# Essential Mathematics for Cambridge Secondary 1: Stage 9

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 latest Cambridge syllabus. The Stage 9 Student Book contains comprehensive coverage of the curriculum framework content, while also covering some of the topics included at Cambridge IGCSE. Summary and review sections after each topic help students retain learning,

while Checkpoint-style questions assist their preparation for assessment. The text provides extensive differentiation support with 'Hints' in the margins to guide middle to lower ability students through the more challenging aspects of the problem-solving and extension questions.

- Front Cover
- Title Page
- Contents
- Introduction
- 1 Integers, powers and roots
- 1.1 Review of directed numbers
- 1.2 Square and cube roots
- 1.3 Powers and indices
- 1.4 Negative indices
- 1.5 Order of operations

- 2 Expressions
- 2.1 Multiplying and dividing algebraic expressions
- 2.2 The index laws
- 2.3 Factorising
- 2.4 Adding and subtracting algebraic fractions
- 2.5 Substitution into expressions
- 2.6 Expanding double brackets
- 2.7 Constructing expressions

- 3 Shapes and geometric reasoning 1
- 3.1 Polygons
- 3.2 More polygons
- 3.3 Angles and lines

- 4 Fractions
- 4.1 Addition and subtraction
- 4.2 Multiplying fractions
- 4.3 Dividing fractions

- 5 Decimals
- 5.1 Integer powers of 10
- 5.2 Dividing by a decimal
- 5.3 Multiplying with decimals
- 5.4 Rounding

- 6 Processing, interpreting and discussing data
- 6.1 Finding average values for large data sets
- 6.2 Selecting the most appropriate average

- 7 Length, mass and capacity
- 7.1 Converting metric units
- 7.2 Converting imperial units

- 8 Equations and inequalities
- 8.1 Solving linear equations
- 8.2 Representing inequalities on a number line
- 8.3 Solving linear inequalities
- 8.4 Trial and improvement
- 8.5 Simultaneous equations

- 9 Shapes and geometric reasoning 2
- 9.1 Three dimensions
- 9.2 Reflection symmetry in three dimensions
- 9.3 Construction of lines
- 9.4 Construction of polygons
- 9.5 Maps and bearings

- 10 Presenting, interpreting and discussing data
- 10.1 Scatter diagrams and correlation
- 10.2 Back to back stem-and-leaf diagrams
- 10.3 Comparing distributions

- 11 Area, perimeter and volume
- 11.1 Area
- 11.2 Volume
- 11.3 Circles
- 11.4 Prisms and cylinders

- 12 Formulae
- 12.1 Deriving formulae and substituting numbers into formulae
- 12.2 Changing the subject of a formula
- 12.3 Formulae involving negative x terms
- 12.4 Formulae involving fractions
- 12.5 Formulae involving squares and square roots

- 13 Position and movement
- 13.1 Tessellation
- 13.2 Loci
- 13.3 Describing transformations
- 13.4 Enlargements

- 14 Sequences
- 14.1 Using the term-to-term rule
- 14.2 Using the position-to-term rule
- 14.3 The nth term of an arithmetic sequence

- 15 Probability
- 15.1 Mutually exclusive outcomes
- 15.2 Sample space diagrams
- 15.3 Experimental probability

- 16 Functions and graphs
- 16.1 Gradients
- 16.2 Straight-line graphs of the form ax 1 by 5 c
- 16.3 Using graphs to solve simultaneous equations
- 16.4 The general equation of a straight line
- 16.5 Finding the inverse of a function
- 16.6 Functions arising from real-life problems
- 16.7 Direct proportion

- 17 Fractions, decimals and percentages
- 17.1 Percentage change
- 17.2 More calculating with percentages

- 18 Planning and collecting data
- 18.1 Planning
- 18.2 Data collection sheets

- 19 Ratio and proportion
- 19.1 Ratio review
- 19.2 Comparing ratios
- 19.3 Proportionality

- 20 Time and rates of change
- 20.1 Average speed
- 20.2 Compound measures

- 21 Pythagoras’ theorem
- 21.1 Pythagoras’ theorem
- 21.2 Applications of Pythagoras’ theorem

- 22 Trigonometry
- 22.1 Naming the sides in a right-angled triangle
- 22.2 Finding a side using the tangent ratio
- 22.3 Finding an angle using the tangent ratio
- 22.4 Finding a side using sine, cosine or tangent
- 22.5 Finding an angle using sine, cosine or tangent

- 23 Matrices andtransformations
- 23.1 Multiplying matrices
- 23.2 Transforming a shape by a matrix
- 23.3 Combined transformations

- Glossary
- Index
- Back Cover