teacher support bookcatalogimages.johnwiley.com.au/attachment/07314... · the teacher support book...

© 2006 John Wiley & Sons Australia, Ltd.89

Teacher support booksupplementary material

CONT

ENTS .

. . . . . . . . .

CONT

ENTS .

. . . . . . . . .

• Teacher notes

• Assessment sheets

• Knowledge and skills grid

• Activities

• Answers

for New South Wales 5.1 Pathway

Teacher notes

© 2006 John Wiley & Sons Australia, Ltd.

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90

TEACHER SUPPLEMENTARY MATERIAL

The supplementary material comprises assessment sheets, a knowledge and skills grid,

activities and answers.

Assessment sheets

The teacher support book contains 11 assessment sheets, one for each chapter. The questions

are designed to assess the relevant ‘knowledge and skills’ dot points linked to the Stage 5.1

outcomes for the New South Wales Mathematics Syllabus. (Some questions are linked to

Stage 4 and Stage 5.2 outcomes.) Codes for each ‘knowledge and skills’ dot point are written

in bold type beneath each question for teachers to see which outcomes are being assessed.

Knowledge and skills grid

The knowledge and skills grid displays each ‘knowledge and skills’ dot point and the codes

used for each dot point for many of Stage 4 and all of the Stage 5.1 outcomes. Some Stage

5.2 outcomes are also included. It also shows where the questions for each dot point are

located.

Activities

The six extra activities are worksheets for teachers to use at their discretion, or at times when

it is difficult to organise lesson preparation.

Answers

The answers section in the teacher support book contains the answers for all questions in the

student homework book, the assessment sheets and the extra activities.


Assessment sheets



Assessment sheet 1.6

Name: ............................................................................

Class: ..................... Due date: ..................................

Parent/Guardian signature: .......................................

Teacher feedback:

Chapter 1 | Number skillspages 1–42

Use mental strategies to evaluate the following four statements.

1 –2 + (–5)NS4.2.2

2 –3 – (–6)NS4.2.2

3 –2 × (–4)NS4.2.3

4 21 ÷ (–3)NS4.2.3

Simplify then evaluate the following two expressions.

5 (–8 + 3) + (–2)NS4.2.4

6 –3 + 4 × 3 – 12 ÷ (–2)NS4.2.5

7 How many significant figures are in the number 2 508 000?

NS5.2.1.1

8 Round the number 16.045 26 to 4 significant figures.

NS5.2.1.2

9 Estimate an answer to 7.867 × 0.458 by first rounding each number

involved in the calculation to

1 significant figure.

NS5.2.1.3

10 Use a calculator to complete the following:

= __________

(to 1 decimal place)

NS5.2.1.4

11 Reduce to simplest form.

NS4.3.3

12 Write as a mixed numeral.

NS4.3.5

Find the value of the following four expressions.

13 –

NS4.3.4

14 2 + 5

NS4.3.6

15 ×

NS4.3.8

4.873 6.945+

2.3816---------------------------------

66

121---------

39

7------

5

6---

2

3---

1

4---

3

8---

4

5---

55

132---------

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16 ÷

NS4.3.8

17 Convert to a decimal.NS4.3.11

18 Convert 0.24 to a fraction in simplest form.NS4.3.12

19 Calculate 6.7 × 4.3, rounding your answer to 1 decimal place.

NS4.3.9, NS4.3.10

20 Express $81 as a percentage of $45.NS4.3.19, NS4.3.16

21 Calculate 15% of $4.60.NS4.3.14

22 Convert 85% to a fraction in simplest form.

NS4.3.13

23 Write 0.75, and 78% in descending

order.

NS4.3.18

24 Write the ratio 1 cm to 1 m as a fraction in simplest form.

NS4.3.20, NS4.3.21

25 The ratio : 2 is equivalent to the ratio 1 : x. Calculate the value of x.

NS4.3.22

The ratio of copper : silver : gold in 18-carat yellow gold is 1 : 1.5 : 7.5. Use this information to answer the following two questions.

26 How much copper is there in a 12.5-g yellow gold necklace?

NS4.3.23

27 How much gold is in the necklace?NS4.3.24, NS4.3.25

28 Why is it necessary to have scientific notation as a form of expressing numbers?

NS5.1.1.10

29 Express the number two hundred and eighty-seven million in scientific notation.

NS5.1.1.11

30 Write the number 4.85 ∞ 10–4 as a basic numeral.NS5.1.1.14

31 Write the numbers 4020, 6.5 × 10–6, 0.003 59 and 8.96 × 103 in ascending order.

NS5.1.1.13, NS5.1.1.15

32 Use a calculator to evaluate the expression (3.04 × 103 + 4.67 × 104) ÷ 6.3 × 105. Give your answer correct to 4 significant figures.

NS5.1.1.12

3

4---

15

32------

2

3---

4

5---

1

3---




Name: ............................................................................

Class: ..................... Due date: ..................................


Teacher feedback:

Chapter 2 | Investingpages 43–62

Express the following four time periods as a fraction of a year.

1 6 months

2 3 months

3 a fortnight

4 20 monthsNS5.1.2.5

Calculate the simple interest earned on the following four investments.

5 $2500 at 7.5% p.a. for 3 years

6 $15 000 at 6.95% p.a. for 1 month

7 $4500 at 6.8% p.a. for 9 months

8 $25 000 at 6.35% p.a. for 22 monthsNS5.1.2.5

Michelle borrows $8500 for 5 years at 7.9% p.a. flat interest rate.

9 How much interest is Michelle charged?

10 What total amount must she repay?NS5.1.2.5

The interest on credit cards is calculated on a daily basis and added to the outstanding balance at the end of the month. Toby’s outstanding balance on 1 December is $4276.90 and he is charged a flat rate of interest of 15.95% p.a. Use this information to answer the following two questions, assuming Toby makes no further purchases during December.

11 What will be the interest charges on Toby’s account for that month?

12 How much will he owe at the end of the month?

NS5.2.1.5

13 Charles invests $5000 at a simple interest rate of 5.4 % p.a. How long would it take for his investment to earn $250? Give your answer to the nearest month.

NS5.1.2.6

14 How much must Janice invest at 5.8% p.a. flat interest to earn a yearly income of $800? Give your answer to the nearest dollar.

NS5.1.2.6

Hoa borrows $15 000 to purchase a car. The terms of the loan are that interest is charged at 9.5% p.a., with the loan plus interest to be repaid in equal monthly instalments over 5 years. Consider this information when answering the following three questions.

15 How much interest will Hoa be charged over the period of the loan?

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16 What is the total he must repay?

17 How much will he repay each month?NS5.1.2.6

18 Find the amount of compound interest earned on $50 000 invested at 7% p.a. over 2 years, with interest compounded annually.

NS5.1.2.7

19 If the interest in question 18 was compounded six-monthly instead of yearly, what would the compound interest amount to?NS5.1.2.7

Noel has saved $75 000 and wants to invest his money for a year. He has two options:Option A 6.13% p.a. flat interestOption B 6% p.a. with interest

compounded every 3 months

20 How much interest would Noel earn with option A?

NS5.1.2.6

21 What interest would he earn with option B?

NS5.1.2.7

22 Which option earns Noel the most money? How much more?

NS5.1.2.7

Refer to the table at the bottom of the page for the following two questions.

23 What compound interest would be earned on an investment of $8200 at 7% p.a. over 10 years?

NS5.1.2.8

24 Find the interest paid on an investment of $15 000 at 8% p.a. over 2 years with interest compounded every 3 months.

NS5.1.2.8

Interest rate per period

Periods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%

1 1.010 1.020 1.030 1.040 1.050 1.060 1.070 1.080 1.090 1.100

2 1.020 1.040 1.061 1.082 1.103 1.124 1.145 1.166 1.188 1.210

3 1.030 1.061 1.093 1.125 1.158 1.191 1.225 1.260 1.295 1.331

4 1.041 1.082 1.126 1.170 1.216 1.262 1.311 1.360 1.412 1.464

5 1.051 1.104 1.159 1.217 1.276 1.338 1.403 1.469 1.539 1.611

6 1.062 1.126 1.194 1.265 1.340 1.419 1.501 1.587 1.677 1.772

7 1.072 1.149 1.230 1.316 1.407 1.504 1.606 1.714 1.828 1.949

8 1.083 1.172 1.267 1.369 1.477 1.594 1.718 1.851 1.993 2.144

9 1.094 1.195 1.305 1.423 1.551 1.689 1.838 1.999 2.172 2.358

10 1.105 1.219 1.344 1.480 1.629 1.791 1.967 2.159 2.367 2.594




Name: ............................................................................

Class: ..................... Due date: ..................................


Teacher feedback:

Chapter 3 | Data representation and analysispages 63–100

Questions 1 to 3 display data in different representations. For each data set, find the mean, median and mode.

1 8, 2, 4, 5, 10, 2, 6, 7DS4.2.1

2

DS4.2.3DS4.2.1

3 Key 1 | 8 = 18

DS4.2.3

4 Five scores have a mean of 6.4. Four of those scores are 5, 7, 8 and 9. What

is the fifth score?

DS4.2.1

Use the following table to answer questions 5–8.

5 Complete the entries in the frequency distribution table.

DS5.1.1.5

6 Calculate the mean.DS5.1.1.7

7 Determine the modal class.DS5.1.1.8

8 Construct a combined histogram and frequency polygon to display the data.

DS5.1.1.6

x 1 2 3 4 5

f 4 7 10 6 3

Stem Leaf

0 2 8 91 5 7 7 92 3 5 5 5 63 0 4 8 84 1 7 95 2

Class

interval

Class

centre

(x)

Frequency

( f )

Frequency ×

class centre

( f × x)

40–49 8

50–59 7

60–69 9

70–79 5

80–89 3

90–99 3

Σ f = Σ( f × x) =

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98

9 Complete the following frequency table by entering the correct values in

the cumulative frequency column.

DS5.1.1.1

Twenty students are asked to roll a die once and note the number that turns up. The results are shown below. 1, 6, 4, 5, 2, 3, 6, 1, 4, 2, 5, 6, 4, 2, 6, 1, 6, 3, 4, 2Use this information to answer the following three questions.

10 Display the results in a frequency table that includes a cumulative frequency

column.

DS5.1.1.1

11 Construct a cumulative frequency histogram and ogive.

DS5.1.1.2

12 Use your result from question 11 to determine the number of students who

rolled a 4 or higher.

DS4.1.5

The percentages obtained by a group of students in their end-of-semester mathematics exam are as follows.42, 32, 62, 24, 70, 82, 94, 54, 37, 74, 28, 85, 66, 53, 73, 64, 65, 49, 72, 39, 87, 69, 48, 79, 89, 50, 46, 29, 77, 83, 67, 27, 77, 95, 55, 43, 74, 88, 68, 52, 35, 76, 37, 84, 66, 59, 75, 90, 55, 43.Use these data to answer questions 13–15.

13 In the space provided, sort the data into a grouped distribution table using

intervals of 10 (starting from 20).

Include a cumulative frequency

column.

DS5.1.1.4, DS5.1.1.5

14 On the grid lines provided, construct a cumulative frequency polygon.

DS5.1.1.2

15 Use the graph from question 14 to find the median score.

DS5.1.1.3

Score

(x)

Frequency

(f)

Cumulative

frequency

(cf)

1 2

2 5

3 4

4 9

5 4

6 6




Name: ............................................................................

Class: ..................... Due date: ..................................


Teacher feedback:

Chapter 4 | Indicespages 101–126

1 State the base and the power for 35.NS5.1.1.1

2 Write 34 in factor form, and then express it as a basic numeral.

NS5.1.1.2

3 Complete the missing values in the following table.

NS5.1.1.5

4 Write 54 × 33 in factor form.NS5.1.1.5

Multiple choice questions 5 to 13.

5 The expression 34 × 32 is the same as:A 3 × 3 B 38

C 3 × 3 × 3 × 3 × 3 × 3 D 18NS5.1.1.6

6 The expression (43)2 is the same as:A 4 × 4 × 4 × 4 × 4 × 4B 4 × 4C 45 D 24NS5.1.1.6

7 The expression 53 ÷ 53 is the same as:A 50

B 1C 53 − 3

D all of theseNS5.1.1.3

8 The expression is the same as:

A

B −12C 4−3

D −43

NS5.1.1.4


A 3 B

C D 27

NS5.1.1.9

10 The expression x11 × x3 is the same as:A x11 × 3 B x11 + 3

C x11 − 3 D x113

PAS5.1.1.1


A y9 ÷ 3 B y9 + 3

C y9 − 3 D y9 × 3

PAS5.1.1.1

Base 2 5 2 1

Power 3 2 3 4

Value 8 27 16

1

43

-----

1

12------

93

9

1

3---

9

1

2---

y9

y3

-----

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12 The expression (12x3y)0 simplifies to:A 1 B 12C 12x3y D (12x3y)1

PAS5.1.1.2

13 The expression –a−3 is the same as:A −3 × a B a × a × a

C D − a × a × a

PAS5.1.1.1

For questions 14 to 25, simplify each expression by using the appropriate index law(s), giving the answer in index form. Where possible, show your working to demonstrate how you arrive at your answer.

14 34 × 35

NS5.1.1.7

15 p3 × p6 ÷ p4

PAS5.1.1.3

16 4x5 × 3x7

PAS5.1.1.3

17 2a2b × 4a5

PAS5.1.1.3

18 a8 ÷ a2

PAS5.1.1.3

19

PAS5.1.1.3

20 (2a)3

PAS5.1.1.3

21

PAS5.1.1.3

22 (3p)2 × (2p)3

PAS5.1.1.3

23 (4g)2 ÷ 2gPAS5.1.1.3

24 (3k)0 × (7k)2

PAS5.1.1.3

25 d4 ÷ (d2)2

PAS5.1.1.3

26 Find the value of .NS5.1.1.8

27 Calculate the value of .NS5.1.1.8

28 Use an appropriate method to simplify

.

PAS5.1.1.3

29 Use an appropriate method to

.

PAS5.1.1.3

1

a3

-----

18d12

12d8

-------------

3x

y------

2

81

1

2---

64

1

3----

a33

100k4




Name: ............................................................................

Class: ..................... Due date: ..................................


Teacher feedback:

Chapter 5 | Purchasingpages 127–148

Soft drink is on special at the supermarket this week. A pack of 18 cans costs $8.99 while a 12-pack costs $5.88. Use this information to answer the following three questions.

1 What is the cost per can in the 18-can pack?

2 What is the cost per can in the 12-can pack?

3 Which pack is the better buy?NS5.1.2.10

Juice Pops are sold in a pack of 6 × 250-mL bottles. They are advertised as ‘2 packs for $3.98’.

4 What is the cost per bottle?

5 What is the cost per litre?NS5.1.2.10

6 Karly paid $2.24 for 400 g of mince. What is the price of mince per kg?

NS5.1.2.10

7 Yoghurt can be purchased as 2 × 200-g tubs for $1.98 or a 1-kg tub for $4.95. Which is the better buy?

NS5.1.2.10

8 A digital set top box is discounted from $149 to $129 for a cash customer. What percentage discount is this?

NS5.1.2.9

9 An arm-band MP3 player has a marked price of $125. A cash purchaser is allowed a 15% discount. What is the cash price?

NS5.1.2.9

10 The Camera House has a sale. One particular camera is advertised as shown in the figure below.

Is the advertising correct or misleading? Give a reason to support your answer.

NS5.1.2.9

11 Melissa used her credit card to purchase an airline ticket costing $875. Interest on the credit card is charged at the rate of 12.5% p.a. How much interest would Melissa be charged after 1 month?

NS5.1.2.9

Camera

SALE

IKON 2400 model

pay only $297 for Cash

SAVE $160.90 – that’s 35% off

TODAY ONLY

House

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A credit card company charges interest at the rate of 16% p.a. The outstanding balance on Ronald’s card at the end of May is $1850. Use this information to answer questions 12 to 14.

12 Calculate the interest due for the month of May.

NS5.1.2.5

13 The minimum payment due is 5% of the balance or $10, whichever is the greater. If Ronald pays the minimum, how much does he pay?

NS5.1.2.9

14 Ronald makes no further purchases during June. Calculate the interest due on his credit card for June.

NS5.1.2.5

A DVD recorder can be purchased using the options advertised in the following figure.

15 How much would you pay if you bought the recorder on terms?

NS5.1.2.9

16 What is the total interest charged?NS5.1.2.9

17 What is the annual rate of interest?NS5.1.2.6

The purchase price of a second-hand car is $7500. Alex pays 10% deposit and borrows the balance from a finance company. He agrees to pay simple interest of 10.5% p.a., and repay the total owing over a period of 5 years in equal monthly instalments. Use this information to answer the following five questions, showing your working in the space provided.

18 How much deposit does Alex pay?

19 How much does Alex borrow from the finance company?

20 Calculate the interest Alex pays over the period of the loan.

21 What is the total amount Alex must repay to the finance company?

22 Determine the repayment Alex must make each month.

NS5.1.2.9

DVD Recorder

CASH PRICE $299 or

$30 per month for 12 monthsOFFER VALID TODAY ONLY




Name: ............................................................................

Class: ..................... Due date: ..................................


Teacher feedback:

Chapter 6 | Algebra and linear equationspages 149–176

Simplify each of the following four expressions.1 3a + 4b – 2a – 6b

PAS4.3.1

2 2g × 4wPAS4.3.3

3

PAS4.3.3

4 6m × 3n × 2mPAS4.3.3

Evaluate the following four expressions if x = –3, y = 2 and z = 6.

5 x + y + zPAS4.3.6

6 x × y × zPAS4.3.6

7 x2 – y2

PAS4.3.6

8

PAS4.3.6

The formula used to calculate the surface area of a cylinder is SA = 2pr (r + h), where r represents the radius of the cylinder, h is the height of the cylinder and SA is the surface area.

9 Using π = 3.14, calculate the surface area of a cylinder with a radius of

6.5 cm and a height of 12 cm. Give

your answer to the nearest cm2.

PAS4.3.6

Expand the following four expressions and simplify where appropriate.

10 3(k + 2)PAS4.3.5

11 4a(a – 5)PAS4.3.5

12 6x(x – y)PAS4.3.5

13 7g(g + 9) + 4(g – 5)PAS4.3.5

Factorise each of the following expressions by taking out a common factor.

14 3d – 15PAS4.3.2

8xyz

12xz-----------

x z+

x y+------------

h

r•

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15 10m + 25nPAS4.3.2

16 12x2 + 4xPAS4.3.2

17 27p3 – 18p2

PAS4.3.2

Simplify each of the following algebraic fractions. Show all working in the space provided.

18 +

PAS4.3.4

19 +

PAS4.3.4

20 ×

PAS4.3.4

21 ÷

PAS4.3.4

Solve the following four equations by undoing the operations that have been performed on the pronumerals.

22 p + 12 = 5PAS4.4.1

23 3k – 7 = 12PAS4.4.1

24 = 2

PAS4.4.1

25 3f – 5 = 7f + 2PAS4.4.1

Substitute the number in the grouping symbols into its associated equation to determine whether it is a solution to the equation.

26 x – 3 = –5 (–2)PAS4.4.2

27 3m + 7 = 2 (3)PAS4.4.2

28 2k + 9 = 4 (–2 )PAS4.4.2

29 3b – 5 = 6b – 8 (1)PAS4.4.2

30 I think of a number then multiply it by 5. If I add 4 then divide by 4, my

answer is 16. Form an equation, letting

x represent the number I am thinking

of. Then solve the equation to

determine the number.

PAS4.4.3

x

2---

x

3---

1

2---

1

x---

6

5x------

10x

3---------

12xz

7-----------

3z

14------

a

8--- 1

2---

1

2---




Name: ............................................................................

Class: ..................... Due date: ..................................


Teacher feedback:

Chapter 7 | Geometrypages 177–228

1 Find the complement and supplement of 71°.

SGS4.2.6

Find the value of the pronumeral in each of the following diagrams. In each case provide a reason for your answer.

2

3

4

5

6

7

8

9

10SGS4.2.14

11 Fill in the gaps for each of the following.

a 25 mm = __________ cm

b 4200 cm = __________ kmMS4.1.4

12 Calculate the perimeter of the following figure.

MS5.1.1.3

13 Calculate the area of the shape in question 12.MS5.1.1.2

40º 5x

y

x

28º

x

19º

x

y

30º

x

35ºy

50º

x

2xy

50º

69º

x y

118º

x

75º2x

9 cm

6 cm

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Calculate the area of the following two shapes.

14

15

MS5.1.1.1

16 Calculate the perimeter and the area of the following sector.

MS5.2.1.1

17 Calculate the perimeter and the area of the following figure.

MS5.2.1.2

Calculate the surface area and the volume for the following two figures.

18

MS4.2.1, MS4.2.3

19

MS4.2.1, MS4.2.3

20 A water tank in the shape of a cylinder has a base diameter of 1 m and a

height of 2 m. How many litres (to the

nearest litre) could the tank hold when

full?

MS4.2.2, MS4.2.4

28 cm

6 cm 6 cm

4 mm

3 mm

3.2 mm

6 mm

10 mm

75°

4 cm

6 m

3 m

2 m

8.2 cm

3.5 cm

4.9 cm




Name: ............................................................................

Class: ..................... Due date: ..................................


Teacher feedback:

Chapter 8 | Coordinate geometrypages 229–266

Consider the straight lines with the equations y = -3, x = 3, y = 0 and x = 0 in answering questions 1 and 2.

1 Complete the tables of values and then use the coordinates to plot each line on

the one set of axes using the grid lines

provided.

PAS5.1.2.7

a y = –3

b x = 3

c y = 0

d x = 0

2 What do you notice about the graphs of the straight lines y = 0 and x = 0?

PAS5.1.2.9, PAS5.1.2.10

3 Complete the two table of values below and plot the graphs of

y = 2x + 3 and y = −2x + 3 on the one

set of axes using an appropriate scale

on the grid lines provided.

PAS5.1.2.11

a y = 2x + 3

b y = –2x + 3

4 Identify the x- and y-intercepts of the straight lines y = 2x + 3 and

y = −2x + 3.

PAS5.1.2.8

5 Describe the slopes of the two graphs drawn in question 3 as positive or negative by following the line from

left to right.

PAS5.1.2.5

x –2 –1 0 1 2

y

x

y –2 –1 0 1 2

x –2 –1 0 1 2

y

x

y –2 –1 0 1 2

x –2 –1 0 1 2

y

x –2 –1 0 1 2

y

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108

6 The graph of y = 4x − 2 is shown on

the grid lines provided. Using the two

points given, construct a right-angled

triangle and use it to find the gradient

of the line.

PAS5.1.2.4

7 Find the gradient of the linear graph

shown.

PAS5.1.2.6

8 For the graph given below, find:

iii the gradient, m

iii the y-intercept, b

iii the rule, using your values for m

and b found above.

PAS5.2.3.12

9 In the space provided, sketch the

graph of y = 2x − 3 using the

gradient–intercept method.

PAS5.2.3.10

10 Find the gradient of the line joining

the two points (−2, 2) and (0, 6).

PAS5.2.3.6

11 Determine the midpoint of the interval

from the diagram given.

PAS5.1.2.1

12 Plot the points A(−3, 1) and B(3, −2)

onto a set of axes on the grid lines

provided. Join AB and draw a vertical

line through A and a horizontal line

through B. Let these lines intersect at

C to form a right-angled triangle ABC.

PAS5.1.2.2

13 Use Pythagoras’ theorem to find the

length of AB in question 12 above.

PAS5.1.2.3

–5 –4 –3 –2 –1 1 2 3 4 5

–5

–4

–3

–2

–1

1

2

3

4

5

0 x

y

y = 4x–2

y

x0

–1

–2

–3

–4

4

3

2

1

1 2 3 4 5 –4 –3 –2 –1

(–2, –4)

(4, 3)

x

y

–1–1 1 2 3 4–2–3–4

1

2

3

4

–2

–3

–4

0

6

4

2

2 4 6 8 10 0x

y


A four-sided die, numbered from 1 to 4, is rolled and the outcomes noted. Use this information to answer questions 1 to 5.1 Give the sample space for the

experiment.

NS4.4.2

2 List the set of prime numbers possible.NS4.4.1

3 What is the chance that a 1 will result?NS4.4.3

4 Express the probability of rolling an even number as a fraction.

NS4.4.4

5 What is the chance that a 6 will result?NS4.4.5

A card is chosen from a normal deck of playing cards. Answer questions 6 to 8 for this experiment.

6 If this card is a red picture card, list possible outcomes.

NS4.4.1

7 Describe the elements in the complementary event.

NS4.4.7

8 Calculate the probability of this complementary event.

NS4.4.8

9 A bag contains red, blue and orange balls. If the chance of drawing out a

red ball is and the chance of drawing

out a blue ball is , what is the chance

of drawing out an orange ball?

NS4.4.6

10 A game consists of throwing two dice. The two numbers on the upper faces

are multiplied. You win if this

resulting number is odd and you lose

if it is even. Is this game fair? Justify

your answer with mathematical

evidence.

NS5.1.3.4

11 A biased coin has resulted in 24 heads from 60 tosses. What is the relative

frequency of obtaining a tail on the

next toss?

NS5.1.3.1

1

2---

1

3---



Name: ............................................................................

Class: ..................... Due date: ..................................


Teacher feedback:

Chapter 9 | Probabilitypages 267–294

1010



1010

110

A school has an enrolment of 350 students. The number of students visiting the canteen for lunch each day last week is shown in the following table.

12 What is the probability that a student will visit the canteen next Monday?

NS5.1.3.2

13 What is the probability a student will not visit the canteen next Friday?

NS5.1.3.2

A card is drawn from a normal deck of playing cards and its suit noted. The card is replaced before another card is drawn. The results of 100 draws gave the following results.

14 Complete the following:

P(Heart) = =

NS5.1.3.3

15 Determine the experimental probability of drawing a red card on

the next trial.

NS5.1.3.4

16 What is the experimental probability that the next card will not be a

diamond?

NS5.1.3.4

Each letter of the words MATHS QUEST is written on a card and the cards are then shuffled. One card is chosen at random.

17 What is the probability that the card has an E on it?NS5.1.3.4

18 What is the probability that the card has a vowel written on it?NS5.1.3.4

19 What is the probability there is a consonant written on the card?

NS5.1.3.4

20 What is the total of the probabilities in questions 18 and 19?NS4.4.6

Day Number of students

Monday 56

Tuesday 37

Wednesday 45

Thursday 52

Friday 63

Card Number

Heart 22

Diamond 34

Club 28

Spade 16

100---------



Assessment sheet10.6

Name: ............................................................................

Class: ..................... Due date: ..................................


Teacher feedback:

Chapter 10 | Right-angled trigonometrypages 295–334

Use the following figure to answer questions 1 and 2.

1 a Which side is the hypotenuse?

b Which side is adjacent to the angle θ?

c Which side is opposite the angle θ?MS5.1.2.1

2 Write an expression for each of the following.

a sin α

b tan θ

c cos αMS5.1.2.4, MS5.1.2.5

Use the following figure to answer questions 3 to 5.

3 Measure the lengths of the sides WN and PN. Use these measurements to

calculate the value of tan W (correct to

2 decimal places).

4 Measure the lengths of the sides WX and AX. Use these measurements to

calculate the value of tan W (correct to

2 decimal places).

5 Comment on your answers to questions 3 and 4.MS5.1.2.3

6 The sides of a triangle are sometimes labelled

with lower-case letters

of the opposite angle.

Use this technique to

label the sides of the

following triangle.

MS5.1.2.2

7 Use a calculator to determine each of the following, correct to 4 decimal

places.

a cos 12°

b sin 29°

c tan 83°MS5.1.2.6

For the figures provided in questions 8 to 10, calculate the value of the pronumeral correct to 1 decimal place.

8

9

10

MS5.1.2.8

x

θ

y

z

α

X

A

P

W

N

T R

M

x

42°

3.5 cm

35 mm

67°

b

27º

16 mm

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112

A stake is used to support a tree so that the tree grows vertically, as shown in the diagram. Use this information to answer questions 11 and 12.

MS5.1.2.8

11 Calculate the length of the stake, to the nearest metre.

12 How far from the base of the tree is the base of the stake on the ground?

13 Find the size of the angle θ in each of the following, to the nearest degree.

a tan θ = 4.1473

b cos θ = 0.7936

c sin θ = 0.4398

Find the values of the unknown angles in the following two triangles to the nearest degree.

14

15

MS5.1.2.9

16 Label the angle of elevation in the figure below.

MS5.1.2.10

17 From the top of a 20-m vertical cliff, Jim views a boat at sea at an

angle of depression of 22º. What

distance is the boat from the shore?

MS5.1.2.11

A ladder leans against a brick wall, as shown in the diagram. Use the measurements provided to answer the following two questions.

18 What angle does the base of the ladder make with the ground, to the nearest

degree?

MS5.1.2.9

19 How far up the wall does the ladder reach?

MS5.1.2.8

x

3.2

cm

6.2 cm

y

12.8

mm

5.3 mm

22º

20 m

2.57 m

4 m

1.5

m

50°

Sta

ke



Assessment sheet11.6

Name: ............................................................................

Class: ..................... Due date: ..................................


Teacher feedback:

Chapter 11 | Graphspages 335–368

Consider the straight line graph of the equation 3x + 6y = 9 when answering the following three questions.

1 Determine the x-intercept.PAS5.1.2.8

2 Find the y-intercept.PAS5.1.2.8

3 In the space provided, sketch a graph of the equation.

4 What is the equation of the x-axis?PAS5.1.2.9

5 Write the equation of the y-axis.PAS5.1.2.10

6 Describe the graph of the line x = 5.PAS5.1.2.7

7 Use substitution to determine whether the point (–1, –1) lies on the line

6x – 2y = –4. Show your working in

the space provided.

PAS5.1.2.13

Consider the quadratic equation y = x2 – x – 6 when answering the following four questions.

8 Complete this table of values.

PAS5.1.2.12

9 Plot these points on the following grid to show the graph of y = x2 – x – 6.

PAS5.1.2.12

10 From your graph, determine the coordinates of the x-intercepts.

PAS5.1.2.8

11 State the coordinates of the y-intercept.

PAS5.1.2.8

x –3 –2 –1 0 1 2 3 4

y

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114

The graph of y = x2 is a simple concave-up parabola. Describe the changes which would occur in moving from this curve to the following three parabolas. Provide a sketch of each parabola on a separate set of axes in the space provided (along with a sketch of y = x2). State the coordinates of the turning point for each parabola.

12 y = x2 + 4PAS5.1.2.12

13 y = –x2

PAS5.1.2.12

14 y = (x + 2)2

PAS5.1.2.12

Consider the exponential function y = 2x in answering the following three questions.


PAS5.1.2.12

16 Plot the points on this grid.PAS5.1.2.12

17 What are the coordinates of the y-intercept?

PAS5.1.2.8

Consider the hyperbola y = when

answering the following three questions.


PAS5.1.2.12

19 Plot the points on this grid.PAS5.1.2.12

20 Give the equations of the two asymptotes.

PAS5.1.2.9, PAS5.1.2.10x –3 –2 –1 0 1 2 3

y

x –4 –3 –2 –1 0 1 2 3 4

y

2x---

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