Preliminary Exam Preparation, Study Notes

Table of Contents

Chapter One: Linear Equations and Functions 2

Algebraic Terms 2

Formulas 2

Expanding Expressions 2

Solving Equations 2

Equations Involving Algebraic Fractions 2

Equations and Formulas 2

Linear Functions 2

The Gradient as a Rate of Change 3

Linear Modelling 3

Chapter Four: Statistical Samples and Displays 4

Statistical Investigations 4

Interpreting Graphs 4

Types of Data 4

Sample Types 4

Sampling techniques 4

Constructing graphs 5

Misleading graphs 5

Frequency histograms and polygons 5

Dot plots 5

Stem and Leaf plots 5

Radar Charts 5

Chapter Five: Ratios and Similar Figures 6

Simplifying Ratios 6

The Unitary Method 6

Dividing a Quantity into a Given Ratio 6

Scale Factors and Centre of Enlargement 6

Properties of Similar Figures 6

Using Shadows and Similar Triangles 6

Scale Drawings 6

Floor Plans and Elevations 7

Symbols and Calculations from Plans and Elevations 7

Chapter Six: Earning and Taxation 8

Wages, salaries and overtime 8

Commission, Piecework and Royalties 8

Bonuses and Allowances 8

Gross and Net Pay 8

Household Bills 9

Budgeting 9

Income tax 9

Goods and Services Tax 9

Chapter Seven: Trigonometry 10

Pythagoras’ theorem 10

Investigating the Tangent Ratio 10

Investigating the Sine Ratio 10

Investigating the Cosine Ratio 10

Mixed Problems 10

Bearings 10

HELP PAGES 246 to 287 11

Chapter Eight: Rates and Linear Modelling 12

Rates 12

Rate Problems 12

Speed and Fuel Consumption 12

Converting Rates 13

Graphing Linear Functions 13

Direct Linear Variation 13

Conversion Graphs 13

Linear Modelling 14

Chapter Nine: Probability 15

The Language of Probability 15

Outcomes and Sample Spaces 15

Multistage Events 15

Performing Simple Experiments 15

Experimental Probability 15

Theoretical Probability 15

Complementary Events 15

Chapter Ten: Savings and Investment 16

Simple Interest 16

Compound Interest 16

Account Fees and Charges 16

Investing...