HIGHER SCHOOL CERTIFICATE EXAMINATION 1999 MATHEMATICS IN PRACTICE 2 UNIT Time allowed—Two hours and a half (Plus 5 minutes reading time) DIRECTIONS TO CANDIDATES • Only Board-approved calculators are to be used. • The mark out of 80 will be converted to a mark out of 100. Section I (30 marks) • This Section contains 30 multiple-choice questions. • Attempt ALL questions. • All questions are of equal value. • Complete your answers in either blue or black pen on the Answer Sheet provided. • Allow about one hour for Section I. Section II (50 marks) • Attempt ALL questions. • All questions are of equal value. • Answer the questions in the spaces provided in this paper. • Write your Student Number and Centre Number in the spaces provided on the first page of each question. • Show all necessary working. • Marks may be deducted for careless or badly arranged work. • Allow about one hour and a half for Section II. 587
Transcript
HIGHER SCHOOL CERTIFICATE EXAMINATION
1999
MATHEMATICS INPRACTICE
2 UNITTime allowed—Two hours and a half
(Plus 5 minutes reading time)
DIRECTIONS TO CANDIDATES
• Only Board-approved calculators are to be used.
• The mark out of 80 will be converted to a mark out of 100.
Section I (30 marks)
• This Section contains 30 multiple-choice questions.
• Attempt ALL questions.
• All questions are of equal value.
• Complete your answers in either blue or black pen on the Answer Sheet provided.
• Allow about one hour for Section I.
Section II (50 marks)
• Attempt ALL questions.
• All questions are of equal value.
• Answer the questions in the spaces provided in this paper.
• Write your Student Number and Centre Number in the spaces provided on the first page ofeach question.
• Show all necessary working.
• Marks may be deducted for careless or badly arranged work.
• Allow about one hour and a half for Section II.
587
SECTION I
Attempt ALL questions.
All questions are of equal value.
Instructions for answering multiple-choice questions
• Complete your answers in either blue or black pen.
• Select the alternative A, B, C or D that best answers the question. Fill in the responseoval completely.
Sample: 2 + 4 = (A) 2 (B) 6 (C) 8 (D) 9
If you think you have made a mistake, put a cross through the incorrect answer and fill inthe new answer.
If you change your mind and have crossed out what you consider to be the correct answer,then indicate the correct answer by writing the word correct and drawing an arrow asfollows.
A B C D
correct
A B C D
A B C D
2
1 Below is the logo of the Chase Manhattan Bank.
What is the name given to the shaded shapes in this logo?
(A) Rectangle (B) Parallelogram
(C) Rhombus (D) Trapezium
2 At a sale, a dress that normally sells for $150 is marked down to sell at $120.
The percentage discount is
(A) 5% (B) 20% (C) 25% (D) 30%
3 Jayde has 3 black T-shirts, 4 white T-shirts and 2 blue T-shirts in a drawer.
If she chooses one at random, what is the probability that it will be blue?
(A) (B) (C) (D) 27
49
39
29
$150$120
3
The position of Kalgoorlie on the map is
(A) 31°S 122°E (B) 31°N 122°E
(C) 31°S 122°W (D) 31°N 122°W
5 Mishka has a dress on lay-by at a department store. The price of the dress is $225. Mishkapaid a deposit of 20%, and she will pay the remainder in 12 equal weekly repayments.Calculate the value of each weekly repayment.
(A) $15·00 (B) $17·08 (C) $18·75 (D) $22·50
WESTERN
AUSTRALIA
Albany
Bunbury
FremantlePerth
Geraldton
Kalgoorlie
115 120 125
35
30
25
4
4
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6 By measuring and calculating, determine which of the following is closest to the area ofthe shaded cross.
(A) 11 cm2 (B) 12 cm2 (C) 13 cm2 (D) 26 cm2
7 Which of the following is the highest interest rate?
(A) 0·04% per day (B) 0·27% per week
(C) 1·2% per month (D) 14·5% per annum
8 The graph below shows the main countries of birth of Australian immigrants.
The total number of immigrants from the UK, Ireland and New Zealand is greater thanthe number of immigrants from China by a factor of
(A) 3 (B) 12 (C) 14 (D) 15
UK and Ireland
New Zealand
Italy
Former YugoslavRepublic
Greece
Germany
China
0 200 400 600 800 1000 1200
Population (in thousands)
Cou
ntri
es
5
9 Kim’s airline ticket for a return trip from Sydney to Melbourne includes the followingtimes.
The flight time from Melbourne to Sydney is one hour and five minutes. On what dateand at what time did Kim arrive in Sydney on her return flight?
(A) 3 July, 5:05 pm (B) 7 July, 12:20 pm
(C) 7 July, 1:25 am (D) 7 July, 1:25 pm
10 The table below gives the weekly premiums for a life insurance policy.
Which category has a premium equal to the average of these premiums?
(A) Female, smoker, under 50
(B) Male, smoker, under 50
(C) Female, non-smoker, over 50
(D) Male, non-smoker, over 50
Under 50
Over 50
Smoker
$7·25
$8·85
Non-smoker
$4·75
$6·35
AGE MALE
Smoker
$6·50
$8·10
Non-smoker
$4·25
$5·95
FEMALE
Time
1600
1220
Void
Date
03 July
07 July
Void
Flight
AN 033
AN 020
Void
FROM
Sydney
TO
Melbourne
TO
Sydney
6
11 The Daily Star newspaper charges the following rates for classified advertising:
• first 10 words: 70 cents per word;
• additional words: 65 cents per word;
• border: add $10·00.
Candice advertised a garage sale in the Daily Star.
The cost for placing this advertisement was
(A) $13·50 (B) $14·00 (C) $23·50 (D) $24·00
Jordan drives from Summerville to Springtown at an average speed of 80 km/h. How longdoes the trip take (to the nearest minute)?
18 The graph below shows the Gross National Product (GNP) and life expectancy for anumber of different countries. Each ◆ represents one country.
Jill and Jack made the following statements about the graph:
JILL: ‘The graph shows that a life expectancy greater than 75 years only occurs incountries with a GNP greater than $5000.’
JACK: ‘The overall trend is that as a country’s GNP increases, so does the lifeexpectancy of its people.’
(A) Both statements are true.
(B) Only Jill’s statement is true.
(C) Only Jack’s statement is true.
(D) Both Jill and Jack are wrong.
The exchange rate is $A1 = $US0·625.
If Sebastian and his wife go on this expedition, how much will it cost them in Australiandollars?
(A) 7 100 (B) 9 088 (C) 11 360 (D) 18 176
ANTARCTICAICEBREAKING EXPEDITIONS
Inclusive price: $US5680 per person
19
40 45 50 55 60 65 70 75 800
5 000
10 000
15 000
20 000
25 000
Life expectancy (years)
GN
P ($
US
per
pers
on)
GROSS NATIONAL PRODUCT versus LIFE EXPECTANCY
10
20 The graph below is based on the results of surveys in which people living in Sydney wereasked whether they were likely to leave Sydney during the 2000 Olympic Games.
The population of Sydney is approximately 3 800 000. Based on the Winter 1998 resultsof the surveys, how many Sydneysiders are ‘very likely’ to leave during the2000 Olympics?
(A) 19 (B) 20 (C) 722 000 (D) 760 000
21 When it is 11 am in Perth, the time in Christchurch is 3 pm on the same day.
Danielle lives in Perth and wishes to watch a live telecast of a test match played inChristchurch. The first section of the match commences at 10:30 am (Christchurch localtime) and lasts for 2 hours.
What time will it be in Perth when the first section of the match finishes?
(A) 6:30 am (B) 8:30 am (C) 2:30 pm (D) 4:30 pm
(Summer 1995) (Winter 1998)5
10
15
20
Perc
enta
ge o
f Sy
dney
side
rsESCAPING THE OLYMPICS
Quite likelyto leave
Very likelyto leave
KEY
11
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USE THE MAP BELOW TO ANSWER QUESTIONS 22 and 23.
22 Which of the following is the best approximation for the distance by road from ConnellanAirport to Uluru (Ayers Rock)?
(A) 10 km (B) 25 km (C) 200 km (D) 250 km
23 The direction of Connellan Airport from Kata Tjuta (The Olgas) is
24 A brick wall is 17 m long and 1·8 m high. One side of this wall is to be painted using2 coats of paint. One tin of paint will cover 6 square metres of the wall. How many tinsof paint will be needed?
(A) 5 (B) 6 (C) 10 (D) 11
Lasseter Highway
YularaResort
ToAlice Springs
Docker River Road
Valley of the W
inds
Mt. Olga069
(546)
Kata Tjuta (The Olgas)
Uluru (Ayers Rock)
NgaGorge
ConnellanAirport
SCALE 1 : 250 000
N
12
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25 The table below shows data for land use in Australia.
Joe wishes to draw a pie chart using the percentages given in the table. The correct sizefor the angle of the permanent pastures sector is closest to
(A) 4° (B) 54° (C) 97° (D) 194°
26 Temperature can be measured in degrees Fahrenheit or degrees Celsius. The formula forchanging a temperature in degrees Fahrenheit (F) to a temperature in degrees Celsius (C) is
.
Use this formula to convert 113°F to degrees Celsius.
(A) 30·8°C (B) 45°C (C) 62·8°C (D) 145·8°C
C F= −( )59
32
Percentage
6%
1%
54%
19%
20%
100%
Land use
Arable land
Permanent crops
Permanent pastures
Forests and woodland
Other uses
TOTAL
13
27 Contour lines in a topographical map are lines joining places of equal elevation abovesea-level. The diagram shows the contour lines of a hill. The number on each contour lineis the height above sea-level.
Which one of the following best represents the shape of the cross-section AB of the hill?
28 Property values in a country town are predicted to decrease at a rate of 6% p.a.
If this prediction is correct, how much will a property valued at $275 000 be worth in2 years time?
1999HIGHER SCHOOL CERTIFICATE EXAMINATIONMATHEMATICS IN PRACTICE2 UNIT—SECTION II
Q.33
STUDENT NUMBER
CENTRE NUMBER
25
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QUESTION 33 (Continued)
(b) The plan shows a three-bedroom house with optional fourth bedroom and rumpus roomincorporated in the design.
Bed 43·25 × 3·00(optional)
Rumpus7·02 × 4·7(optional)
Family3·31 × 3·50
Laundry
Bathroom
Bed 33·25 × 3·00
Kitchen3·99 × 3·61
Dine3·75 × 3·50
Bed 23·25 × 3·00
Bed 13·78 × 3·50
Lounge5·10 × 4·86
Garage5·63 × 5·45
Verandah
Bathroom
Entry
All dimensionsin metres
26
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QUESTION 33 (Continued)
The cost of building the three-bedroom house (without options) is $95 000. Theadditional bedroom costs $5000 to build, and the rumpus room costs $8000.
(i) What is the total cost of building the house, including the fourth bedroom and therumpus room?
(a) To win a game of ‘Losso’, Sally must correctly choose six numbers from the numbers1 to 42. There are 5 245 786 different combinations of six numbers.
What is the probability that Sally chooses the winning numbers?
(iv) The column graph below is based on the data for average life expectancy. Drawthe column for Fiji on this graph.
AVERAGE LIFE EXPECTANCY
(d) In the United States of America there are 99 million households with TV sets. Regularsurveys are conducted to determine the number of households that watch particularTV shows. One company that conducts these surveys uses a random sample of 50 000households.
(i) What percentage of households with TV sets is surveyed?
(iii) Of the households surveyed, 30 000 watched a music awards telecast. Based onthis sample, how many of the 99 million households watched these awards?
