Heinemann Maths Zone

Contents Chapter 1 Money calculations

Replay worksheets R1.1 Expressing fractions as decimals R1.2 Expressing decimals as fractions R1.3 Operating with fractions R1.4 Simple decimal arithmetic R1.5 Ratio and fractions R1.6 Dividing an amount in a given

ratio R1.7 Finding a percentage R1.8 Solving linear equations R1.9 Order of operations R1.10 Solving linear equations R1.11 Volume of a rectangular prism R1.12 Supplementary angles R1.13 Adding and subtracting like

terms R1.14 Dividing with pronumerals R1.15 Factorisation R1.16 Areas of rectangles and

triangles R1.17 Areas of squares, rectangles,

right-angled triangles and circles

R1.18 Perimeter R1.19 A deck of playing cards R1.20 3D shapes R1.21 Time Consolidation worksheets C1.1 Simple interest C1.2 Finding the discounted price C1.3 Finding the percentage profit or

loss C1.4 Percentage calculations C1.5 Simple interest C1.6 Money calculations word search C1.7 Money calculations crossword Homework sheets 1.1 Money calculations 1.2 Money calculations Assignment 1

Chapter 2 Exponents and surds Replay worksheets R2.1 Factor trees and prime factors R2.2 Index and factor form R2.3 Evaluating indices R2.4 Squares and square roots R2.5 Multiplication of fractions R2.6 Improper fractions

R2.7 Multiplying and dividing fractions

R2.8 Evaluating surds R2.9 Simplifying addition and

subtraction R2.10 Perimeter R2.11 Areas of squares, rectangles,

right-angled triangles and circles

R2.12 Volume R2.13 Time R2.14 Plotting linear graphs R2.15 Solving equations by performing

the same operation on both sides Consolidation worksheets C2.1 Working with numbers in index

form C2.2 Raising a number in index form

to a power C2.3 Estimating square and cube

roots C2.4 Multiplying surds C2.5 Simplifying surds C2.6 Exponents and surds word

search C2.7 Exponents and surds crossword Homework sheets 2.1 Exponents and surds 2.2 Exponents and surds Assignment 2

Chapter 3 Measurement Replay worksheets R3.1 Time R3.2 Multiplying and dividing by

powers of 10 R3.3 Rounding to two decimal places R3.4 Time conversions R3.5 Substitution R3.6 Perimeter R3.7 Perimeter and area R3.8 Expansion R3.9 Factorisation R3.10 Plotting linear graphs R3.11 Solving one-step linear

equations Consolidation worksheets C3.1 Converting units C3.2 Understanding length units C3.3 Relating distance, time and

speed

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C3.4 Perimeter involving parts of circles

C3.5 Perimeter, area and converting units

C3.6 Surface area C3.7 Surface area, volume and

capacity C3.8 Measurement word search C3.9 Measurement crossword Homework sheets 3.1 Measurement 3.2 Measurement 3.3 Measurement Assignment 3

Chapter 4 Pythagoras and trigonometry Replay worksheets R4.1 Rounding to two decimal places R4.2 Using the calculator for square

roots R4.3 Solving one-step linear

equations R4.4 Angles in a right-angled triangle R4.5 Ratios, fractions and

simplification R4.6 Complementary and

supplementary angles Consolidation worksheets C4.1 Setting up Pythagoras’ Theorem C4.2 Finding the hypotenuse C4.3 Finding a side other than the

hypotenuse C4.4 Pythagoras’ Theorem C4.5 Identifying sides in triangles C4.6 Using the correct trigonometric

ratio C4.7 Finding the equation C4.8 Finding side lengths C4.9 Finding the hypotenuse C4.10 Finding an angle C4.11 Pythagoras and trigonometry

word search C4.12 Pythagoras and trigonometry

crossword Homework sheets 4.1 Pythagoras and trigonometry 4.2 Pythagoras and trigonometry 4.3 Pythagoras and trigonometry Assignment 4

Chapter 5 Expanding and factorising Replay worksheets R5.1 Terms R5.2 Coefficients R5.3 Like terms R5.4 Substitution R5.5 Perimeter R5.6 Highest common factor (HCF) Consolidation worksheets C5.1 More difficult applications of the

Distributive Law C5.2 Binomial expansion C5.3 Expanding perfect squares C5.4 Simplifying and expanding C5.5 Factorising using common

factors C5.6 Factorising with negative

common factors C5.7 Factorising perfect squares C5.8 Factorising quadratic trinomials C5.9 Expanding and factorising word

search C5.10 Expanding and factorising

crossword Homework sheets 5.1 Expanding and factorising 5.2 Expanding and factorising 5.3 Expanding and factorising Assignment 5

Chapter 6 Linear relationships Replay worksheets R6.1 Solving simple linear equations R6.2 Expanding algebraic

expressions R6.3 Equations and inequations R6.4 Plotting linear graphs R6.5 Subtracting directed numbers R6.6 Multiplication and division of

directed numbers Consolidation worksheets C6.1 Solving more difficult linear

equations C6.2 Linear equations where the

unknown appears more than once

C6.3 Linear equations with fractions on both sides

C6.4 x-intercepts and y-intercepts C6.5 Positive and negative gradients C6.6 Finding the gradient using the

rule

Heinemann Maths Zone

C6.7 Finding the y-intercept and the gradient from the equation

C6.8 Linear relationships word search

C6.9 Linear relationships crossword Homework sheets 6.1 Linear relationships 6.2 Linear relationships 6.3 Linear relationships Assignment 6

Chapter 7 Quadratics Replay worksheets R7.1 Solving linear equations R7.2 Rounding off to two decimal

places R7.3 x-intercepts and y-intercepts R7.4 Substitution R7.5 Plotting linear graphs R7.6 Similar figures R7.7 Expanding R7.8 Factorising algebraic

expressions Consolidation worksheets C7.1 Turning points C7.2 Axes of symmetry C7.3 x-intercepts and y-intercepts C7.4 Transformations of y = x2 C7.5 Further transformations C7.6 Null Factor Law C7.7 Using the x-intercepts to find the

turning point C7.8 Quadratic outcomes word

search C7.9 Quadratic outcomes crossword Homework sheets 7.1 Quadratics 7.2 Quadratics Assignment 7

Chapter 8 Space Replay worksheets R8.1 Drawing angles R8.2 Naming angles R8.3 Complementary and

supplementary angles R8.4 Solving linear equations R8.5 Distance and bearings Consolidation worksheets C8.1 Opposite angles and angles on

parallel lines C8.2 Congruent figures C8.3 Similar triangles

C8.4 Naming quadrilaterals C8.5 Space word search C8.6 Space crossword Homework sheets 8.1 Space 8.2 Space 8.3 Space Assignment 8

Chapter 9 Chance Replay worksheets R9.1 Simplifying fractions R9.2 Converting common fractions to

decimals R9.3 Expressing fractions as

percentages R9.4 Listing possible outcomes R9.5 Simple probabilities R9.6 Operations with fractions R9.7 Addition of three fractions Consolidation worksheets C9.1 Using a table to list the sample

space C9.2 Odds and probabilities C9.3 Chance word search C9.4 Chance crossword Homework sheets 9.1 Chance 9.2 Chance Assignment 9

Chapter 10 Data Replay worksheets R10.1 Frequency tables R10.2 Distance–time graphs R10.3 The mean R10.4 Number patterns Consolidation worksheets C10.1 Mean, median, mode C10.2 Stem-and-leaf plots C10.3 Finding the median from a stem-

and-leaf plot C10.4 Data word search C10.5 Data crossword Homework sheets 10.1 Data 10.2 Data Assignment 10

Heinemann Maths Zone

Worksheet solutions Chapter 1 Worksheet solutions Chapter 2 Worksheet solutions Chapter 3 Worksheet solutions Chapter 4 Worksheet solutions Chapter 5 Worksheet solutions Chapter 6 Worksheet solutions Chapter 7 Worksheet solutions Chapter 8 Worksheet solutions Chapter 9 Worksheet solutions Chapter 10 Worksheet solutions

Heinemann eMaths Zone

R1.1

Expressing fractions as decimals

Decimals are a simple way of writing fractions that have denominators of 10, 100, 1000, 10 000, 100 000 etc. You need to remember that each 0 in the denominator corresponds to a decimal place. So, for a denominator of 10, there will be one decimal place, whereas for a denominator of 1000 there will be three decimal places.

Express each of the following fractions as a decimal.

(a) 103 (b)

10071 (c)

10006

(a) 103 = 0.3

(b) 10071 = 0.71

Zeros are needed to give three decimal places.

(c) 1000

6 = 0.006

1 Write the number of decimal places there would be if each of the following fractions was written as a

decimal.

(a) 710

…… place (b) 81100

…… places (c) 721000

…… places

(d) 3151000

…… places (e) 810

…… place (f) 7100

…… places

2 Express each of the following fractions as a decimal.

(a) 810

= 0. …… (b) 23100

= 0. …… (c) 1711000

= 0. ………

(d) 9100

= 0.09

Zero needed to give

two decimal places.

(e) 71000

= 0. ……… (f) 8100

= 0. ………

(g) 721000

= 0. …………… (h) 91100

= 0. ………… (i) 510

= 0. …………

Heinemann eMaths Zone

C1.3

Finding the percentage profit or loss

To find the percentage profit or loss you need to use the following formulae.

1 % Profit (based on cost price) = 1

100profit×

CP 2 % Loss (based on cost price) =

1100loss

×CP

3 % Profit (based on selling price) = 1

100profit×

SP 4 % Loss (based on selling price) =

1100loss

×SP

1 Complete the following to calculate the percentage profit or loss based on the cost price each time.

(a) CP = $60 SP = $85

Profit = 85 – 60 = $25

% Profit (on CP) = . . . . . .60

×100

1 = 41.67%

(b) CP = $70 SP = $40

Loss = 70 – …… = ……

% Loss (on CP) = ... ...70

×100

1 = ……%

(c) CP = $70 SP = $100

Profit = …… – …… = ……

% Profit (on CP) = …… ×. . . . . .

1 = ……%

(d) CP = $100 SP = $250

…… = …… – …… = ……

% …… (on CP) = …… ×. . . . . .

1 = ……%

(e) CP = $270 SP = $150

Loss = …… – …… = ……

% Loss (on CP) = …… ×. . . . . .

1 = ……%

(f) CP = $365 SP = $99

…… = …… – …… = ……

% …… (on CP) = …… ×. . . . . .

1 = ……%

2 For each example in Question 1, complete the following to calculate the percentage profit or loss based on the selling price.

(a) Profit = ………

% Profit (on SP) = 2585

×100

1 = ……%

(b) Loss = ………

% Loss (on SP) = . . . . . .40

×. . . . . .

1 = ……%

(c) Profit = ………

% Profit (on SP) = ……×. . . . . .

1 = ……%

(d) ……… = ………

% …… (on SP) = …… ×. . . . . .

1 = ……%

(e) Loss = ………

% Loss (on SP) = …… ×. . . . . .

1 = ……%

(f) ……… = ………

% …… (on SP) = …… ×. . . . . .

1 = 268.69%

Heinemann eMaths Zone

Name:

Class: Due date:

Parent’s signature/comment:

1 4

2 5

3 6

Evaluate:

(a)

-1

×

3

(b)

2

÷

-

210------ 3

5---

69---

23---

A driver is paid

$

12.50 per hour for a 35-hour week and time-and-a-half for each additional hour.

One week she worked 42 hours. What was she paid?

1.1 1.2

Evaluate the following using your calculator. Where necessary, give your answers correct to two decimal places.

(a)

-10.86

+

3.412

−

8.515

(b)

-11.5

×

-0.857

(c)

18.65

÷

-5.38

Ann is paid

$

100 per week plus 12.5% of the value of the plants she sells.

One week she sold

$

1200 worth of plants. What did she earn?

Ding works part-time at the local ‘Food and More’ convenience store. He is paid $8.50 per hour. How much does he earn if he works 20 hours?

Calculate the net income when gross income

=

$1025, tax

=

$162.40 and superannuation

=

$47.20

The following questions refer to Exercises 1.1–1.3 in

Heinemann eMaths Zone

. If you are unsure of how to do a question, try looking at a worked example or other information in the section shown under the question number. Show all working in the space provided.

Money calculations

1.1

1.1 1.2

1.2 1.3