# Essential Mathematics for Cambridge Secondary 1: Stage 8

The Essential Mathematics for Cambridge Secondary 1 series has been created for the international student. Written by an expert author team with an experienced examiner, it provides complete coverage of the previous Cambridge syllabus. The Student Book provides engaging exercises that promote problem solving and investigative strategies. Inclusion of summary and review sections after each topic help students retain learning, while Checkpoint-style questions assist

their preparation for assessment. Learning Outcomes are provided at the start of each chapter to clearly map topics in the text to the previous syllabus. Numerous exercises are included, with clear progression, and problem-solving and real life applications embedded throughout. Helpful hints throughout

the text guide students and remind them of the key pieces of information required.

- Front Cover
- Title Page
- Contents
- Introduction
- 1 Integers, powers and roots
- 1.1 Working with integers
- 1.2 Division and mental strategies
- 1.3 Order of operations
- 1.4 Powers
- 1.5 Roots
- 1.6 Prime factors
- 1.7 Highest common factors and lowest common multiples

- 2 Expressions
- 2.1 Using letters for unknown numbers
- 2.2 Multiplying algebraic terms
- 2.3 Collecting like terms
- 2.4 Expanding brackets
- 2.5 Substitution into an expression

- 3 Shapes and geometric reasoning 1
- 3.1 Parallel lines
- 3.2 Angles and triangles
- 3.3 Congruent shapes
- 3.4 Quadrilaterals
- 3.5 Classification of quadrilaterals
- 3.6 Nets of solids
- 3.7 Symmetry

- 4 Fractions
- 4.1 Comparing fractions
- 4.2 Addition and subtraction of fractions and mixed numbers
- 4.3 Multiplying and dividing an integer by a fraction

- 5 Decimals
- 5.1 Integer powers of 10
- 5.2 Rounding
- 5.3 Calculating with decimals
- 5.4 Fractions and decimals

- 6 Processing, interpreting and discussing data
- 6.1 Calculating statistics from data sets
- 6.2 Calculating statistics from grouped data
- 6.3 Making comparisons

- 7 Length, mass and capacity
- 7.1 The metric system
- 7.2 Area and volume
- 7.3 Non-metric units

- 8 Equations
- 8.1 Solving equations using flow diagrams
- 8.2 Solving equations with the unknown on one side
- 8.3 Solving equations with the unknown on both sides

- 9 Shapes and geometric reasoning 2
- 9.1 Constructions
- 9.2 Triangles
- 9.3 Circles
- 9.4 Scale drawings

- 10 Presenting, interpreting and discussing data
- 10.1 Frequency diagrams for grouped data
- 10.2 Pie charts
- 10.3 Line graphs
- 10.4 Stem-and-leaf diagrams

- 11 Area, perimeter and volume
- 11.1 Circles
- 11.2 Area of a parallelogram
- 11.3 Area of a triangle
- 11.4 Area of a trapezium
- 11.5 Area of a circle
- 11.6 Compound areas

- 12 Formulae
- 12.1 Deriving formulae
- 12.2 Substitution into formulae
- 12.3 Further substitution into formulae

- 13 Position and movement
- 13.1 Transformations
- 13.2 Enlargement
- 13.3 Midpoints

- 14 Sequences
- 14.1 Linear sequences of numbers
- 14.2 Linear sequences from patterns of shapes
- 14.3 The nth term of a linear sequence of numbers

- 15 Probability
- 15.1 Calculating probabilities
- 15.2 Listing outcomes
- 15.3 Estimating probabilities

- 16 Functions and graphs
- 16.1 Mapping diagrams
- 16.2 Functions
- 16.3 Linear graphs
- 16.4 Finding the equation of a line from its graph
- 16.5 Equations of the form y = mx + c

- 17 Fractions, decimals and percentages
- 17.1 Finding equivalent fractions, decimals and percentages
- 17.2 Increasing and decreasing by a percentage
- 17.3 Finding percentages

- 18 Planning and collecting data
- 18.1 Identifying and collecting data
- 18.2 Frequency tables for continuous data
- 18.3 Two-way tables

- 19 Ratio and proportion
- 19.1 More ratio
- 19.2 Dividing in a given ratio
- 19.3 Direct proportion – the unitary method

- 20 Time and rates of change
- 20.1 Travel graphs
- 20.2 Other graphs

- 21 Sets
- 21.1 Set notation
- 21.2 Further set notation
- 21.3 Using sets to solve problems

- 22 Matrices
- 22.1 Multiplying a row matrix by a column matrix
- 22.2 Multiplying matrices
- 22.3 2 × 2 matrices

- Glossary
- Index
- Back Cover