mathematics sctest 06

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Mathematics

2006 School Certificate Test

S1

General Instructions

Reading time: 5 minutes

Working time: 2 hours

There will be a short breakbetween Section 1 and Section 2

Write using black or blue pen

You may use a pencil to drawor complete diagrams

Attempt ALL questions

Calculators may be used inSection 2 only

A formulae sheet is providedwith this paper

Write your Centre Numberand Student Number at thetop of pages 3 and 35

Total marks 100

Section 1

Pages 310

25 marks

Time allowed for this section is 30 minutes

Questions 125 25 marks

Section 2

Pages 1141

75 marks

Time allowed for this section is 1 hour and

30 minutes

This section has TWO parts

Part A Questions 2680 55 marksPart B Questions 8184 20 marks


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2

Formulae

For use in both SECTION 1 and SECTION 2

Circumference of a circle diameter or r= 2 aadius

Area of a circle

C d C r= =

=

2

rradius squared

Area of a parallel

A r=

2

oogram base perpendicular height

Ar

=

= A bh

eea of a rhombus half the product of the di= aagonals

Area of a trapezium ha

A xy=

=

1

2

llf the perpendicular height the sum of the parallel sides

Volume of

A h a b= +( )

12

aa prism base area height

Volume of

=

= V Ah

a cylinder radius squared height=

=

V r h2

= Simple interest principal annual intereest rate number of years

Pythagor

= I PRT

aas theorem states: Ina right-angled triaangle, the hypotenuse squared is equal to

the sum of the squares ofthe other two sides

c a b2 2 2= +

Board of Studies NSW 2006


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S2

25 marks

Time allowed for this section is 30 minutes

Answer Questions 125 in the spacesprovided

Calculators are NOT to be used in thisSection

There will be a short break betweenSection 1 and Section 2

Centre Number

Student Number

Section 1


Mathematics

3


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4

Answer the questions in the spaces provided.

1 8.49 + 2.1 =

.............................................................................................................................................

.............................................................................................................................................

.............................................................................................................................................

What is the value of cos ?

.............................................................................................................................................

.............................................................................................................................................

3 In the 1849 California gold rush, 40 thousand miners extracted 10 million dollarsworth of gold.

What was the average value of gold found by each miner?

.............................................................................................................................................

.............................................................................................................................................

.............................................................................................................................................

.............................................................................................................................................

4 How many thirds are there in 2?

.............................................................................................................................................

.............................................................................................................................................

5NOT TOSCALE

13

12

2


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5

5 270 mL of water is to be poured into a measuring cylinder.

Draw a line on the measuring cylinder to show how high the water would reach.

6 The selling price of balsamic vinegar is 2 times the wholesale price. The

wholesale price is $14.

What is the selling price of the vinegar?

.............................................................................................................................................

.............................................................................................................................................

7 336 21 = 16

What is the value of 336 2.1?

.............................................................................................................................................

.............................................................................................................................................

8 Arrange the following from smallest to largest.

, 0.5, 5%, 5

.............................................................................................................................................

.............................................................................................................................................

9 If the sun rises at 5.20 am and sets at 8.06 pm, how many hours and minutes arethere from sunrise to sunset?

.............................................................................................................................................

.............................................................................................................................................

15

12

mL

100

200

300


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6

10 Robert wishes to download a 6000 kilobyte file. His internet connection has aspeed of 20 kilobytes per second.

How many minutes will it take to download this file?

.............................................................................................................................................

.............................................................................................................................................

11 Add 0.3

to .

.............................................................................................................................................

.............................................................................................................................................

12 A (2, 4) and B (1, 0) are points on the number plane.

Calculate the length ofAB.

.............................................................................................................................................

.............................................................................................................................................

13 A spinner is in the shape of a regular hexagon. Each section is to be labelledeither red, blue, or green.

Label the sections so that the probability of this spinner landing on red is , on

blue is and on green is .1213

16

xO

y

B

(1, 0)

A (2, 4)

12


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7

14 where is a whole number.

What is the largest possible value for ?

.............................................................................................................................................

.............................................................................................................................................

15 The area of a rhombus is 36 cm2. One of the diagonals is twice as long as the other.

Find the lengths of the diagonals.

.............................................................................................................................................

.............................................................................................................................................

.............................................................................................................................................

Use the net below to answer Questions 16 and 17.

16 What is the name of the solid formed by this net?

.............................................................................................................................................

17 Calculate the volume of this solid.

.............................................................................................................................................

.............................................................................................................................................

.............................................................................................................................................

7 unitsunits7 units

3

5

2


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8

18 Consider the pattern.

53 = 125

54 = 625

55

= 312556 = 15625

Use this pattern to write the last three digits of 515.

.............................................................................................................................................

19 Greg and Megan are cycling around a track in the same direction. To completeeach lap, Greg takes 20 seconds and Megan takes 16 seconds.

Megan passes Greg.

After how many seconds will Megan pass Greg again?

.............................................................................................................................................

.............................................................................................................................................

.............................................................................................................................................

20 Mason records the weights of four parcels. He notes that the median is 4 kg,the mode is 5 kg and the mean is 4 kg.

What is the weight of each parcel?

.............................................................................................................................................

.............................................................................................................................................

.............................................................................................................................................

21 The ratio of $10 notes to $20 notes in my wallet is 4 : 5. There are 27 notes altogether.

What is the total value of the 27 notes?

.............................................................................................................................................

.............................................................................................................................................

.............................................................................................................................................

.............................................................................................................................................

12


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9

22 Sumayia claims that 22 23 = 45.

Explain why Sumayia is incorrect.

.............................................................................................................................................

.............................................................................................................................................

.............................................................................................................................................

.............................................................................................................................................

23 The intervalAB has midpointM.

Find the coordinates of B.

.............................................................................................................................................

.............................................................................................................................................

.............................................................................................................................................

24 (9.65 106) (5 104) =

.............................................................................................................................................

.............................................................................................................................................

.............................................................................................................................................

x

B

M (3, 4)A (1, 2)

y

O


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10

25 The diagram shows a sketch (not to scale) of the shape Jo wishes to construct.

Jo has already drawn the sidesAB andADbelow.

Use your instruments to complete the shape accurately.

End of Section 1

BA

D

5 cm

3 cm

6

A

B

C

D

5

23

NOT TOSCALE

Board of Studies NSW 2006


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Section 2

S3

75 marksTime allowed for this section is1 hour and 30 minutes

This section has TWO parts

Part A Questions 2680 55 marksPart B Questions 8184 20 marks

Calculators may be used in this section

Do not commence Section 2 until you areinstructed to do so


Mathematics

11


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12

Part A


Use the Section 2 Part A Answer Sheet for Questions 2680.

Instructions for answering multiple-choice questions

For Questions 2675, select the alternative A, B, C or D that best answers thequestion. Fill in the response oval completely.

Sample: 2 + 4 = (A) 2 (B) 6 (C) 8 (D) 9

A B C D

If you think you have made a mistake, put a cross through the incorrectanswer and fill in the new answer.

A B C D

If you change your mind and have crossed out what you consider to be thecorrect answer, then indicate the correct answer by writing the word correctand drawing an arrow as follows.

correct

A B C D


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13

26 Two angles in this parallelogram are labelled with the letter r.

What type of angles are these?

(A) Alternate

(B) Co-interior

(C) Corresponding

(D) Supplementary

27 How many whole numbers from 10 to 99 have the sum of their digits equal to 9?

(A) 9 (B) 10 (C) 18 (D) 90

28 A survey of car colours was conducted.

Which measure could be used to analyse the data?

(A) Mode (B) Mean (C) Median (D) Range

29 4a3 2a2 =

(A) 6a5 (B) 6a6 (C) 8a5 (D) 8a6

r

r


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14

30 The triangles shown are similar.

Which statement names the triangles with vertices in corresponding order?

(A) ABC CDE

(B) ABC ECD

(C) ABC DEC

(D) ABC EDC

31 What is 0.00457 in scientific notation?

(A) 45.7 104 (B) 4.57 103 (C) 4.57 102 (D) 4.57 103

32 A straight line was created using the following table of values.

What are the x- andy-intercepts for this line?

(A) x-intercept = 6, y-intercept = 2

(B) x-intercept = 0, y-intercept = 0(C) x-intercept = 2, y-intercept = 6

(D) x-intercept = 3, y-intercept = 3

33 Brad and Scott share $60 in the ratio of 3 : 2.

How much does Brad receive?

(A) $20 (B) $24 (C) $30 (D) $36

x 0 1 2 3

y 6 3 0 3

A

B

C

D

E


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15

34 Sharyn was asked to find the value of x.

In two steps, she correctly found the value of x.

Which types of angles could Sharyn have used?

(A) Corresponding and co-interior angles

(B) Vertically opposite and co-interior angles

(C) Alternate and corresponding angles

(D) Corresponding and vertically opposite angles

35 Expand 3(2x + 5).

(A) 5x 15 (B) 6x + 5 (C) 6x + 15 (D) 6x 15

36 Chocolates cost 65 cents each. Janina has $10 and buys as many chocolates as shecan with her money.

How much change will she receive?

(A) 15 cents (B) 25 cents (C) 35 cents (D) 40 cents

100

x


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16

37 The area of the trapezium is 36 cm2.

What are possible values of a and b?

(A) a = 2, b = 4

(B) a = 2, b = 6(C) a = 3, b = 4

(D) a = 3, b = 9

38 Each student in a class was asked to draw a rectangle, an isosceles triangle,a trapezium and an equilateral triangle of any size.

After looking at all of the drawings, what correct conclusion could a studentmake?

(A) All the rectangles will be similar.

(B) All the trapeziums will be similar.

(C) All the isosceles triangles will be similar.

(D) All the equilateral triangles will be similar.

39 Factorise 2x2 + 6x.

(A) 2x(x + 3) (B) 2x(x + 4) (C) 2x(x + 6) (D) 2x(2x + 3)

NOT TOSCALE

6 cm

b cm

a cm


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17

40 ABCD is a kite. BAD = 120 and ADC = 70.

What is the size of BCD?

(A) 60 (B) 100 (C) 110 (D) 120

41 The length and breadth of a rectangle are both doubled.

What effect does this have on the perimeter and area of the rectangle?

(A) Both the perimeter and the area are doubled.

(B) Both the perimeter and the area are multiplied by 4.

(C) The perimeter is multiplied by 4 and the area is doubled.

(D) The perimeter is doubled and the area is multiplied by 4.

NOT TOSCALE

A

120

70

C

D B


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18

42 Samuel travels to work each day by train. To be at work on time he must arriveat Kings Cross station by ten past eight.

What is the latest train Samuel can catch from Sutherland station?

(A) 7.20 am (B) 7.24 am (C) 7.31 am (D) 7.34 am

43 600 people were surveyed about the type of camera they use.

A sector graph was drawn showing the results. The sector representing mobile-phone cameras has an angle of 30 at the centre.

How many people in the survey use mobile-phone cameras?

(A) 12 (B) 20 (C) 50 (D) 180

am am am am am am am am am

Waterfall 7.05 6.53 7.08

Heathcote 6.58 7.13

Engadine 7.01 7.16

Loftus 7.05 7.20

Sutherland 7.15 7.09 7.20 7.24 7.31 7.34

Jannali 7.11 7.22 7.26 7.36

Como 7.14 7.29

Central 7.40 7.43 7.46 7.52 7.57 8.01 8.02 8.06 8.10

Town Hall 7.43 7.46 7.49 7.55 8.00 8.04 8.09 8.13

Martin Place 7.45 7.48 7.53 7.57 8.02 8.06 8.11 8.15

Kings Cross 7.48 7.56 8.00 8.05 8.09 8.14 8.18

Edgecliff 7.50 7.58 8.02 8.07 8.11 8.16 8.20

Bondi Junction 7.53 8.01 8.05 8.10 8.14 8.19 8.23


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19

44 Lilli was asked to graph y = 2x. She used the following table of values to plotthe points.

Which of the following is the correct graph?

45 Evan bought a television set priced at $5000. He bought it on terms by paying$215.25 per month for three years.

How much interest did Evan pay?

(A) $2583 (B) $2749 (C) $7583 (D) $7749

(A)

1

xO

y (B)

1

xO

y

(C)

1

xO

y (D)

1

xO

y

1 1

1 1

x 0 1 2

y 1 2 4


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20

What is the value ofp?

(A) 35 (B) 70 (C) 75 (D) 110

47 In which quadrilaterals do the diagonals always intersect at right angles?

(A) Kite, square, rhombus

(B) Kite, square, rectangle

(C) Rhombus, parallelogram, trapezium

(D) Square, parallelogram, trapezium

48 In two years time, Karishmas age will be three times Emilys age.

Emily is now t years old.

How old is Karishma now?

(A) 3t (B) 3t + 2 (C) 3t + 4 (D) 3t + 6

145 70

NOT TOSCALE

p46


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21

49 A quilt measuring 120 cm by 80 cm is made for Emmas cot.

Borders are added to a central rectangular panel. The borders are the samewidth.

What are possible dimensions of the central panel?

(A) 60 cm 40 cm

(B) 80 cm 40 cm

(C) 80 cm 50 cm

(D) 90 cm 60 cm

50 Wanda uses a discount voucher to reduce the price of petrol by 4 cents per litre.

The original price is 121.9 cents per litre. By what percentage is the pricereduced?

(A) 0.03% (B) 3.28% (C) 4% (D) 4.88%

51 Four players are competing in a tennis tournament. Dick has a 50% chance of

winning this tournament. The other players, Craig, Phil and Terry are equallylikely to win.

What is the probability that Craig wins the tournament?

(A) (B) (C) (D)16

15

14

13

120 cm20 cm120 cm

80 cm0 cm80 cm


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22

52 Tarryn is 15 years and 11 months old on 14 November 2006.

When was Tarryn born?

(A) 14 October 1990

(B) 14 December 1990

(C) 14 October 1991

(D) 14 December 1991

53 Which statement is NOT true?

(A) a6 a3 = a2 (B) a6 a3 = a9 (C) (a6)3= (a3)

6(D) a0 = 1

54 A measurement was given as 5.2 106 mm.

What was measured?

(A) The length of a baby

(B) The height of a building

(C) The altitude of a plane flying

(D) The distance from Earth to the Moon

What fraction of rhombus PQRS is shaded?

(A) (B) (C) (D)38

25

14

13

P R

Q

S

55


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23

56 Fay has borrowed $40 000 to buy a car. She wishes to repay the loan overthree years.

Which of the following borrowing options requires Fay to pay the least amountof simple interest?

(A) 7% per annum for the entire period

(B) 8% per annum after a 6 month interest-free period

(C) 11% per annum after a 12 month interest-free period

(D) 14% per annum after an 18 month interest-free period

Which of the following gives the gradient of line l?

(A) tan (B) tan (C) sin (D) sin

58 A frequency distribution table is shown.

What will be the total of the relative frequencies?

(A) 1 (B) 20 (C) 60 (D) 420

Score FrequencyRelative

frequency

10 5

20 8

30 7

O

y

x

l

57


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24

59 The table shows the number of matches needed to make a certain number oftriangles.

Which rule describes the number pattern in this table?

(A) M = T+ 2 (B) M = T+ 4 (C) M = 2T+ 1 (D) M = 3T

Which of the following is an expression for the area of the rectangle?

(A) 5k + 2 (B) 10k + 4 (C) 4k2 + 2 (D) 4k2 + 8k

61 Natasha and Melissa are playing a game where a standard six-sided die is rolled.

Natasha wins if a prime number is rolled. Melissa wins if an odd numberis rolled.

What is the probability that the number that is rolled is neither prime nor odd?

(A) (B) (C) (D)

62 What is the value of a?

(A) 60 (B) 70 (C) 110 (D) 130

130

60

aNOT TOSCALE

16

23

13

12

4k

k+ 2

60

Triangles (T) 1 3 5

Matches (M) 3 7 11


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25

63 Gordo is a fisherman. Darrin claims that Gordo over-estimates the size of his fishby 25%. Gordo describes one fish as 40 cm long.

What does Darrin claim is the length of Gordos fish?

(A) 10 cm (B) 30 cm (C) 32 cm (D) 50 cm

64 Find the value of .

(A) 1 (B) (C) 0 (D)

65 Which of the following nets could be folded to make the cube shown?

(A) (B)

(C) (D)

23

13

3 31

3

0

2


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26

66 A rhombus of side length 10 cm has diagonals 12 cm and 16 cm.

What is the value of h?

(A) 6 cm (B) 9.6 cm (C) 10 cm (D) 19.2 cm

What is the gradient of the interval PQ?

(A) (B) (C) (D)

68 Ivan invests $70 000 in a term deposit at a compound interest rate of 7% per

annum for two years.

How much interest does he earn?

(A) $4900 (B) $9800 (C) $10 143 (D) $80 143

32

23

32

23

P (1, 5)

O

y

x

Q (4, 3)

67

NOT TOS

CALE

h

10 cm


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27

69 The results of the fastest runners in the Melbourne Marathon are recorded below.

What is the mean time for these runners?

(A) 31.1 minutes

(B) 155.5 minutes

(C) 161.5 minutes

(D) 163 minutes

70 An interval is to be drawn from the origin dividing the shaded region in half.

Name the interval.

(A) OA (B) OB (C) OC (D) OD

1 2 3 4 5

D C B A

6

1

O x

y

2

3

4

5

6

7

8

Class(minutes)

Classcentre

Number ofrunners

141145 143 1

146150 148 2

151155 153 1

156160 158 6

161165 163 11

166170 168 9


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28

71 Triangle ACD is equilateral. The area of ACD is half the area of ABC.

What is the size of ACB?

(A) 75 (B) 80 (C) 90 (D) 100

72 The vertices of a right-angled isosceles triangle are A, B and C. The side AB isdrawn below.

In how many different positions on the page could Cbe placed?

(A) 2 (B) 3 (C) 4 (D) 6

BA

A BD

C

NOT TOSCALE


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29

73 The logo drawn below consists of semicircles, quarter circles and straight lines,as shown.

What is the perimeter of the logo?

(A) 6 + 4 (B) 6 + 5 (C) 6 + 6 (D) 6 + 8

74 In quadrilateral PQRS, P = 120 and R = 50.

The bisectors of Q and S meet at T.

What is the size of QTS in quadrilateral PQTS?

(A) 60 (B) 95 (C) 145 (D) 170

75 a b = 1 .

For example, 5 6 = 1 .

What is the value of (1 2) (3 4)?

(A) 1 (B) (C) (D)78

47

12

56

ab

120

50

PQ

T

R

S

NOT TOSCALE

44

1 2 1

33 33


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30

Section 2 (continued)

Instructions for answering Questions 7680

Questions 7680 contain options a, b, c and d. Each option may be Correct orIncorrect. In each question, one, two, three or four options may be Correct.

For Questions 7680, fill in the response ovals on the Section 2 Part AAnswer Sheet to indicate whether options a, b, c and d are Correct orIncorrect. You must fill in either the Correct or the Incorrect response oval foreach option.

Correct Incorrect

Sample: a. 2 + 4 = 4 + 2 a.b. 2 4 = 4 2 b.c. 2 4 = 4 2 c.d. 2 4 = 4 2 d.

If you think you have made a mistake, put a cross through your answer andfill in your new answer.

Correct Incorrect

a.

If you change your mind and have crossed out what you consider to be theright answer, then indicate your intended answer by writing the wordanswer and drawing an arrow as follows.

answer

Correct Incorrect

a.


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31

76 Students are asked to write expressions that are equivalent to 4.

Indicate whether each of the following is Correct or Incorrect.

77 Mr Parker drew this diagram on a whiteboard.


a. The gradient of the line is .

b. The equation of the line is y = 4x + 2.

c. The coordinates of the x-intercept are (0, 4).

d. The point (2, 3) lies on the line.

78 Raelene earns $600 per week. Naomi earns $1100 per fortnight. Danny earnsmore than Naomi but less than Raelene.

How much could Danny earn each month?


a. $2250 b. $2330 c. $2500 d. $2580

1

2

4

2

O

y

x

a. b c. d.

1

2 64 16 823

12

.


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79 Class 10F of Lightning High counted the number of matches per box. The resultsare displayed in the cumulative frequency histogram and polygon shown.


a. The range is 20.

b. The median is 49.5.

c. The mode is 48.

d. The number of boxes of matches counted is 72.

80 When reading a page of his book, Jarrod declared, There are twice as manypages after this page than before this page.

How many pages could this book contain?


a. 202 b. 303 c. 404 d. 505

0

47 48 49 50Number of matches

Number of matches per box

Cumulativefrequency

51 52

2

4

6

8

10

12

14

16

18

20

22

32


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BLANK PAGE

33


34/42 Board of Studies NSW 2006

BLANK PAGE

34


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S4

35


Mathematics

Section 2 (continued)

Part B


Answer the questions in the spaces provided.

MarksQuestion 81 (5 marks)

Donnas annual salary is $62 400.

(a) Calculate her weekly income.

...............................................................................................................................

...............................................................................................................................

(b) Holiday loading is calculated at 17 % of four weeks pay.

Calculate Donnas holiday loading.

...............................................................................................................................

...............................................................................................................................

(c) Holiday pay consists of normal pay plus holiday loading. Donna takesfour weeks holiday.

Calculate Donnas holiday pay.

...............................................................................................................................

...............................................................................................................................

(d) Donnas employer is abolishing holiday loading. To compensate, heoffers Donna a 1.6% increase in annual salary.

Explain why Donna is better off financially with a 1.6% increase.

...............................................................................................................................

...............................................................................................................................

...............................................................................................................................

...............................................................................................................................

2

1

112

1

Centre Number

Student Number


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36

Question 82 (5 marks)

The line y = 6x 6 is drawn on the number plane below. The line meets thex-axis at pointA.

Question 82 continues on page 37

y= 6x 6

11 22 33 44 5566 55 44 33 22 11 O xA

y

1122334455

5544332211

887766

667788

66


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Marks

37

Question 82 (continued)

(a) Complete the table of values fory = + 3.

(b) Plot the points on the number plane and join them to form the

line y= +

3.

(c) The point B is the intersection of the two linesy = 6x 6 andy = + 3.

What are the coordinates of B?

...............................................................................................................................

(d) The point C is the point where the liney = + 3 meets the x-axis.

Calculate the area of ABC.

...............................................................................................................................

...............................................................................................................................

...............................................................................................................................

...............................................................................................................................

End of Question 82

23x2

13x2

3x

2

1

x 2 0 1

y 0 3

13x

2


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Marks

38


(a) Calculate the perimeter of hexagon ABCDEF.

...............................................................................................................................

...............................................................................................................................

(b) AE = 5 cm

Show, by calculation, that FX = 3.12 cm (correct to 2 decimal places).

...............................................................................................................................

...............................................................................................................................

...............................................................................................................................

...............................................................................................................................

(c) Hence, calculate the area of hexagon ABCDEF.

...............................................................................................................................

...............................................................................................................................

...............................................................................................................................

...............................................................................................................................


2

1

1

3 cmA B

CF X

E D

4 cmNOT TOSCALE


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Marks

39


A new fruit-juice container in the form of a hexagonal prism is constructedusing hexagonABCDEF as the base.

The fruit-juice container is to hold 250 mL. (1 mL = 1 cm3)

(d) Calculate the height of the container to the nearest centimetre.

...............................................................................................................................

...............................................................................................................................

...............................................................................................................................

...............................................................................................................................

End of Question 83

Please turn over

1

NOT TOSCALE


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Marks

40


A wire cable,AB, holds a telecommunications antenna in place.

The length of the cable is 120 metres.

The angle of elevation of the top of the antenna,A, from B is 50.

(a) Label the angle of elevation on the diagram above.

(b) Calculate the height of the antenna, h, to the nearest metre.

...............................................................................................................................

...............................................................................................................................

...............................................................................................................................

...............................................................................................................................


1

1

120 m

A

C

h

B

NOT TOSCALE


41/42

Marks

41


(c) Bruce plans to attach a second cable, AD, to the top of thetelecommunications antenna.

The distance from D to C is twice the distance from B to C.

Bruce reasons that since the distance has doubled, the angle of elevationfrom D to A will be half of 50.

Do you agree with Bruces reasoning? Justify your answer, showing

mathematical calculations.

...............................................................................................................................

...............................................................................................................................

...............................................................................................................................

...............................................................................................................................

...............................................................................................................................

...............................................................................................................................

...............................................................................................................................

End of test

A

C D

h

B

NOT TOSCALE

3


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