Cambridge Lower Secondary · Mathematics 0862 · Stage 8
Checkpoint 8 Maths — Complete Course
The whole Cambridge Lower Secondary Stage 8 Mathematics curriculum — number, algebra, geometry and measure, statistics and probability — with worked examples, diagrams, an interactive quiz on every page and full Checkpoint-style end-of-year practice tests with printable PDFs and mark schemes.
Number
- Order of Operations and Calculating with IntegersWork out calculations with brackets, powers and roots in the correct order, and estimate, multiply and divide positive and negative integers.
- Factors, Multiples, Primes, HCF and LCMFind factors and multiples, test for primes, write numbers as products of prime factors, and use them to find the HCF and LCM in problems.
- Types of Number and Index LawsClassify numbers as natural numbers, integers or rational numbers, and use positive and zero indices with the index laws for multiplication and division.
- Squares, Cubes and Roots (Positive and Negative)Square and cube positive and negative numbers, find both square roots of a number and the single cube root, estimate roots, and use powers and roots in longer calculations.
- Multiplying and Dividing by 0.1 and 0.01, and Significant FiguresUse place value to multiply and divide by 0.1 and 0.01, round any number to a given number of significant figures, and estimate answers by rounding to 1 significant figure.
- Fractions: Recurring Decimals, Mixed Numbers and Order of OperationsRecognise recurring decimals, subtract mixed numbers, multiply a whole number by a mixed number, divide a whole number by a fraction, and use the laws of arithmetic with fractions and decimals.
- Percentage Increase, Decrease and Absolute ChangeIncrease and decrease amounts by a percentage with and without a calculator, use multipliers, and find and compare absolute and percentage changes.
- Ordering and Calculating with DecimalsCompare and order positive and negative decimals and fractions with =, ≠, >, <, ≤ and ≥, then estimate and multiply decimals by decimals and divide by numbers with one decimal place.
- Ratio and ProportionSimplify and compare ratios (including different units), share amounts in ratios with two or more parts, and use the link between ratio and direct proportion to solve real problems.
Algebra
- Algebraic Expressions: Simplifying, Expanding and FactorisingWhat letters mean in expressions, formulae and equations; simplifying with the laws of arithmetic (including squares and cubes); expanding a single bracket and factorising by taking out the highest common factor.
- Writing Expressions and Formulae, and Changing the SubjectTranslate between words and algebraic expressions or formulae (including fractional coefficients), and use inverse operations to change the subject of a formula.
- Equations and InequalitiesTurn word problems into equations, solve equations with brackets, fractions and the unknown on both sides, and use inequalities and number lines to show open and closed intervals.
- Sequences and the nth TermUse term-to-term rules with whole numbers, negatives and fractions, build sequences from shape patterns, and find and use the nth term an + b of a linear sequence.
- Functions and Straight-line Graphs (y = mx + c)Use function machines and inverse operations, write real situations as y = mx + c, plot straight-line graphs from tables of values, and read the gradient and y-intercept.
- Reading and Interpreting Real-life GraphsRead and interpret real-life graphs with several sections or two lines — journeys, costs, filling containers — explain their shape and say what an intersection means.
Geometry and measure
- Quadrilaterals and Regular PolygonsLearn the properties of every special quadrilateral, how they fit into a hierarchy, and why a regular polygon with n sides has n lines of symmetry and rotational symmetry of order n.
- Circumference of a Circle, and Miles and KilometresDiscover π as circumference ÷ diameter, use C = πd and C = 2πr (forwards and backwards), and convert between miles and kilometres with 1 mile ≈ 1.6 km and 1 km ≈ 5/8 mile.
- Area of Parallelograms and TrapeziaSee where the formulae A = bh and A = ½(a + b)h come from, then use them to find areas, missing heights and missing sides in Checkpoint-style problems.
- 3D Shapes: Euler's Formula and Plans and ElevationsCount faces, vertices and edges, use Euler's formula F + V − E = 2 to find missing values or spot impossible shapes, and draw plans and elevations of 3D shapes to scale.
- Volume of Prisms and Surface AreaDerive and use the formula for the volume of a triangular prism, and calculate the surface area of cubes, cuboids, triangular prisms and pyramids.
- Angles in Triangles and on Parallel LinesProve and use the exterior-angle fact for triangles, and find angles on intersecting and parallel lines using vertically opposite, corresponding and alternate angles — with reasons.
- Constructions with Ruler and CompassesConstruct triangles from sides and angles, and use a ruler and compasses to construct the midpoint and perpendicular bisector of a line and the bisector of an angle.
- Bearings and MidpointsRead, measure, draw and calculate three-figure bearings (including back bearings), and use coordinates to find the midpoint of a line segment.
- Translation, Reflection, Rotation and EnlargementTranslate with column vectors, reflect in lines such as x = 2, y = x and y = −x, rotate with a centre, angle and direction, and enlarge from a centre with a scale factor — and describe each transformation fully, with worked examples and a practice quiz.
Statistics and probability
- Data Collection and SamplingPlan a statistical investigation: write related questions and predictions, decide whether data are categorical, discrete or continuous, write and trial good questionnaires, and choose and justify random, systematic, stratified or convenience samples.
- Representing DataOrganise and show data with Venn and Carroll diagrams, two-way tables, dual and compound bar charts, pie charts, frequency diagrams, time series, scatter graphs, stem-and-leaf diagrams and infographics — and choose the right one and explain why.
- Averages, Range and Comparing DistributionsFind the mode, median, mean and range from lists and frequency tables, choose the best average, compare two distributions using centre and spread, and write sensible conclusions about predictions and sampling variation.
- Probability: Complementary and Combined EventsUse P(not A) = 1 − P(A), list all outcomes of two events with lists, tree diagrams and sample-space tables, find theoretical probabilities of combined events, and compare experiments and simulations with theory.
Practice tests
End-of-Stage-8 tests in Checkpoint style: Paper 1 (no calculator) and Paper 2 (calculator), 1 hour and 50 marks each.
- Stage 8 Maths — Practice Test 1A full end-of-Stage-8 maths test in Checkpoint style: Paper 1 (no calculator) and Paper 2 (calculator), 1 hour and 50 marks each, with full worked solutions and a mark scheme.
- Stage 8 Maths — Practice Test 2A full end-of-Stage-8 maths test in Checkpoint style: two 1-hour papers of 50 marks (Paper 1 no calculator, Paper 2 calculator) set around a family holiday in Alexandria, a garden design, a school canteen survey, taxi fares, a cycling race and tiling patterns — with full worked solutions and a mark scheme.
- Stage 8 Maths — Practice Test 3A full end-of-Stage-8 practice test in Checkpoint style: Paper 1 (no calculator) and Paper 2 (calculator), 1 hour and 50 marks each, with worked solutions and a mark scheme.