STP Caribbean Mathematics Book 3
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Description
Contents
Reviews
Language
English
ISBN
9780198426608
Contents
Introduction
1 Making sure of arithmetic
Prime numbers
Factors
Prime factors
Multiples
Sieve of Eratosthenes
Squares
Multiplying a string of numbers
Names for numbers
Addition and subtraction of fractions
Multiplication of fractions
Reciprocals
Division by a fraction
Decimal fractions
Interchanging decimals and fractions
Recurring decimals
Addition and subtraction of decimals
Multiplication of decimals
Division by decimals
Relative sizes
Indices
Laws of indices
Zero and negative indices
Standard form (scientific notation)
Approximations (decimal places and significant figures)
Base 2 and base 3 numbers
Mixed exercises
2 Areas
Areas of familiar shapes
Areas of compound shapes
Area of a trapezium
Shapes that have equal areas
3 Arc length and area of the sector of a circle
The length of an arc
The area of a sector of a circle
4 Prisms and pyramids
Making solids from nets
Prisms
Surface area of a prism
Pyramids
Net for a pyramid
Volume of a pyramid
Surface area of a pyramid
Volume of a cylinder
Curved surface area of a cylinder
Volume of a cone
Surface area of a cone
Mixed exercise
5 Enlargements
Enlargements
Centre of enlargement
Scale factors
Finding an image under enlargement
Fractional scale factors
6 Scale drawing
Scale drawing
Accurate drawing with scaled down measurements
Scale drawings without measurements
Map ratio (or representative fraction)
Angles of elevation
Angles of depression
Enlargement and the effect on areas and volumes
Volumes and scale factor
Mixed exercises
7 Congruent triangles
The basic facts
Congruent shapes
Transformations and congruent figures
Congruent triangles
Three pairs of sides
Two angles and a side
Two sides and an angle
Problems
Using congruent triangles
Properties of parallelograms
Using properties of special quadrilaterals
Review test 1: Chapters 1–7
8 Similarity
Similar figures
Similar triangles
Corresponding vertices
Using the scale factor to find a missing length
Corresponding sides
One pair of equal angles and two pairs of sides
Summary: similar triangles
Mixed exercise
9 Pythagoras’ theorem
Squares and square roots
Pythagoras’ theorem
Finding the hypotenuse
The 3, 4, 5 triangle
Finding one of the shorter sides
Mixed examples
Pythagoras’ theorem using areas
Finding lengths in an isosceles triangle
Finding the distance of a chord from the centre of a circle
Problems using Pythagoras’ theorem
The converse of Pythagoras’ theorem
Mixed exercises
10 Trigonometry
Tangent of an angle
Using a calculator
Finding an angle
Finding a side
Using the hypotenuse
The sine of an angle
The cosine of an angle
Summary
Sines, cosines and tangents
Finding the hypotenuse
Angles of elevation and depression
Mixed exercise
11 Polygons
Polygons
The exterior angle of a regular polygon
The sum of the interior angles of a polygon
Formula for the sum of the interior angles
Mixed problems
Pattern-making with regular polygons
12 Constructions
Basic constructions
To construct a line parallel to a given line through a given point
The rhombus
Properties of the diagonals of a rhombus
Circle constructions
To construct the circumcircle to a given triangle
Constructing regular polygons
Mixed exercises
13 Consumer arithmetic
Percentage change
Earnings
Taxes
Property tax
Saving and borrowing
Telephone bills
Electricity bills
Mixed exercise
14 Simultaneous equations
Equations with two unknown quantities
Elimination method
Harder elimination
Mixed questions
Special cases
Substitution method
Problems
Graphical solutions of simultaneous equations
Mixed exercise
Review test 2: Chapters 8–14
15 Sets
Reminders
Notation
Problems
Number of members
Further problems
Mixed exercise
16 Straight-line graphs
Straight lines
Lines parallel to the axes
Slant lines
Points on a line
Comparing slopes
Gradients
Calculating the gradient of a line
The intercept on the y-axis
Parallel lines
Different forms of the equation of a straight line
Getting information from the equation of a line
The equation of a line through two given points
Problems
Mixed exercises
17 Linear equations and inequalities
Linear equations
Multiplication and division of fractions
Fractional equations
Problems
Substituting numerical values into formulae involving fractions
Solving inequalities
Using two-dimensional space
18 Algebraic products
Brackets
The product of two brackets
Finding the pattern
Important products
The difference between two squares
Harder expansions
Summary
Mixed exercises
19 Algebraic factors
Finding factors
Common factors
Factorising by grouping
Factorising quadratic expressions
Calculations using factorising
Mixed questions
Mixed exercises
20 Algebraic fractions
Simplifying fractions
Factors
Further simplifying
Multiplying and dividing fractions
Lowest common multiple
Addition and subtraction of fractions
Mixed questions
Solving equations with fractions
Mixed exercises
21 Quadratic equations
Multiplication by zero
Quadratic equations
Solution by factorisation
Summary
Problems
Mixed exercises
22 Probability
Outcomes of experiments
Probability
Experiments where an event can happen more than once
Certainty and impossibility
Probability that an event does not happen
The number of times an event is likely to happen
Using probability to help decision making
Mixed exercise
Review test 3: Chapters 15–22
Review test 4: Chapters 1–22
Glossary
Answers
Index
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