares and rationalise denominators
Number - Structure and Calculation N9
Calculate with and interpret standard form A x 10^n, where 1 < A < 10 and n is an integer
Number - Fractions, Decimals and Percentages N10
Work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2, or 0.375 and 3/8).
Number - Fractions, Decimals and Percentages N10 (Higher Only)
Includes changing recurring decimals into their corresponding fractions and vice versa
Number - Fractions, Decimals and Percentages N11
Identify and work with fractions in ratio problems
Number - Fractions, Decimals and Percentages N12
Interpret fractions and percentages as operators
Number - Measures and Accuracy N13
Use standard units of mass, length, time, money and other measures (including standard compound measures) using decimal quantities where appropriate
Number - Measures and Accuracy N14
Estimate answers; check calculations using approximation and estimation, including answers obtained using technology
Number - Measures and Accuracy N15
Round numbers and measures to an appropriate degree of accuracy (eg to a specified number of decimal places or significant figures); use inequality notation to specify simple error intervals due to truncation or rounding
Number - Measures and Accuracy N16
Apply and interpret limits of accuracy (Higher - Including Upper and Lower Bounds)
Algebra - Notation, vocabulary and manipulation A1
Use and interpret algebraic notation, including
- ab in place of a x b
- 3y in place of y + y + y and 3 x y
- a^2 in place of a x a, a^3 in place of a x a x a, a^2b in place of a x a x b
- a/b in place of a ÷ b
- coefficients written as fractions rather than decimals
- brackets
Algebra - Notation, vocabulary and manipulation A2
Substitute numerical values into formulae and expressions, including scientific formulae
Algebra - Notation, vocabulary and manipulation A3
Understand and use the concepts and vocabulary of expressions, equations, formulae, identities, inequalities, terms and factors
Algebra - Notation, vocabulary and manipulation A4
Simplify and manipulate algebraic expressions (including those involving surds, and for higher - algebraic fractions) by:
- collecting like terms
- multiplying a single term over a bracket
- taking out common factors
- expanding products of two binomials
- factorising quadratic expressions of the form x2 + bx + c (higher: ax2 + bx + c), including the difference of two squares (higher - completing the square)
- simplifying expressions involving sums, products and powers, including the laws of indices.
Algebra - Notation, vocabulary and manipulation A5
Understand and use standard mathematical formulae; rearrange formulae to change the subject
Algebra - Notation, vocabulary and manipulation A5 (Higher Only)
Algebra - Notation, vocabulary and manipulation A6
Know the difference between an equation and an identity; argue mathematically to show algebraic expressions are equivalent, and use algebra to support and construct arguments
Algebra - Notation, vocabulary and manipulation A6 (Higher Only)
Includes Proof
Algebra - Notation, vocabulary and manipulation A7
Where appropriate, interpret simple expressions as functions with inputs and outputs
Algebra - Notation, vocabulary and manipulation A7 (Higher Only)
Also interpret the reverse process as the ‘inverse function’; interpret the succession of two functions as a ‘composite function’
Algebra - Graphs A8
Work with coordinates in all four quadrants
Algebra - Graphs A9
Plot graphs of equations that correspond to straight-line graphs in the coordinate plane; use the form y = mx + c to identify parallel lines (higher - includes perpendicular lines); find the equation of the line through two given points, or through one point with a given gradient
Algebra - Graphs A10
Identify and interpret gradients and intercepts of linear functions graphically and algebraically
Algebra - Graphs A11
Identify and interpret roots, intercepts, and turning points of quadratic functions graphically; deduce roots algebraically (higher - and turning points by completing the square)
Algebra - Graphs A11 (Higher Only)
And turning points by completing the square
Algebra - Graphs A12
Recognise, sketch and interpret graphs of linear functions, quadratic functions, simple cubic functions and the reciprocal function, y = 1/x
Algebra - Graphs A12 (Higher Only)
Also includes exponential functions y = k^x for positive values of k, and the trigonometrical functions (with arguments in degrees) y = sin x, y = cos x and y = tan x for angles of any size
Algebra - Graphs A13 (Higher Only)
Sketch translations and reflections of a given function
Algebra - Graphs A14
Plot and interpret graphs (including reciprocal graphs) and graphs of non-standard functions in real contexts, to find approximate solutions to problems such as simple kinematic problems involving distance, speed and acceleration
Algebra - Graphs A14 (Higher Only)
Plot and interpret graphs (including reciprocal graphs and exponential graphs) and graphs of non-standard functions in real contexts, to find approximate solutions to problems such as simple kinematic problems involving distance, speed and acceleration
Algebra - Graphs A15 (Higher Only)
Calculate or estimate gradients of graphs and areas under graphs (including quadratic and other non-linear graphs), and interpret results in cases such as distance-time graphs, velocity-time graphs and graphs in financial contexts
Algebra - Graphs A16 (Higher Only)
Recognise and use the equation of a circle with centre at the origin; find the equation of a tangent to a circle at a given point
Algebra - Solving Equations and Inequalities A17
Solve linear equations in one unknown algebraically (including those with the unknown on both sides of the equation); find approximate solutions using a graph
Algebra - Solving Equations and Inequalities A18
Solve quadratic equations algebraically by factorising; find approximate solutions using a graph
Algebra - Solving Equations and Inequalities A18 (Higher Only)
Solve quadratic equations (including those that require rearrangement) algebraically by factorising, by completing the square and by using the quadratic formula; find approximate solutions using a graph
Algebra - Solving Equations and Inequalities A19
Solve two simultaneous equations in two variables
(linear / linear or higher - linear / quadratic) algebraically; find approximate solutions using a graph
Algebra - Solving Equations and Inequalities A19 (Higher Only)
Linear / Quadratic
Algebra - Solving Equations and Inequalities A20 (Higher Only)
Find approximate solutions to equations numerically using iteration
Algebra - Solving Equations and Inequalities A21
Translate simple situations or procedures into algebraic expressions or formulae; derive an equation (or two simultaneous equations), solve the equation(s) and interpret the solution
Algebra - Solving Equations and Inequalities A22
Solve linear inequalities in one variable; represent the solution set on a number line
Algebra - Solving Equations and Inequalities A22 (Higher Only)
Solve linear inequalities in one or two variables and quadratic inequalities in one variable; represent the solution set on a number line, using set notation and on a graph
Algebra - Sequences A23
Generate terms of a sequence from either a term-to-term or a position-to-term rule
Algebra - Sequences A24
Recognise and use sequences of triangular, square and cube numbers, simple arithmetic progressions, Fibonacci-type sequences, quadratic sequences and simple geometrical progressions (r^n where n is an integer and r is a rational number > 0. Higher - r could be a surd)
Algebra - Sequences A25
Deduce expressions to calculate the nth term of linear sequences
Algebra - Sequences A25 (Higher Only)
Also quadratic sequences.
Ratio, Proportion and Rates of Change R1
Change freely between related standard units (eg time, length, area, volume / capacity, mass) and compound units (eg speed, rates of pay, prices, density, pressure) in numerical and algebraic contexts
Ratio, Proportion and Rates of Change R2
Use scale factors, scale diagrams and maps
Ratio, Proportion and Rates of Change R3
Express one quantity as a fraction of another, where the fraction is less than 1 or greater than 1
Ratio, Proportion and Rates of Change R4
Use ratio notation, including reduction to simplest form
Ratio, Proportion and Rates of Change R5
Divide a given quantity into two parts in a given part : part or part : whole ratio; express the division of a quantity into two parts as a ratio; apply ratio to real contexts and problems (such as those involving conversion, comparison, scaling, mixing, concentrations)
Ratio, Proportion and Rates of Change R6
Express a multiplicative relationship between two quantities as a ratio or a fraction
Ratio, Proportion and Rates of Change R7
Understand and use proportion as equality of ratiosNULL
Ratio, Proportion and Rates of Change R8
Relate ratios to fractions and to linear functions
Ratio, Proportion and Rates of Change R9
Define percentage as ‘number of parts per 100’; interpret percentages and percentage changes as a fraction or a decimal, and interpret these multiplicatively; express one quantity as a percentage of another; compare two quantities using percentages; work with percentages greater than 100%; solve problems involving percentage change, including percentage increase / decrease and original value problems, and simple interest including in financial mathematics
Ratio, Proportion and Rates of Change R10
Solve problems involving direct and inverse proportion, including graphical and algebraic representations
Ratio, Proportion and Rates of Change R11
Use compound units such as speed, rates of pay, unit pricing, density and pressure
Ratio, Proportion and Rates of Change R12
Compare lengths, areas and volumes using ratio notation; make links to similarity (including trigonometric ratios) and scale factors
Ratio, Proportion and Rates of Change R13
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 (Higher also need to be able to construct these proportion equations)
Ratio, Proportion and Rates of Change R14
Interpret the gradient of a straight line graph as a rate of change; recognise and interpret graphs that illustrate direct and inverse proportion
Ratio, Proportion and Rates of Change R15 (Higher Only)
Interpret the gradient at a point on a curve as the instantaneous rate of change; apply the concepts of average and instantaneous rate of change (gradients of chords and tangents) in numerical, algebraic and graphical contexts
Ratio, Proportion and Rates of Change R16
Set up, solve and interpret the answers in growth and decay problems, including compound interest
Geometry and Measures - Properties and Constructions G1
Use conventional terms and notations: points, lines, vertices, edges, planes, parallel lines, perpendicular lines, right angles, polygons, regular polygons and polygons with reflection and / or rotation symmetries; use the standard conventions for labelling and referring to the sides and angles of triangles; draw diagrams from written description
Geometry and Measures - Properties and Constructions G2
Use the standard ruler and compass constructions (perpendicular bisector of a line segment, constructing a perpendicular to a given line from / at a given point, bisecting a given angle); use these to construct given figures and solve loci problems; know that the perpendicular distance from a point to a line is the shortest distance to the line
Geometry and Measures - Properties and Constructions G3
Apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles; understand and use alternate and corresponding angles on parallel lines; derive and use the sum of angles in a triangle (eg to deduce and use the angle sum in any polygon, and to derive properties of regular polygons)
Geometry and Measures - Properties and Constructions G4
Derive and apply the properties and definitions of: special types of quadrilaterals, including square, rectangle, parallelogram, trapezium, kite and rhombus; and triangles and other plane figures using appropriate language
Geometry and Measures - Properties and Constructions G5
Use the basic congruence criteria for triangles (SSS, SAS, ASA, RHS)
Geometry and Measures - Properties and Constructions G6
Apply angle facts, triangle congruence, similarity and properties of quadrilaterals to conjecture and derive results about angles and sides, including Pythagoras’ theorem and the fact that the base angles of an isosceles triangle are equal, and use known results to obtain simple proofs
Geometry and Measures - Properties and Constructions G7
Identify, describe and construct congruent and similar shapes, including on coordinate axes, by considering rotation, reflection, translation and enlargement (including fractional scale factors, and for higher - negative scale factors)
Geometry and Measures - Properties and Constructions G8 (Higher Only)
Describe the changes and invariance achieved by combinations of rotations, reflections and translations
Geometry and Measures - Properties and Constructions G9
Identify and apply circle definitions and properties, including: centre, radius, chord, diameter, circumference, tangent, arc, sector and segment
Geometry and Measures - Properties and Constructions G10 (Higher Only)
Apply and prove the standard circle theorems concerning angles, radii, tangents and chords, and use them to prove related results
Geometry and Measures - Properties and Constructions G11
Solve geometrical problems on coordinate axes
Geometry and Measures - Properties and Constructions G12
Identify properties of the faces, surfaces, edges and vertices of: cubes, cuboids, prisms, cylinders, pyramids, cones and spheres
Geometry and Measures - Properties and Constructions G13
Construct and interpret plans and elevations of 3D shapes
Geometry and Measures - Properties and Constructions G14
Use standard units of measure and related concepts (length, area, volume / capacity, mass, time, money etc)
Geometry and Measures - Properties and Constructions G15
Measure line segments and angles in geometric figures, including interpreting maps and scale drawings and use of bearings
Geometry and Measures - Properties and Constructions G16
Know and apply formulae to calculate: area of triangles, parallelograms, trapezia; volumes of cuboids and other right prisms (including cylinders)
Geometry and Measures - Properties and Constructions G17
Know the formulae: circumference of a circle = 2pr = pd, area of a circle = pr2; calculate: perimeters of 2D shapes, including circles; areas of circles and composite shapes; surface area and volume of spheres, pyramids, cones and composite solids
Geometry and Measures - Properties and Constructions G18
Calculate arc lengths, angles and areas of sectors of circles
Geometry and Measures - Properties and Constructions G19
Apply the concepts of congruence and similarity, including the relationships between lengths in similar figures
Geometry and Measures - Properties and Constructions G19 (Higher Only)
Apply the concepts of congruence and similarity, including the relationships between lengths, areas and volumes in similar figures
Geometry and Measures - Properties and Constructions G20
Know the formulae for: Pythagoras’ theorem, a2 + b2 = c2, and the trigonometric ratios, sin, cos and tan, and apply them to find angles and lengths in right-angled triangles in two dimensional figures (Higher - includes 3D)
Geometry and Measures - Properties and Constructions G21
Know the exact values of sin(x) and cos(x) for x= 0°, 30°, 45°, 60° and 90°; know the exact value of tan(x) for x = 0°, 30°, 45° and 60°
Geometry and Measures - Properties and Constructions G22 (Higher Only)
Know and apply the sine rule, and cosine rule, a2 = b2 + c2 - 2bc cos A, to find unknown lengths and angles
Geometry and Measures - Properties and Constructions G23 (Higher Only)
Know and apply Area = 1/2 ab sin C to calculate the area, sides or angles of any triangle
Geometry and Measures - Properties and Constructions G24
Describe translations as 2D vectors
Geometry and Measures - Properties and Constructions G25
Apply addition and subtraction of vectors, multiplication of vectors by a scalar, and diagrammatic and column representations of vectors
Geometry and Measures - Properties and Constructions G25 (Higher Only)
And use vectors to construct geometric arguments and proofs
Probability P1
Record, describe and analyse the frequency of outcomes of probability experiments using tables and frequency trees
Probability P2
Apply ideas of randomness, fairness and equally likely events to calculate expected outcomes of multiple future experiments
Probability P3
Relate relative expected frequencies to theoretical probability, using appropriate language and the 0 - 1 probability scale
Probability P4
Apply the property that the probabilities of an exhaustive set of outcomes sum to 1; apply the property that the probabilities of an exhaustive set of mutually exclusive events sum to 1
Probability P5
Understand that empirical unbiased samples tend towards theoretical probability distributions, with increasing sample size
Probability P6
Enumerate sets and combinations of sets systematically, using tables, grids, Venn diagrams and tree diagrams
Probability P7
Construct theoretical possibility spaces for single and combined experiments with equally likely outcomes and use these to calculate theoretical probabilities
Probability P8
Calculate the probability of independent and dependent combined events, including using tree diagrams and other representations, and know the underlying assumptions
Probability P9 (Higher Only)
Calculate and interpret conditional probabilities through representation using expected frequencies with two-way tables, tree diagrams and Venn diagrams
Statistics S1
Infer properties of populations or distributions from a sample, whilst knowing the limitations of sampling
Statistics S2
Interpret and construct tables, charts and diagrams, including frequency tables, bar charts, pie charts and pictograms for categorical data, vertical line charts for ungrouped discrete numerical data, tables and line graphs for time series data and know their appropriate use
Statistics S3 (Higher Only)
Construct and interpret diagrams for grouped discrete and continuous data, ie histograms with equal and unequal class intervals and cumulative frequency graphs, and know their appropriate use
Statistics S4
Interpret, analyse and compare the distributions of data sets from univariate empirical distributions through:
(a) appropriate graphical representation involving discrete, continuous and grouped data (higher - includes box plots) (b)
appropriate measures of central tendency (median, mean, mode and modal class) and spread (range, including consideration of outliers, higher includes quartiles and inter-quartile range)
Statistics S5
Apply statistics to describe a population
Statistics S6
Use and interpret scatter graphs of bivariate data; recognise correlation and know that it does not indicate causation; draw estimated lines of best fit; make predictions; interpolate and extrapolate apparent trends whilst knowing the dangers of so doing
