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Glossary
Chapter 1: Number systems and the four operations
- Overview
- 1.1 The number systems ℕ, ℤ and ℚ
- 1.2 Adding and subtracting integers
- 1.3 Multiplying and dividing integers
- 1.4 The order of operations and brackets
- 1.5 Commutative, associative and distributive properties
- 1.6 Surds and irrational numbers
- Review
Chapter 2: Powers and index laws
- Overview
- 2.1 Index form and powers
- 2.2 The laws of indices
- 2.3 Zero and negative indices
- 2.4 Fractional indices and roots
- Review
Chapter 3: Factors, multiples and primes
- Overview
- 3.1 Factors, multiples and divisibility
- 3.2 Prime numbers and prime factorisation
- 3.3 The highest common factor and the lowest common multiple
- Review
Chapter 4: Accuracy and standard form
- Overview
- 4.1 Rounding and significant figures
- 4.2 Estimating and checking a result
- 4.3 Standard form
- Review
Chapter 5: Fractions, decimals and percentages
- Overview
- 5.1 Equivalent fractions and ordering
- 5.2 Adding and subtracting fractions
- 5.3 Multiplying and dividing fractions
- 5.4 Fractions, decimals and percentages
- 5.5 Percentage increase and decrease
- Review
Chapter 6: Ratio, proportion and rates
- Overview
- 6.1 Ratio notation and simplifying
- 6.2 Dividing a quantity in a given ratio
- 6.3 Direct proportion
- 6.4 Inverse proportion
- 6.5 Absolute and relative comparison
- 6.6 Speed, distance and time
- Review
Chapter 7: Money and financial mathematics
- Overview
- 7.1 Profit, loss and percentage profit
- 7.2 Mark-up and margin
- 7.3 VAT and bills
- 7.4 Income tax and net pay
- 7.5 Simple and compound interest
- 7.6 Value for money and comparing offers
- 7.7 Currency conversion
- Review
Chapter 8: Sets
- Overview
- 8.1 Sets and set notation
- 8.2 Subsets, the universal set and the null set
- 8.3 Intersection, union and set difference
- 8.4 Venn diagrams with two and three sets
- 8.5 Order of operations on sets
- 8.6 Commutative and associative set operations
- Review
Chapter 9: Patterns and sequences
- Overview
- 9.1 Repeating patterns and tables
- 9.2 The general term of a linear pattern
- 9.3 Quadratic patterns and their general term
- 9.4 Linear, quadratic and exponential growth
- 9.5 Converting between representations
- Review
Chapter 10: Expressions and substitution
- Overview
- 10.1 Generating and interpreting expressions
- 10.2 Substituting values into expressions
- 10.3 Equality and the meaning of an equation
- Review
Chapter 11: Expanding, factorising and simplifying
- Overview
- 11.1 Adding and subtracting algebraic expressions
- 11.2 Multiplying out a single bracket
- 11.3 Multiplying two brackets
- 11.4 Common factors and factorising
- 11.5 Factorising quadratic expressions
- 11.6 The difference of two squares
- 11.7 Dividing a cubic or quadratic by a linear expression
- Review
Chapter 12: Equations and inequalities
- Overview
- 12.1 Solving linear equations
- 12.2 Equations with brackets and fractions
- 12.3 Simultaneous equations by substitution
- 12.4 Simultaneous equations by elimination
- 12.5 Linear inequalities
- 12.6 Graphing the solution set of an inequality
- 12.7 Choosing a method: graphic, numeric or algebraic
- Review
Chapter 13: Formulae
- Overview
- 13.1 Using formulae
- 13.2 Changing the subject of a formula
- 13.3 Formulae with brackets and fractions
- Review
Chapter 14: Functions and graphs
- Overview
- 14.1 The idea of a function
- 14.2 Function notation and evaluating functions
- 14.3 Graphing linear functions
- 14.4 Graphing quadratic functions
- 14.5 Interpreting graphs in context
- Review
Chapter 15: Units of measure and time
- Overview
- 15.1 Units of length, mass and capacity
- 15.2 Converting between units
- 15.3 Time, timetables and time zones
- 15.4 Choosing sensible units and estimating
- Review
Chapter 16: Perimeter, area and volume
- Overview
- 16.1 Perimeter and area of rectangles and triangles
- 16.2 The circumference and area of a circle
- 16.3 Areas of composite figures
- 16.4 Nets of solids
- 16.5 Volume of prisms, cylinders and spheres
- 16.6 Surface area and curved surface area
- 16.7 Volume and surface area of composite solids
- Review
Chapter 17: Coordinate geometry
- Overview
- 17.1 The coordinate plane and plotting points
- 17.2 Distance and midpoint
- 17.3 Slope of a line
- 17.4 Parallel and perpendicular lines
- 17.5 The equation of a line
- 17.6 The general form ax + by + c = 0
- 17.7 Graphs in context and rate of change
- Review
Chapter 18: Pythagoras and trigonometry
- Overview
- 18.1 Pythagoras' theorem
- 18.2 Finding a missing side
- 18.3 The trigonometric ratios
- 18.4 Finding a missing side using a ratio
- 18.5 Finding a missing angle
- 18.6 Angles of elevation and depression
- 18.7 Choosing Pythagoras or trigonometry
- Review
Chapter 19: Transformations and symmetry
- Overview
- 19.1 Translation
- 19.2 Axial symmetry and reflection
- 19.3 Central symmetry
- 19.4 Rotation
- 19.5 Axes of symmetry
- 19.6 Combining transformations
- Review
Chapter 20: Synthetic geometry, constructions and proof
- Overview
- 20.1 Axioms, theorems, corollaries and converses
- 20.2 The constructions
- 20.3 Angles and parallel lines
- 20.4 Congruent triangles
- 20.5 The isosceles triangle and its converse
- 20.6 Parallelograms and their corollaries
- 20.7 Similar triangles and proportionality
- 20.8 The theorem of Pythagoras as a theorem
- 20.9 Circles and their theorems
- 20.10 Constructing a proof
- 20.11 Evaluating someone else's proof
- Review
Chapter 21: Probability
- Overview
- 21.1 Listing outcomes and the sample space
- 21.2 Probability as a number from 0 to 1
- 21.3 Equally likely outcomes
- 21.4 The complement of an event
- 21.5 Two events and the addition rule
- 21.6 Independent events and the multiplication rule
- 21.7 Probability from a table or a diagram
- 21.8 Expected frequency
- Review
Chapter 22: Statistics
- Overview
- 22.1 Populations, samples and surveys
- 22.2 Choosing a sample and avoiding bias
- 22.3 Tallying and frequency tables
- 22.4 Bar charts, line plots and histograms
- 22.5 Measures of centre: mean, median and mode
- 22.6 Measures of spread: range and interquartile range
- 22.7 Scatter graphs and correlation
- 22.8 Interpreting data and questioning a claim
- 22.9 Misleading graphs and how to spot them
- Review
About this book

Chapter 18: Pythagoras and trigonometry

Pythagoras' theorem, the trigonometric ratios, and solving right-angled triangles.

The chapter problem

How tall is the school building?. You cannot climb it, so you will measure it from the ground — using an angle and a distance. By the end of the chapter you can choose between Pythagoras and a ratio, and say why you chose it.

Where it is used: Surveying, construction, navigation, and any height or distance you cannot reach.

Your turn to connect it: Where would being able to work out an unmeasurable distance be useful?

Sections

18.1 Pythagoras' theorem — tier O · refs GT.4
18.2 Finding a missing side — tier O · refs GT.4
18.3 The trigonometric ratios — tier O · refs GT.4
18.4 Finding a missing side using a ratio — tier O · refs GT.4
18.5 Finding a missing angle — tier O · refs GT.4
18.6 Angles of elevation and depression — tier O · refs GT.4
18.7 Choosing Pythagoras or trigonometry — tier O · refs GT.4