hsc mathematics 12 general 2 revision & exam workbook · 2017-11-25 · 238 excel essential...

Excel ESSENTIAL SKILLS HSC Mathematics General 2 Revision & Exam Workbook

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Get the Results You Want!

YEAR

12HSC Mathematics General 2 Revision & Exam Workbook

AS Kalra

9781741254617 TP 2015.indd 1 15/06/2015 1:57 pm

Free-to-download Sample HSC Exams with answers

237Chapter 19—Sample HSC Examinations

Sample HSC Examination 1Chapter 19

Total time: 2½ hours Total marks: 100

SECTION I Marks: 25

Instructions • Attempt Questions 1 to 25. • Allow about 35 minutes for this section. • Each question is worth 1 mark. • Circle only ONE option.

1 Which of these relationships shows a strong positive correlation?

A B C D

2 The figure drawn is a closed cylinder. Which of the following expressions will give the surface area of the cylinder?

A π × 82 + 2 × π × 8 × 25 B 2 × π × 82 + 2 × π × 8 × 25

C 2 × π × 42 + 2 × π × 4 × 25 D π × 42 + 2 × π × 4 × 25

3 Energy is used at the rate of 20 joules per second. The power developed is:

A 100 W B 25 W C 20 W D 5 W

4 A die is thrown and a coin is tossed at the same time. Find the probability of throwing a number less than 4 and a head.

A B C D

5 As shown in the figure, a square is drawn in a circle of radius 6 cm. The area of the shaded region is given by:

A π × 122 – 122 B π × 62 – 122

C π × 62 – 62 D π × 62 – 12 × 6

6 A car that was purchased for $39 900 is worth $20 400 after 5 years. The annual amount of depreciation, using the straight line method, is:

A $3900 B $4080 C $7980 D $12 060

7 Solve 3(x – 2) = .A x = –4 B x = 4 C x = –2 D x = 2

8 Find angle θ correct to the nearest degree.

A 37° B 41°

C 53° D 49°

9 2.5 g of a medicine is used to make a 200-mL solution. The concentration of this medicine, in mg/mL, is:

A 0.125 B 1.25 C 12.5 D 125

172 excel HSc GeNeRAl mAtHemAticS ReviSioN ANd exAm woRkbook

Sample HSC ExaminationsSamp l e HSC Exami n at i o n 1 S EC TI ON IInstructions • This section consists of 25 objective-response questions. • Each question is worth 1 mark. • Circle only ONE option. • Calculators may be used.

Time allowed: 30 minutes Total marks: 25

1 Simplify 2x(3x – 1) – 3x(x + 1).

A 3x2 – 5x B 3x2 + 5x C 3x2 – x D 3x2 + x


A π × 82 + 2 × π × 8 × 25 B 2 × π × 82 + 2 × π × 8 × 25

C 2 × π × 42 + 2 × π × 4 × 25 D π × 42 + 2 × π × 4 × 25

3 The solution to the equation 10x = 500 is approximately equal to

A 2 B 2.6 C 2.7 D 50


A 12 B

13 C

14 D

16

5 As shown in the figure a square is drawn in a circle of radius 6 cm. The area of the shaded region is given by

A π × 122 – 122 B π × 62 – 122

C π × 62 – 62 D π × 62 – 12 × 6

6 Simplify 8x – 5(x – 4).

A 13x + 20 B 3x + 20 C 3x – 20 D 3x – 4

7 Solve 3(x – 2) = 32x

.

A x = –4 B x = 4 C x = –2 D x = 2


A 37° B 41°

C 53° D 49°

9 There are 5 white marbles, 6 yellow marbles and 7 black marbles in a box. One marble is drawn at random. What is the probability that the marble is white?

A 13

B 23

C 518

D 718

Chapter 14

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1 Simplify 2x(3x – 1) – 3x(x + 1).

A 3x2 – 5x B 3x2 + 5x C 3x2 – x D 3x2 + x


A π × 82 + 2 × π × 8 × 25 B 2 × π × 82 + 2 × π × 8 × 25

C 2 × π × 42 + 2 × π × 4 × 25 D π × 42 + 2 × π × 4 × 25


A 2 B 2.6 C 2.7 D 50


A 12 B

13 C

14 D

16


A π × 122 – 122 B π × 62 – 122

C π × 62 – 62 D π × 62 – 12 × 6


A 13x + 20 B 3x + 20 C 3x – 20 D 3x – 4

7 Solve 3(x – 2) = 32x

.

A x = –4 B x = 4 C x = –2 D x = 2


A 37° B 41°

C 53° D 49°


A 13

B 23

C 518

D 718

Chapter 14

25 cm

8 cm

0

θ3

4





1 Simplify 2x(3x – 1) – 3x(x + 1).

A 3x2 – 5x B 3x2 + 5x C 3x2 – x D 3x2 + x


A π × 82 + 2 × π × 8 × 25 B 2 × π × 82 + 2 × π × 8 × 25

C 2 × π × 42 + 2 × π × 4 × 25 D π × 42 + 2 × π × 4 × 25


A 2 B 2.6 C 2.7 D 50


A 12 B

13 C

14 D

16


A π × 122 – 122 B π × 62 – 122

C π × 62 – 62 D π × 62 – 12 × 6


A 13x + 20 B 3x + 20 C 3x – 20 D 3x – 4

7 Solve 3(x – 2) = 32x

.

A x = –4 B x = 4 C x = –2 D x = 2


A 37° B 41°

C 53° D 49°


A 13

B 23

C 518

D 718

Chapter 14

25 cm

8 cm

0

θ3

4


1—2

1—3

1—4

1—6

3x—2

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238 Excel ESSENTIAL SKILLS HSC Mathematics General 2 Revision & Exam Workbook

Sample HSC Examination 110 Stamp duty on new vehicles is given.

Car value Stamp duty$59 113 or less 3% ($6 for every $200 or part thereof)

Over $59 113 5% ($10 for every $200 or part thereof)

Calculate the stamp duty payable on a car worth $29 850.

A $895.50 B $897 C $900 D $1773.40

11 Use the sine rule to find the length of the side x correct to one significant figure.A 7 cm B 5 cm

C 4 cm D 8 cm

12 A bathroom tap generally runs at 8 L of water per minute. Tim leaves the tap running while he brushes his teeth for 3½ minutes each day. The water he has wasted in a week is about:A 160 L B 180 L C 200 L D 220 L

13 Lauren’s z-score on a particular test was 1.5. If the class average and standard deviation were 64 and 8 respectively, Lauren’s mark was: A 52 B 65.5 C 76 D 86

14 Which of the following equals 220 bytes?A 1 kilobyte B 1 megabyte C 1 gigabyte D 1 terabyte

15 Saccio earns commission selling musical instruments and equipment. He is paid a retainer of $100 per week as well as 5% commission on sales up to $10 000 and 7% commission on additional sales over $10 000. What does he earn in a week where he sells $12 500 worth of goods?A $675 B $775 C $875 D $975

16 David buys a sound system for $2849 including GST of 10%. How much GST was paid by David?A $28.49 B $284.09 C $284.90 D $259

17 The cost of hiring a venue involves a fi xed cost of $300 then varies directly with the number of people in attendance. If it costs $450 for 30 people, how much would it cost to hire the venue for 40 people?

A $480 B $490 C $500 D $550

18 The gradient of the line l is:

A –15 B –5

C +15 D +5

x5

1

yl

C

A

B x50°60°

5.7

cm

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Sample HSC Examination 119 Luanne bought two tickets in a raffl e. The tickets cost $5 each.

500 tickets are sold and there is one prize of $1000. Luanne’s fi nancial expectation is:A –$10 B –$6 C –$1 D $4

20 A new laptop was purchased for $1800 on 15 June using a credit card. Simple interest was charged at a rate of 23.42% p.a. for purchases using the credit card. No other purchases were made and there is no interest-free period. Interest is charged on both the date of purchase and date of payment. What was the total amount owing on 7 July the same year?A $1826.56 B $1827.72 C $2656.41 D $2771.90

21 A plank is 8 cm wide to the nearest centimetre. The percentage error is:A ±12.5% B ±8% C ±6.25% D ±4%

22 Consider the following chart.

1.430405060708090

100

Wei

ght

(kg)

110120130140150160170180

1.5 1.6 1.7Height (m)

1.8 1.9 2.0

Morbidly obese

Obese

Overweight

Healthy weight

Underweight

Very underweight

A 1.8-m tall man has a weight of 120 kg. What is the least amount of weight he needs to lose so that he is no longer in the obese category?A 10 kg B 20 kg C 30 kg D 40 kg

23 Which of the following is a linear function?

A y = x3 + 1 B y = 2x2 – 5 C y = 3x – 7 D y = 12x

24 In the following diagram, what is the true bearing of P from Q?A 015° B 075°

C 105° D 285°

25 Emiko used the capture/recapture technique to estimate the number of frogs living around a pond. Initially, she caught, marked and released 26 frogs. When she returned a week later, only 16 of the 24 frogs she caught were marked. What is the approximate population of frogs around the pond?A 17 B 34 C 39 D 42

N

N15°

P

S

EW Q


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Sample HSC Examination 1SECTION II Marks: 75

Instructions • Attempt Questions 26 to 30. • Allow about 1 hour 55 minutes for this section. • Show all relevant mathematical reasoning and/or calculations.

Question 26

a Given that E = MV

2

2 fi nd E when M = 80 and V = 5. 1 mark

__________________________________________________________________________________________

__________________________________________________________________________________________

__________________________________________________________________________________________

b The graph shows the life expectancy in Cambodia between 1960 and 2010.

196030

40

50

60

70

Life

exp

ecta

ncy

(yea

rs)

1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

i Except for the dip in the 1970s and 1980s, the trend is approximately linear. Calculate the slope of this (approximately linear) graph. 1 mark

_______________________________________________________________________________________

_______________________________________________________________________________________

ii What is the minimum life expectancy of Cambodians during this time, and when does it occur? 2 marks

_______________________________________________________________________________________

iii Suggest a possible reason for the dip in the 1970s and 1980s. 1 mark

_______________________________________________________________________________________

c The average speed of a cyclist is 10.5 m/s. Find this speed in kilometres per hour. 1 mark

__________________________________________________________________________________________

__________________________________________________________________________________________

__________________________________________________________________________________________


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Sample HSC Examination 1Question 26 continued

d Solve the following equations.

i 7x – 20 = 3x + 16 2 marks

_______________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________

ii !x + 3 = 8 2 marks

_______________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________

e A radial survey of a fi eld is given.

i Find the size of ∠AOB. 1 mark

_______________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________

ii Calculate the area of nAOB to the nearest square metre. 2 marks

_______________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________

iii Find the distance from A to B to the nearest metre. 2 marks

_______________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________

A 060°

73 m100 m

D 320°

O

98 mB

130°

205°

69 m

C


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Sample HSC Examination 1Question 27

a i Solomon invests $25 000 in an account earning 6% p.a. interest, compounded quarterly. How much is his investment worth, to the nearest whole dollar, at the end of 5 years? 2 marks

_______________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________

ii Sally invests $3000 at the end of every 6 months in an account that earns 8% p.a. interest, compounded 6-monthly. Using the table below, calculate the amount her investment is worth, to the nearest dollar, at the end of 5 years. 2 marks

Future value of $1Interest rate per period

Period 3% 4% 5% 6% 10%1 1.0000 1.0000 1.0000 1.0000 1.0000

2 2.0300 2.0400 2.0500 2.0600 2.1000

3 3.0909 3.1216 3.1525 3.1836 3.3100

4 4.1836 4.2465 4.3101 4.3746 4.6410

5 5.3091 5.4163 5.5256 5.6371 6.1051

10 11.4639 12.0061 12.5779 13.1808 15.9374

20 26.8704 29.7781 33.0660 36.7856 57.2750

_______________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________

iii How much more would Solomon need to have invested to have the same amount as Sally at the end of the 5 years? Give your answer to the nearest dollar. 2 marks

_______________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________


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b A mobile phone plan has a 25-cent connection fee then charges 31 cents for each ½ minute block.Calculate the cost for a 4-min 39-s call. 2 marks

__________________________________________________________________________________________

__________________________________________________________________________________________

c A delegation of three people is to be chosen from a group of eight people.

i How many different delegations are possible? 2 marks

_______________________________________________________________________________________

_______________________________________________________________________________________

ii Each of the members of the delegation must make a speech at the meeting they are to attend. The order in which the three members will speak will be listed in the agenda for the meeting. In how many ways can three chosen members of the delegation be listed to speak? 2 marks

_______________________________________________________________________________________

_______________________________________________________________________________________

d A scientist has developed a new screening test for a virus. The test was trialled on people who had been exposed to the virus but before any symptoms had time to develop. A positive result meant that the test showed the person had the virus. After several days it was possible to see which people actually had the virus and hence whether the test results were correct. The results are shown in the two-way table below.

Test positive Test negative TotalHad virus 102 37 139

Did not have virus 26 135 161

Total 128 172 300

i How many people had a false result to their test? 1 mark

_______________________________________________________________________________________

_______________________________________________________________________________________

ii Find the probability, as a percentage, that the test was accurate. 1 mark

_______________________________________________________________________________________

_______________________________________________________________________________________

iii What is the probability that a person with a positive test actually had the virus? 1 mark

_______________________________________________________________________________________

_______________________________________________________________________________________


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a Angela borrowed $30 000 at 9.5% p.a. simple interest so that she could furnish her home unit. She repaid the loan, plus interest, with equal monthly instalments over 5 years.

i Calculate the amount of interest charged. 2 marks

_______________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________

ii How much was each monthly instalment? 1 mark

_______________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________

b The table gives an average water use per person per day.

Use Litres/dayBath/shower 72

Sink 18

Toilet 35

Washing clothes 45

Washing dishes 29

Cooking 8

Miscellaneous 6

Total

i Complete the table to insert the value for total. 1 mark

ii Some people will look at this table and argue that they don’t use this much water. How can you respond? 1 mark

_______________________________________________________________________________________

iii How much water is used in the sink over a year? 1 mark

_______________________________________________________________________________________

iv How much water (in kilolitres) does the average person use in a year? 1 mark

_______________________________________________________________________________________


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v One of these areas uses 21.1% of the daily water use. Which is it? 1 mark

_______________________________________________________________________________________

vi What percentage of water is spent on washing dishes? 1 mark

______________________________________________________________________________________

vii A water-effi cient toilet can save about 20% on a person’s water use of that device.

A What is the daily saving in this area? 1 mark

___________________________________________________________________________________

B What is the annual saving in this area? 1 mark

___________________________________________________________________________________

c The distance, d metres, that an object falls is proportional to the square of the time, t seconds. An object dropped from a plane falls 45 m in 3 seconds. How far will it fall in 8 seconds? 2 marks

__________________________________________________________________________________________

__________________________________________________________________________________________

__________________________________________________________________________________________

__________________________________________________________________________________________

__________________________________________________________________________________________

d The body mass index can be calculated from BMI = weight 1kg 2

height 1m 2 × height 1m 2A man has a BMI of 29 and a height of 1 m 80 cm. Calculate his weight. 2 marks

__________________________________________________________________________________________

__________________________________________________________________________________________


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a John leaves Sydney (34°S, 150°E) at 2 pm Wednesday by plane on a 7-hour fl ight to Singapore (1°N, 104°E).

i What is the time difference between Sydney and Singapore? 2 marks

_______________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________

ii What time is it in Singapore when the plane leaves Sydney? 1 marks

_______________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________

iii If another fl ight leaves Singapore at 10 am (local time) Wednesday when does it arrive in Sydney? (The fl ight time is 7 hours.) 2 marks

_______________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________

b A and B are two locations on the Equator with longitudes 60°E and 20°W respectively. Find, to the nearest kilometre, the distance along the Equator from A to B. (The radius of the Earth is 6400 km.) 2 marks

__________________________________________________________________________________________

__________________________________________________________________________________________

__________________________________________________________________________________________

c A class of Year 12 students recorded their bodyweight and displayed the data in the back-to-back stem-and-leaf plot shown:

Boys Girls4 9

6 2 5 3 4 6 7 8 9

8 7 4 2 1 0 6 0 0 2 3 8

5 5 4 0 7 2 5

1 8

7 9

i Determine the upper and lower quartiles for the boys’ data. 2 marks

_______________________________________________________________________________________


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ii Show if there is an outlier in the boys’ data. 2 marks

_______________________________________________________________________________________

d A company manufactures cylindrical pipes all of length 70 cm. The approximate capacity, in litres, of the pipes for different diameters is shown by the graph.

Capacity(litres)

600

550

500

450

400

350

300

250

200

150

100

50

10 20 30 40 50 60 70 80 90 100 110 120

Diameter (cm)

i What would be the diameter of a pipe with capacity 100 litres? 1 mark

_______________________________________________________________________________________

_______________________________________________________________________________________

ii Carmel predicted that a pipe with diameter 120 cm would have a capacity of 600 litres. Do you agree with this prediction? Briefl y comment. 2 marks

_______________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________

iii If the capacity can be approximated using the formula C = 0.055d 2, fi nd the capacity when d = 120. 1 mark

_______________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________


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a Twenty-fi ve swimmers participated in an interstate diving competition. Each dive was awarded points on a scale of 1 to 10. The distribution of the point scores is shown in the following table.

Point score 4 5 6 7 8 9 10

Number of swimmers 2 1 3 5 6 5 3

i Find the mean. 1 mark

_______________________________________________________________________________________

_______________________________________________________________________________________

ii Find the standard deviation correct to two decimal places. 1 mark

_______________________________________________________________________________________

_______________________________________________________________________________________

iii How many of the scores lie within two standard deviations of the mean? 1 mark

_______________________________________________________________________________________

_______________________________________________________________________________________

iv If one of the 25 swimmers is chosen at random, what is the probability that this swimmer’s dive score is less than 7? 2 marks

_______________________________________________________________________________________

_______________________________________________________________________________________

b Two red and eight blue pens are in a box. Leah selects two pens at random, without replacement.

i Complete the tree diagram, by writing the probabilities on each of the branches. 1 mark

ii What is the probability that the pens are different colours? 1 mark

_______________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________

1st pen

2nd pen

R

B

RB

B

R


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iii What is the probability that at least one of the pens is red? 1 mark

_______________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________

c A water reservoir is constructed as shown.

30 m

33 m

26 m

25 m20 m

60 m

15 m

12 m19 m

10 m

One end is semicircular, while the other end is rectangular. The length of the reservoir is 60 m, with rectangular cross-sections at regular intervals as shown.

i Calculate the area of the semicircular end. 2 marks

_______________________________________________________________________________________

ii Calculate the area of the opposite rectangular end. 1 mark

_______________________________________________________________________________________

iii Using two applications of Simpson’s rule, calculate the area of the tank, correct to the nearest tenth of a cubic metre. 3 marks

_______________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________

iv How many litres of water can the tank hold? 1 mark

_______________________________________________________________________________________


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Sample HSC Examination 2Total time: 2½ hours Total marks: 100

SECTION I Marks: 25

Instructions • Attempt Questions 1 to 25. • Allow about 35 minutes for this section. • Each question is worth 1 mark. • Circle only ONE option.

1 The graph shows the typing speed for a student.

00

20

40

60

80

100

120

1

Wor

ds p

er m

inut

e

2 3 4 5Weeks of practice

6 7 8 9 10

Based on the line of best fit, what would be the approximate typing speed, in words per minute, of a person who has practised for 8 weeks?

A 40 B 48 C 62 D 81

2 The locations of Hong Kong and Sydney are (22° N, 115° E) and (33° S, 150° E) respectively. The difference in longitude between Hong Kong and Sydney is:

A 11° B 35° C 55° D 265°

3 Present value of $1Interest rate per month

r 0.0038 0.0042 0.0046 0.0050 0.0054 0.0058N24 22.8966 22.7846 22.6734 22.5629 22.4531 22.3441

36 33.5866 33.3457 33.1072 32.8710 32.6372 32.4057

48 43.8010 43.3888 42.9819 42.5803 42.1839 41.7926

60 53.5610 52.9393 52.3275 51.7256 51.1332 50.5502

72 62.8866 62.0213 61.1724 60.3395 59.5224 58.7206

Susie’s monthly repayment for a car loan of $6000 with interest charged at 7% p.a. over 5 years is:

A $115.22 B $118.69 C $139.59 D $140.26

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Sample HSC Examination 24 Each division represents 10 m.

Calculate the approximate area of this lake.

A 39 m2 B 390 m2

C 3900 m2 D 39 000 m2

5 John is driving a car at a constant speed of 120 km/h. What distance will he cover in 1 hour and 15 minutes?A 96 km B 125 km C 145 km D 150 km

6 For the set of scores 30, 60, 70, 30, 50 fi nd the difference between the mode and the median.A 10 B 20 C 30 D 40

7 The graph shows a typical household’s water use.

A typical family uses 240 kL water each year. From this graph, approximately how much water was used in the garden?A 80 000 L B 100 000 L C 120 000 L D 140 000 L

8 For the formula V = u + at, fi nd the value of V if u = 32, a = 3.5 and t = 6.A 11 B 53 C 213 D 672

9 Clark’s formula for calculating the medicinal dosage for children isweight 1kg 2 × adult dosage

70What weight should a child be to receive one-quarter the adult dosage of the medicine?A 15 kg B 17.5 kg C 20 kg D 22.5 kg

10 Simplify 16x – 12 + 4x + 2.

A 12x – 10 B 12x + 10 C 20x + 10 D 20x – 10

11 How many fi les of size 4.8 MB can be stored on a hard drive of 4 GB?

A 4 × 1024 ÷ 4.8 B 4 × 1024 × 4.8 C 4 × 4.8 ÷ 1024 D 1024 ÷ (4 × 4.8)

10 m

Kitchen

Laundry

Bathroom

Garden

Toilet


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Sample HSC Examination 212 Which of the following formulae can be used to fi nd the length x?

A a2 = b2 + c2 – 2bc cos A B cos A = b2 + c2 − a2

2bc

C A = 12 ab sin C D

asin A

= bsin B

13 Find the interquartile range for the stem-and-leaf plot shown.

A 20 B 20.5

C 25 D 38

14 Anne buys 2 tickets in a raffl e in which 50 tickets are sold and there are 2 prizes. What is the probability of Anne winning both prizes?

A 250+ 1

50 B

250× 1

50 C

250+ 1

49 D

250× 1

49

15 A concrete pipe has an inner diameter of 20 cm and is 3 cm thick. What volume of concrete is used to make a pipe section 15 m long?

A 0.3 m3 B 0.43 m3 C 3251.55 m3 D 6078.98 m3

16 By applying one application of Simpson’s rule, which of the following expressions will give the area of the fi eld?

A 403

(55 + 280 + 35) B 803

(55 + 280 + 35)

C 403

(55 + 70 + 35) D 803

(55 + 70 + 35)

17 Life expectancy in China in 1960 was 43.5 years. In 2010 it was 73.3 years. The percentage increase in these 50 years is:

A 29.8% B 40.7% C 54.4% D 68.5%

18 In the triangle drawn, the value of y is given by:A y = 9 cos 63° B y = 9 sin 63°

C y = 9

cos 63° D y =

9sin 63°

19 32x5y3 ÷ 20x2y4 =

A 85x7y7 B

8x3

5y C

85x3y D

8x10

5y12

x Q

P

R

23 cm

110

30

2 1 1 3 6 8

3 2 3 4 5 9

4 1 2 4 6 8

5 3 4 5 8 9

35 m70 m55 m

40 m 40 m

63

9y


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Sample HSC Examination 220 In the solution of the equation below, which lines do not follow correctly from the previous lines?

3(x – 5) = 5x + 9 3x – 5 = 5x + 9 Line 1 5 = 2x + 9 Line 2 –4 = 2x Line 3 –2 = x Line 4

A Lines 2 and 4 B Lines 1 and 2 C Lines 1 and 3 D Lines 2 and 3

21 Increase $5000 by 20% and then decrease the fi nal amount by 20%. The answer is:

A $4800 B $5000 C $5400 D $6000

22 Matthew took out a loan of $9000 at the fl at interest rate of 8% p.a. over a term of 36 months. How much will he have to repay?

A $6840 B $11 337 C $11 160 D $2160

23 The equation of this graph could be:

A y = x2 + 3 B y = x3 + 3

C y = 3x D y = 3x

24 The mean of a set of 6 scores is 35. What is the new mean of a set of scores after a score of 56 is added?

A 39 B 3.75 C 38 D 15

25 Find the volume of the triangular prism.

A 1560 cm3 B 1200 cm3

C 300 cm3 D 600 cm3

y

31

1 x

20 cm

Q R

P

12 c

m

13 cm

S

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Sample HSC Examination 2SECTION II Marks: 75

Instructions • Attempt Questions 26 to 30. • Allow about 1 hour 55 minutes for this section. • Show all relevant mathematical reasoning and/or calculations.

Question 26

a i Given that x3 = 2.16 × 108, fi nd the value of x. 1 mark

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ii Find the exact value of 23(m3 – m2 + m) when m = –3. 1 mark

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iii Solve for x: 4(x – 3) = 9 – 3(x + 2). 2 marks

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b i A car travels at 90 km/h for 214 hours and at 110 km/h for 13

4 hours. Find the total distance travelled. 1 mark

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ii If this distance is travelled on 50 L of petrol how far would the car travel on 35 L of petrol? 1 mark

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c The graph shows the line of best fi t in an experiment where the burning time of a candle was measured.

00

2

4

6

8

10

12

14

16

18

20

22

24

26

28

0.5

Burn

ing

tim

e (m

inut

es)

1 1.5 2 2.5Length of candle (cm)

3 3.5 4 4.5 5

i Name the dependent variable. 1 mark

______________________________________________________________________________________

ii What is the y-intercept of this line? 1 mark

______________________________________________________________________________________

iii What is the signifi cance of the y-intercept? 1 mark

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iv What is the gradient of the line, correct to one decimal place? 2 marks

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v Write the equation of the line in the form y = mx + b in terms of the given variables. 2 marks

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d If the average peak rate for electricity is $0.25 per kilowatt-hour, calculate the cost of running a 200-watt TV for 7 hours and a 180-watt computer for 8 hours during peak time. 2 marks

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a Penny made up a game to be played by tossing a die. If the uppermost face shows a 6 the player wins $4, if it shows a 4 the player wins $3 and if it shows a 2 the player wins $2. If the player tosses an odd number, she or he loses $1.

i What is the fi nancial expectation when playing this game? 2 marks

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ii If Penny charged $1 to play the game, would you recommend someone to play the game?Justify your answer. 2 marks

______________________________________________________________________________________

______________________________________________________________________________________

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b The following survey is a fi eld book entry when a block of land was surveyed. All dimensions are in metres.

B

70D 25 50

15 12 C0A

i Draw a sketch of the block of land. 2 marks

ii Calculate the area of the block of land. 2 marks

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iii Find the length of the boundary ADB, to the nearest metre. 2 marks

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c Cairo (30°N, 31°E) and Durban (30°S, 31°E) lie on the same great circle.

i What is the angular distance between these two cities along the great circle? 1 mark

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ii Find the distance between the two cities along the great circle, in kilometres.(You may assume the radius of the Earth is 6400 km.) 1 mark

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d For calculating medicinal doses,

Young’s formula (children 1–12 years): Dosage = age of child 1 in years 2 × adult dosage

age of child 1 in years 2 + 12

Clark’s formula: Dosage = weight in kg × adult dosage

70

i If the usual adult dose of a drug is 60 mg, use Young’s formula to fi nd the dose for a child of 7 years, weighing 28 kg. 1 mark

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ii Use Clarke’s formula to calculate the dose for a child of 7 years, weighing 28 kg. 1 mark

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iii Suggest a reason for why the doses calculated above using the two formulae are different. 1 mark

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a The weight of the contents of cans of a particular brand of dog food is normally distributed with mean 757 g and standard deviation 3.5 g. There are 24 cans per carton. In a shipment of 20 cartons of this dog food, how many cans would you expect to have less than the labelled weight of 750 g? 3 marks

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b The graph shows the life expectancy of people from Cambodia and Myanmar (formerly known as Burma).

196030

40

50

60

70

Life

exp

ecta

ncy

(yea

rs)

1965 1970 1975 1980 1985Year

1990 1995

Cambodia

Myanmar

2000 2005 2010

i When did the life expectancy for someone from Myanmar reach 60 years of age? 1 mark

_______________________________________________________________________________________

ii How many years later did an average Cambodian reach a life expectancy of 60 years than someone from Myanmar? 1 mark

_______________________________________________________________________________________

iii The curve for Myanmar is approximately linear. Assuming it is a line, calculate the gradient of this curve. 2 marks

_______________________________________________________________________________________

iv By how many years is the life expectancy for someone from Myanmar increasing each decade? 1 mark

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c The points P, Q and R on the diagram represent three towns. Q is due west of P. The bearing of R from P is 240° and the bearing of R from Q is 205°. The distance from Q to R is 58 km.

Q P

R

58 km

i What is the size of ∠PQR? 2 marks

_______________________________________________________________________________________

_______________________________________________________________________________________

ii What is the size of ∠QPR? 2 marks

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iii Find the distance from P to R, to the nearest kilometre. 2 marks

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iv What is the bearing of P from R? 1 mark

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a Ben invests $5000 into a savings fund. Interest is paid at the rate of 6.5% p.a. compounded monthly on this amount. How much will the investment be worth at the end of 25 years? (Give your answer to the nearest dollar.) 2 marks

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b In a certain state the stamp duty for a new private car is as shown. 2 marks

Car value Stamp duty$600 or less $20

$601 to $35 000 3% ($3 for every $100 or part thereof)

$35 001 to $40 000 $1050 + 11% for the proportion over $35 000

$40 001 and over 4% ($4 for every $100 or part thereof)

How much more in stamp duty is paid for a vehicle costing $40 000 than one costing $20 000?

__________________________________________________________________________________________

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c Tim wants to fence a small rectangular yard for his dog. He intends to use the back wall of his shed as one side and an existing fence as another side so that he only needs to fence two sides as shown in the diagram. He has enough materials to fence 8 m. The length of one side is x m.

i Show that the area A m2 of the yard is given by A = 8x − x2 2 marks

_______________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________

The graph of A = 8x – x2 is a parabola as shown below.

Existingfence

x

Shed

A = 8x – x2

A

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ii What value of x will make the area a maximum? 1 mark

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iii What is the largest possible area of the yard? 1 mark

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iv What shape is the yard when the area is a maximum? 1 mark

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v Tim decides his dog needs a bigger yard. He has worked out the maximum area for different lengths of fence. These results are shown in the table.

Length of fence (l) 10 12 14 16 18 20 22 24

Maximum area (M) 25 36 49 64 81 100 121 144

Write an equation that describes the relationship between M and l. 2 marks

_______________________________________________________________________________________

d A survey was taken of the number of phone calls made in a business offi ce over a 24-hour period.

i How many calls were made altogether? 1 mark

_______________________________________________________________________________________

ii What percentage of calls were made between 12 pm and 4 pm? 1 mark

_______________________________________________________________________________________

iii Offpeak calls occur between 8 pm and 8 am. If the total cost for these calls is $11, calculate the charge for each call. 2 marks

_______________________________________________________________________________________

Freq

uenc

y

0

20

30

40

50

10

8 am

– 12

pm

12 p

m –

4 pm

4 pm

– 8

pm

8 pm

– 12

am

12 a

m –

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4 am

– 8

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a Calculate the difference in the surface area of a tennis ball (radius 3.5 cm) and a soccer ball (radius 10 cm). Give your answer correct to two signifi cant fi gures. 3 marks

__________________________________________________________________________________________

__________________________________________________________________________________________

b Students in two classes recorded how many sit-ups they could complete in one minute. The results are shown on the box-and-whisker plots below.

5 10 15 20 25 30 35 40 45 50 55 60 65 70

Class 2

Class 1

i Describe the general shape of the data for class 1. 1 mark

_______________________________________________________________________________________

ii What percentage of students in class 2 completed between 35 and 50 sit-ups? 1 mark

_______________________________________________________________________________________

iii Given that there is an equal number of students in both classes, compare and contrast the results. 2 marks

_______________________________________________________________________________________

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c The angle of depression made by a ladder against a wall is 70°. If a 3m ladder positioned at the same spot reaches 1.5 m lower down the wall, calculate its angle of elevation to the nearest degree. 2 marks

A

D

B C

70°

3 m

1.5 m

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d Michelle and Holly decide to set aside regular sums of money to save for future expenses. Use the table below to answer the following questions.

Future value of $1Interest rate per period

Period 3% 4% 5% 6% 10%1 1.0000 1.0000 1.0000 1.0000 1.0000

2 2.0300 2.0400 2.0500 2.0600 2.1000

3 3.0909 3.1216 3.1525 3.1836 3.3100

4 4.1836 4.2465 4.3101 4.3746 4.6410

5 5.3091 5.4163 5.5256 5.6371 6.1051

10 11.4639 12.0061 12.5779 13.1808 15.9374

20 26.8704 29.7781 33.0660 36.7856 57.2750

i Michelle chooses to set aside $600 every 6 months. If she earns 10% interest per annum, how much will she have in 5 years? 2 marks

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ii If Holly saves $1200 per year, how much will her investment amount to in 5 years, if interest is charged at the same rate? 1 mark

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iii Both girls have a savings goal of $10 000. How much more would they each have to put into their savings account to reach their goal in 5 years? Answer to the nearest dollar. 3 marks

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Answers

291Answers

PAGE 231 1 a 0.8 kW × 3.5 hours = 2.8 kWh b 2.8 kWh × 0.24 dollars per kWh = $0.67 c 1.2 × 2 = 2.4 kWh d 2.4 × 0.24 = $0.58 e 0.5 × 4 = 2.0 kWh f 2.0 × 0.24 = $0.48 g 3.0 × 40 = 120 kWh h 120 × 0.24 = $28.80 i 0.54 × 168 = 90.72 kWh j 90.72 × 0.24 = $21.77 k 0.028 × 1000 = 28 kWh l 28 × 0.24 = $6.72 m 0.15 × 42 = 6.3 kWh n 6.3 × 0.24 = $1.51 2 a i 202 × 10 × 0.21 = $424.20 ii 221 × 10 × 0.21 = $464.10 iii 160 × 10 × 0.21 = $336.00 iv 240 × 10 × 0.21 = $504.00 b Not a strong relationship. Sets W and Z are almost the same size yet there is around an $80 difference in their running costs over 10 years. c 24 × 365 = 8760 hours d 0.25 W = 0.000 25 kW, or 2.5 × 10–4 kW so energy used for the year is 0.000 25 × 8760 = 2.19 kWh. Cost = 2.19 × 0.21 = $0.46 e $0.46 × 5 = $2.30

PAGE 232 1 a 0.51 b 1 star is pegged at 1; 2 stars is 0.8 × 1 = 0.8; 3 stars is 0.8 × 0.8 × 1 = 0.64; and so 4 stars is 0.8 × 0.8 × 0.8 × 1 = 0.512 which is the value on the graph. c From the graph this is 0.45 d energy effi cient e False. Between 1 and 2 stars there is a 0.2 drop. Between, say, 4 and 5 stars the drop is 0.51 – 0.41 = 0.1 drop. 2 a i 0.77 × 0.77 = 0.5929 ii 0.77 × 0.77 × 0.77 = 0.4565 iii (0.77)4 = 0.3515 iv (0.77)5 = 0.2707 b From part (a) you can see a formula developing. CEC = 0.77star rating – 1. Using this, the comparative energy consumption is 0.777 = 0.1605.

PAGE 233 1 a b 2027 c In 2040 the cost is $184 per MWh. This is

18 400 cents per 1000 kWh. Hence the cost is 18.4¢/kWh. d Except for existing coal, the costs of generating electricity by various means will slowly decrease over the decades. e i Existing coal ii Solar f Coal g Nuclear h No, although the trend appears to be heading in that direction. We have no idea whether the trend will continue well past 2050. It may stabilise at some point above coal. i Coal is a non-renewable resource. This means at some time (several hundred years from now) the amount of coal still available to be burned will be far less. Costs for coal-generated electricity will rise and coal use will ultimately cease altogether. 2 a 100 – (76.7 + 1.0 + 15.0 + 4.7 + 1.5) = 1.1% b Solar, tidal, geothermal etc. c Coal, oil, natural gas d 76.7 + 1.0 + 15.0 = 92.7% e These non-renewable resources will eventually run out. (It is more likely it will become too expensive to remove the few remaining isolated remnants from the grounds.) Also if we are to have an impact on reducing CO2 emissions, we need to develop alternative CO2-neutral sources of energy.

PAGE 234 1 A 2 B 3 C 4 A 5 C 6 D 7 A 8 B 9 D

PAGES 235-236 10 a 346 × 7.5 = 2595 Wh = 2.595 kWh b 0.346 kW are used each hour, and this costs $0.0590. So 1 kWh = $0.0590/0.346 = $0.170 or 17¢/kWh c $0.0590 × 7.5 × 365 = $161.51

(Or, if using 365.25 days, $0.0590 × 7.5 × 365.25 = $161.62.) 11 a 3 months: June, July, August b i 437.76312 688

= $0.0014

ii 295.220.0594

= 4970 iii 5103 × 0.0396 = $202.08 iv 437.76 + 295.22 + 202.08 = $935.06

12 a i To walk 10 km takes 2 h (2 × 60 × 60 = 7200 seconds). Energy = 100 × 7200 = 720 000 J = 720 kJ

ii To ride 10 km takes 1025

h = 25 = 24 minutes = 24 × 60 = 1440 seconds. Energy = 100 × 1440 = 144 000 J = 144 kJ

b The energy required to cover this distance by bike is 144720

= 15 of the energy used in walking. So riding a bike is about 5 times as

effi cient as walking.13 a 4 stars b Values are discrete, not continuous. You can have, say, 2 stars, 2½ stars, 3 stars etc. but you can’t have 2¾ stars.

c No, the points do not line up in a straight line. The drop decreases with higher star ratings. d Around 310

of the BEC14 Electricity used = 2.6 × 8 × 30 = 624 kWh. Cost = 624 × 0.22 = $137.28

CHAPTER 19—Sample HSC ExaminationsPAGES 237-249 1 A 2 C 3 C 4 C 5 D 6 A 7 B 8 C 9 C 10 C 11 A 12 C

13 C ( 1.5 = x −64

8, therefore x = 8 × 1.5 + 64, x = 76) 14 B 15 B ( earnings = 100 + 0.05 × 10000 + 0.07 × 2500, earnings = $775)

16 D 17 C (variable cost = (450 – 300) ÷ 30 , variable cost = $5 per person. Total cost = 300 + 5 × 40, total cost = $500) 18 A

19 B 20 A (Amount owing = 1800 + 1800 × 0.2342 × 23365

, amount owing = $1826.56) 21 C 22 B 23 C 24 D 25 C

Elec

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Year

Estimated costs of producing electricity in Australia

1002010 2055

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coal (new)coal (existing)

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Answers

291Answers





PAGE 234 1 A 2 B 3 C 4 A 5 C 6 D 7 A 8 B 9 D



= $0.0014

ii 295.220.0594

= 4970 iii 5103 × 0.0396 = $202.08 iv 437.76 + 295.22 + 202.08 = $935.06










13 C ( 1.5 = x −64



19 B 20 A (Amount owing = 1800 + 1800 × 0.2342 × 23365


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Answers


26 a 1000 b i gradient = (62 – 42)/50 = 0.4 ii Around 1977 the life expectancy was about 33 years. iii Perhaps war, famine, a brutal dictatorship. c 37.8 km/h d i x = 9 ii x = 61 e i 70° ii 3361 m2 iii 100 m

27 a i FV = 25 000a1 + 6%4

b5 × 4

, FV = $33 671 (to the nearest dollar) ii FV = 3000 × 12.0061 , FV = $36 018 (to the nearest dollar)

iii 36 018 = PV(1.015)20 , PV = , PV = $26 743 (to the nearest dollar) Therefore, he would need to have invested 26 743 – 25 000 = $1743 more to have the same amount as Sally at the end of 5 years. b In 4 min 39 s there are 10 half-minute blocks.

Cost = 25 + 10 × 31 = 335 cents = $3.35 c i 56 ii 6 d i 63 ii 79% iii 5164

28 a i $14 250 ii $737.50

b i 213 ii While they may not use much water, others do. This table is an average taken from many water users.

iii 18 × 365 = 6570 L iv 213 × 365 = 77 745 L = 77.745 kL v 21.1100

× 213 = 45 L, so it is washing clothes. vi 29213

×1001=13.6%

vii A Saving 20100

× 35 = 7 L/day. B 7 × 365 = 2555 L c 320 m d 29 = w

11.8 2 2. ∴ W = 29 × (1.8)2 = 93.96 kg

29 a i 3 hours and 4 minutes ii 10:56 am iii 8:04 pm b 8936 km c i Lower quartile = 61 upper quartile = 75 ii 1.5 × IQR = 1.5 × 14 = 21. Upper ”fence“ = 75 + 21 = 96. So 97 is an outlier.d i approximately 43 cm ii No, it would have a capacity of more than 600 litres. By extending the graph we can see that it will reach 600 litres before it reaches 120 cm. iii 792 litres

30 a i 7.56 ii 1.68 iii 23 iv 625

b i

1st pen

2nd pen

R

B

RB

B

R

15

19

79

29

89

45

ii 1645

iii 1745

c i Area = 12

π r 2, where r = 5 m ∴ A = 12 × π × 52 = 39.3 m2 ii Area = 30 × 33 = 990 m2

iii The areas of the three internal cross-sections are: A1 = 15 × 12 = 180 m2; A2 = 20 × 19 = 380 m2; A3 = 25 × 26 = 650 m2

Using Simpson’s rule twice: V1 = 153

× {39.3 + 4 × 180 + 380} = 5696.5 m3; V2 = 153

× {380 + 4 × 650 + 990} = 19 850 m3. This gives a

total volume of V = 5696.5 + 19 850 = 25 546.5 m3.iv Now 1 m3 = 1000 L ∴ 25 546.5 m3 = 25 546 500 L

PAGES 250-263 1 D 2 B 3 B (7% p.a. = 0.0058 per month and 5 years = 60 months) 4 C 5 D 6 B 7 B 8 B 9 B 10 D 11 A 12 D 13 B (Median = 40, LQ = 30, UQ = 50.5, IQR = UQ – LQ, IQR = 50.5 – 30, IQR = 20.5) 14 D 15 A 16 A 17 D 18 C 19 B 20 B 21 A 22 C 23 D (This is an exponential graph which passes through (1,3), thus D is the only possible equation.) 24 C 25 D

26 a i 600 ii –26 iii x = 217 b i 395 km ii 276.5 km c i Candle burning time ii 0

iii With no length of candle, there will not be any burning time. iv gradient (m) = 126 −0 213.5 −0 2 =7.4

v Burning time (minutes) = 7.4 × length of candle (cm). (Note b = y-intercept = 0)

d 200 × 7 + 180 × 8 = 2840 watts, 2840 ÷ 1000 = 2.84 kW Therefore, the cost is 2.84 × $0.25 = $0.7127 a i $1 ii Yes. If the cost is $1 the game is fair. The fi nancial expectation is $0.b i ii 1295 m2 iii 88 m c i 60° ii 6702 km

d i Dose = 17 ×60 217 +12 2 = 22.1 mg ii Dose =

128 ×60 270

= 24 mg

iii One formula uses the child’s age, the other the child’s weight. Children of a certain age can vary in weight and so the calculations can yield differing results.

B

D

A

C

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Answers



27 a i FV = 25 000a1 + 6%4

b5 × 4




28 a i $14 250 ii $737.50


iii 18 × 365 = 6570 L iv 213 × 365 = 77 745 L = 77.745 kL v 21.1100


×1001=13.6%

vii A Saving 20100

× 35 = 7 L/day. B 7 × 365 = 2555 L c 320 m d 29 = w

11.8 2 2. ∴ W = 29 × (1.8)2 = 93.96 kg


30 a i 7.56 ii 1.68 iii 23 iv 625

b i

1st pen

2nd pen

R

B

RB

B

R

15

19

79

29

89

45

ii 1645

iii 1745

c i Area = 12




× {39.3 + 4 × 180 + 380} = 5696.5 m3; V2 = 153

× {380 + 4 × 650 + 990} = 19 850 m3. This gives a







d i Dose = 17 ×60 217 +12 2 = 22.1 mg ii Dose =

128 ×60 270

= 24 mg


B

D

A

C

1512

35

25

20


Answers



27 a i FV = 25 000a1 + 6%4

b5 × 4




28 a i $14 250 ii $737.50


iii 18 × 365 = 6570 L iv 213 × 365 = 77 745 L = 77.745 kL v 21.1100


×1001=13.6%

vii A Saving 20100

× 35 = 7 L/day. B 7 × 365 = 2555 L c 320 m d 29 = w

11.8 2 2. ∴ W = 29 × (1.8)2 = 93.96 kg


30 a i 7.56 ii 1.68 iii 23 iv 625

b i

1st pen

2nd pen

R

B

RB

B

R

15

19

79

29

89

45

ii 1645

iii 1745

c i Area = 12




× {39.3 + 4 × 180 + 380} = 5696.5 m3; V2 = 153

× {380 + 4 × 650 + 990} = 19 850 m3. This gives a







d i Dose = 17 ×60 217 +12 2 = 22.1 mg ii Dose =

128 ×60 270

= 24 mg


B

D

A

C

1512

35

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Answers



27 a i FV = 25 000a1 + 6%4

b5 × 4




28 a i $14 250 ii $737.50


iii 18 × 365 = 6570 L iv 213 × 365 = 77 745 L = 77.745 kL v 21.1100


×1001=13.6%

vii A Saving 20100

× 35 = 7 L/day. B 7 × 365 = 2555 L c 320 m d 29 = w

11.8 2 2. ∴ W = 29 × (1.8)2 = 93.96 kg


30 a i 7.56 ii 1.68 iii 23 iv 625

b i

1st pen

2nd pen

R

B

RB

B

R

15

19

79

29

89

45

ii 1645

iii 1745

c i Area = 12




× {39.3 + 4 × 180 + 380} = 5696.5 m3; V2 = 153

× {380 + 4 × 650 + 990} = 19 850 m3. This gives a







d i Dose = 17 ×60 217 +12 2 = 22.1 mg ii Dose =

128 ×60 270

= 24 mg


B

D

A

C

1512

35

25

20


Answers



27 a i FV = 25 000a1 + 6%4

b5 × 4




28 a i $14 250 ii $737.50


iii 18 × 365 = 6570 L iv 213 × 365 = 77 745 L = 77.745 kL v 21.1100


×1001=13.6%

vii A Saving 20100

× 35 = 7 L/day. B 7 × 365 = 2555 L c 320 m d 29 = w

11.8 2 2. ∴ W = 29 × (1.8)2 = 93.96 kg


30 a i 7.56 ii 1.68 iii 23 iv 625

b i

1st pen

2nd pen

R

B

RB

B

R

15

19

79

29

89

45

ii 1645

iii 1745

c i Area = 12




× {39.3 + 4 × 180 + 380} = 5696.5 m3; V2 = 153

× {380 + 4 × 650 + 990} = 19 850 m3. This gives a







d i Dose = 17 ×60 217 +12 2 = 22.1 mg ii Dose =

128 ×60 270

= 24 mg


B

D

A

C

1512

35

25

20


Answers

293Answers

28 a 12 cans b i 1995 ii Cambodians reached this life expectancy age in 2005, around 10 years later.

iii gradient = 164 −43 2

12010 −1960 2 = 0.42 iv Each decade, life expectancy increases by an average of 4.2 years.

c i 115° ii 30° iii 105 km iv 060°

29 a FV = 5000 a1 +6.5%12

b25×12

, FV = 25 280.989 22… , FV = $25 281

b $40 000 vehicle: $1050 + 0.11 × 5000 = $1600; $20 000 vehicle: 0.03 × 20 000 = $600. Difference = $1600 – $600 = $1000 c i If the length is x m, the breadth is (8 – x) m. The area is x(8 – x) m2.

ii x = 4 iii 16 m2 iv Square v M = 14l 2 or M = a l

2b

2

d i Total calls = 25 + 50 + 40 + 25 + 10 + 15 = 165 calls ii 50165

×100 =30.3% iii 50 calls were made in this period, so each call

costs 1150=$0.22 or 22c.

30 a 4p × 10² – 4p × 3.5² = 1102.6990… = 1100 cm²(to 3sf) b i The data for Class 1 is symmetrical ii 25% iii Both classes have the same median (35), while the data for class 2 is more spread out at both ends.

c Angle BCD = 70° – Angle ACD. If angle ACD = sin–11.5sin203

, then the new angle of elevation is 60° to the nearest degree.

d i 600 × 12.5779 = $7546.74 ii 1200 × 6.1051 = $7326.12 iii Michelle: 10000 ÷ 12.5779 = 795.05, 795.05 – 600 = 195.05 Michelle needs to save $195 more per 6 months. Holly: 10000 ÷ 6.1051 = 1637.97, 1637.97 – 1200 = 437.97 Holly needs to save $438 more per year.


Answers

291Answers





PAGE 234 1 A 2 B 3 C 4 A 5 C 6 D 7 A 8 B 9 D



= $0.0014

ii 295.220.0594

= 4970 iii 5103 × 0.0396 = $202.08 iv 437.76 + 295.22 + 202.08 = $935.06










13 C ( 1.5 = x −64



19 B 20 A (Amount owing = 1800 + 1800 × 0.2342 × 23365


Elec

tric

ity

cost

s ($

/MW

h)

Year


1002010 2055

solar

windnuclear


20502045204020352030202520202015

2030405060708090

100110120130140150160170180190200210220230240250


Answers

293Answers

28 a 12 cans b i 1995 ii Cambodians reached this life expectancy age in 2005, around 10 years later.

iii gradient = 164 −43 2

12010 −1960 2 = 0.42 iv Each decade, life expectancy increases by an average of 4.2 years.

c i 115° ii 30° iii 105 km iv 060°

29 a FV = 5000 a1 +6.5%12

b25×12

, FV = 25 280.989 22… , FV = $25 281

b $40 000 vehicle: $1050 + 0.11 × 5000 = $1600; $20 000 vehicle: 0.03 × 20 000 = $600. Difference = $1600 – $600 = $1000 c i If the length is x m, the breadth is (8 – x) m. The area is x(8 – x) m2.

ii x = 4 iii 16 m2 iv Square v M = 14l 2 or M = a l

2b

2

d i Total calls = 25 + 50 + 40 + 25 + 10 + 15 = 165 calls ii 50165

×100 =30.3% iii 50 calls were made in this period, so each call

costs 1150=$0.22 or 22c.

30 a 4p × 10² – 4p × 3.5² = 1102.6990… = 1100 cm²(to 3sf) b i The data for Class 1 is symmetrical ii 25% iii Both classes have the same median (35), while the data for class 2 is more spread out at both ends.

c Angle BCD = 70° – Angle ACD. If angle ACD = sin–11.5sin203

, then the new angle of elevation is 60° to the nearest degree.

d i 600 × 12.5779 = $7546.74 ii 1200 × 6.1051 = $7326.12 iii Michelle: 10000 ÷ 12.5779 = 795.05, 795.05 – 600 = 195.05 Michelle needs to save $195 more per 6 months. Holly: 10000 ÷ 6.1051 = 1637.97, 1637.97 – 1200 = 437.97 Holly needs to save $438 more per year.


© P

asca

l Pre

ss IS

BN

978

1 7

4125

461

7


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