Brain & Mind Academy · Sopaan Practice Series

International GCSE Mathematics A

Learning sheets for all 33 chapters, mixing Collins International GCSE Maths for Edexcel (Book 1) with Pearson Edexcel International GCSE (9–1) Mathematics A Student Book 2 by topic. Each learning objective has a learning sheet, Collins practice, Pearson practice where Book 2 covers it, and a 30-minute test.

33 chapters159 learning objectives4,475 questions

Number Chapters 1–10

Chapter 1

Number

Multiples and factors · Primes, squares and cubes · Products of prime numbers · HCF and LCM

4 LOs97 questionsDusty blue
Chapter 2Book 1 + Book 2

Fractions and percentages

Equivalent fractions and mixed numbers · Fractions, decimals, percentages and recurring decimals · Percentages in real life · Reverse percentages · Interest, depreciation and repeated change

5 LOs159 questionsLavender
Chapter 3

The four rules

Order of operations (BIDMAS) · Choosing the correct operation · Fraction of a quantity · Adding and subtracting fractions · Multiplying and dividing fractions

5 LOs122 questionsTeal
Chapter 4

Directed numbers

Directed numbers and the number line · Adding and subtracting directed numbers · Multiplying and dividing directed numbers

3 LOs83 questionsOchre
Chapter 5Book 1 + Book 2

Squares, cubes and roots

Squares and square roots · Cubes and cube roots · Rational and irrational numbers; simplifying surds · Expanding brackets with surds · Rationalising the denominator

5 LOs144 questionsSage
Chapter 6Book 1 + Book 2

Set language and notation

Inequalities · Sets and set notation · Venn diagrams, complements and shading · n(A), subsets and practical problems

4 LOs134 questionsSlate
Chapter 7Book 1 + Book 2

Ratio, proportion and speed

Ratio and simplest form · Sharing in a ratio and map scales · Speed · Density and pressure · Direct proportion

5 LOs138 questionsPlum
Chapter 8Book 1 + Book 2

Approximation and limits of accuracy

Rounding whole numbers · Rounding decimals · Significant figures and calculator work · Estimating calculations · Upper and lower bounds · Bounds in calculations

6 LOs158 questionsOcean
Chapter 9Book 1 + Book 2

Standard form

Writing numbers in standard form · Calculating with standard form · Solving problems with standard form

3 LOs83 questionsOlive
Chapter 10Book 1 + Book 2

Applying number and using calculators

Metric units: length, mass and capacity · Converting area and volume units · Reading scales · Time and timetables · Currency conversions · Using a calculator efficiently

6 LOs152 questionsRose clay

Algebra Chapters 11–22

Chapter 11Book 1 + Book 2

Algebra and formulae

The language of algebra · Substitution into formulae · Rearranging formulae · More complicated formulae

4 LOs96 questionsMoss
Chapter 12Book 1 + Book 2

Algebraic manipulation

Simplifying expressions · Single brackets and common factors · Expanding two or more brackets · Factorising quadratics · Algebraic fractions · Algebraic proof

6 LOs158 questionsTerracotta
Chapter 13Book 1 + Book 2

Solutions of equations

Linear equations · Setting up equations and equations with fractions · Quadratic equations by factorisation · Completing the square and the quadratic formula · Linear simultaneous equations · Linear and non-linear simultaneous equations

6 LOs162 questionsDusty blue
Chapter 15

Straight line graphs

Coordinates and midpoints · Drawing straight line graphs · Gradient · y = mx + c and finding equations · Parallel and perpendicular lines · Graphs and simultaneous equations

6 LOs133 questionsTeal
Chapter 16Book 1 + Book 2

Graphs of functions

Quadratic graphs · Solving equations with graphs · Cubic and reciprocal graphs · Gradients of curves · Graphs of sin x, cos x and tan x · Transformations of graphs

6 LOs176 questionsOchre
Chapter 17Book 1 + Book 2

Integer sequences

Continuing sequences · The nth term formula · nth term of an arithmetic sequence · Sum of an arithmetic sequence

4 LOs121 questionsSage
Chapter 18Book 1 + Book 2

Indices

Index notation, power 0 and power 1 · Negative indices · Laws of indices · Fractional indices: roots · Negative fractional indices and index equations

5 LOs157 questionsSlate
Chapter 19Book 1 + Book 2

Direct and inverse proportion

Direct proportion · Proportion with squares, cubes and roots · Inverse proportion · Proportion graphs and tables

4 LOs135 questionsPlum
Chapter 20Book 1 + Book 2

Inequalities and regions

Solving linear inequalities · Inequalities on a number line · Quadratic inequalities · Regions on a graph · More complex regions

5 LOs132 questionsOcean
Chapter 21Book 1 + Book 2

Functions

Function notation · Domain and range · Inverse functions · Composite functions

4 LOs136 questionsOlive
Chapter 22Book 1 + Book 2

Calculus

Gradient of a curve · Differentiating powers of x · Tangents and rates of change · Turning points · Motion of a particle

5 LOs157 questionsRose clay

Geometry and trigonometry Chapters 23–30

Chapter 23Book 1 + Book 2

Angle properties

Angle facts and parallel lines · Triangles and quadrilaterals · Regular and irregular polygons · Tangents and angles in circles · Cyclic quadrilaterals and the alternate segment theorem · Chords and intersecting chords

6 LOs179 questionsMoss
Chapter 24Book 1 + Book 2

Geometrical terms and relationships

Angles and bearings · Congruent and similar shapes · Areas of similar shapes · Volumes of similar shapes

4 LOs135 questionsTerracotta
Chapter 25

Geometrical constructions

Constructing triangles and shapes · Perpendicular and angle bisectors · Scale drawings

3 LOs75 questionsDusty blue
Chapter 26Book 1 + Book 2

Trigonometry

Pythagoras' theorem · Sine, cosine and tangent · Problems, bearings, elevation and depression · Trigonometry in 3D · Obtuse angles and trig graphs · Sine rule, cosine rule and area

6 LOs179 questionsLavender
Chapter 27Book 1 + Book 2

Mensuration

Area and perimeter of 2-D shapes · Circles, semicircles and quadrants · Arcs and sectors · Cuboids and prisms · Cylinders · Pyramids, cones and spheres

6 LOs183 questionsTeal
Chapter 28

Symmetry

Lines of symmetry · Rotational symmetry · Symmetry of special shapes

3 LOs70 questionsOchre
Chapter 29Book 1 + Book 2

Vectors

Vectors and column vectors · Adding, subtracting and scalar multiples · Vectors in terms of a and b · Vector geometry and proof · The magnitude of a vector

5 LOs157 questionsSage
Chapter 30

Transformations

Translations · Reflections in horizontal and vertical lines · Reflections in y = x and y = −x · Rotations · Enlargements

5 LOs118 questionsSlate

Statistics and probability Chapters 31–33

Chapter 31Book 1 + Book 2

Statistical representation

Frequency tables and pictograms · Bar charts · Pie charts · Drawing histograms · Interpreting histograms

5 LOs127 questionsPlum
Chapter 32

Statistical measures

Mode and median · Mean and range · Which average to use · Averages from frequency tables · Grouped data · Quartiles and cumulative frequency

6 LOs147 questionsOcean
Chapter 33Book 1 + Book 2

Probability

Probability scale and P(not A) · Addition rule, data and expected frequency · Venn diagrams and conditional probability · Combined events and sample spaces · Tree diagrams: independent events · Dependent events and conditional probability

6 LOs203 questionsOlive