2006 School Certificate Specimen Test

MATHEMATICS
Introduction
This document accompanies the specimen test for the 2006 School Certificate test in
Mathematics. A mapping grid is also included with the test. It shows how each
question in the test relates to the relevant syllabus outcomes and content, and to the
performance bands used to report student achievement in the test.

In 2006, the first cohort of students studying the Mathematics Years 7–10 Syllabus
(2002) will sit for the School Certificate Mathematics test. The scope of the test and
the test specifications have been reviewed for 2006, and this specimen test is
indicative of the type of test that will be produced for 2006 and subsequent years.
Because much of the content of the new syllabus is similar to that in the previous
syllabuses, many of the questions in past School Certificate Mathematics tests would
continue to be suitable for tests from 2006. The inclusion of questions from past tests
in the specimen paper reflects this.

The purpose of the School Certificate tests

The School Certificate credential marks the end of compulsory schooling. It records
student achievement in the courses studied in Stage 5, and provides results in five
state-wide tests in areas considered foundational to subsequent achievement. Further
information about the School Certificate can be found on the Board’s Assessment
Resource Centre (http://www.arc.nsw.edu.au/).

A major purpose of the School Certificate tests at the end of Year 10 is to strengthen
the foundation skills students need to pursue further learning or to succeed in the
workplace.

The scope of the School Certificate tests

The tests focus on foundational aspects of their related syllabuses, and do not cover all
areas of the syllabus. The Mathematics test scope statement provides further details of
the relationship between the School Certificate Mathematics test and the Mathematics
syllabus.

Specimen tests
Specimen tests are produced in accordance with the Board’s Principles for Setting
School Certificate Tests and Developing Marking Guidelines in a Standards-
Referenced Framework, published in Board Bulletin Volume 10 Number 1 (March
2001). Questions are closely related to a subset of syllabus outcomes from the related
course. The test as a whole is structured to show how appropriate differentiation of
student performance at all levels on the performance scale can be obtained.

The Mathematics specimen test

The specimen test is an example of the type of test that could be prepared within the
School Certificate Mathematics test specifications. Tests in Mathematics will be based
on a representative sample of syllabus outcomes. The mapping grid accompanying the
specimen test shows how the test as a whole samples a range of content and
outcomes, and allows all students the opportunity to demonstrate their level of
achievement.

The range and balance of outcomes tested in the School Certificate tests in 2006 and
subsequent years may differ from those addressed in the specimen test.

There are a number of points to note in considering the Mathematics specimen test:
• The School Certificate Mathematics test will be based on the Working
Mathematically strand of the syllabus, as it relates to the content strands up to
and including Stage 5.1. Note that some syllabus topics in the Stage 5.1
content have not previously been within the scope of the School Certificate
Mathematics test. Trigonometry (MS5.1.2), Coordinate Geometry (PAS5.1.2),
Rational Numbers (NS5.1.1) and Algebraic Techniques (PAS5.1.1) (including
index laws and scientific notation) are topics in this category.
• The simple interest formula, I = PRT, (Mathematics Years 7–10 syllabus
(2002), NS5.1.2 Consumer Arithmetic, page 70) has been added to the
formulae sheet.
• Calculators are not to be used in Section 1 of the test. Number sense and
mental computation are fundamentals emphasised in Section 1, reflecting the
syllabus advice that ‘students maintain and develop their mental arithmetic
skills, rather than relying on their calculators for every calculation’
(Mathematics Years 7–10 syllabus (2002), page 5).
• A short break will occur following the expiry of working time for Section 1.
During this period responses to Section 1 will be collected, and preparations
made for the commencement of Section 2. Calculators may be used in
Section 2.
• In Section 2 Part A, there are five questions in a multiple correct-incorrect
format. These questions have four alternatives, of which one, two, three, or all
four, may be correct. These questions assist students to see that many
questions in mathematics may have several answers, and reward students for
the ability to discern these possibilities. This format directs students to
consider and choose an appropriate response for each alternative.
• The four questions in Section 2 Part B, worth 5 marks each, are made up of
parts. The number of parts and their mark values may vary from year to year.
 Mathematics
2006 School Certificate Specimen Test

General Instructions Total marks – 100

■ Reading time: 5 minutes Section 1

Pages 3–10
■ Working time: 2 hours
■ There will be a short break 25 marks
between Section 1 and Section 2 Time allowed for this section is 30 minutes
■ Write using black or blue pen
Questions 1–25 25 marks
■ You may use a pencil to draw
or complete diagrams Section 2
■ Attempt ALL questions Pages 12–42
■ Calculators may be used in 75 marks
Section 2 only Time allowed for this section is 1 hour and
■ A formulae sheet is provided 30 minutes
with this paper
■ Write your Centre Number This section has TWO parts
and Student Number at the
top of pages 3 and 35 Part A – Questions 26–80 55 marks
Part B – Questions 81–84 20 marks

Print run
Formulae
For use in both SECTION 1 and SECTION 2

Circumference of a circle = π × diameter or 2 × π × radius

⎡⎣C = π d⎤⎦ ⎡⎣C = 2 π r ⎤⎦

Area of a circle = π × radius squared

⎡A = π r 2 ⎤
⎣ ⎦

Area of a parallelogram = base × perpendicular height

⎡⎣ A = bh⎤⎦

Area of a rhombus = half the product of the diagonals

⎡ 1 ⎤
⎢ A = xy ⎥
⎣ 2 ⎦

Area of a trapezium = half the perpendicular height × the sum of the parallel sides
⎡ 1 ⎤
⎢ A = h ( a + b )⎥
⎣ 2 ⎦

Volume of a prism = base area × height

⎡⎣V = Ah⎤⎦

Volume of a cylinder = π × radius squared × height

⎡V = π r 2 h⎤
⎣ ⎦

Simple interest = principal × annual intereest rate × number of years

⎡⎣I = PRT ⎤⎦

Pythagoras’ theorem states: In a right-angled tria

angle, the hypotenuse squared is equal to
the sum of the squares of the other two sides
⎡c 2 = a 2 + b 2 ⎤
⎣ ⎦

–2–
© Board of Studies NSW 2006
 2006 School Certificate Specimen Test
Mathematics Centre Number

Student Number

Section 1

25 marks
Time allowed for this section is 30 minutes

Answer Questions 1–25 in the spaces

provided

Calculators are NOT to be used in this

Section

There will be a short break between

Section 1 and Section 2

Print run
Answer the questions in the spaces provided.

1 What number is halfway between −3 and 7?

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

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

1 1
2 1– × – =
2 5
.............................................................................................................................................

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

3 O is the centre of the circle. Use the words from the list to complete the sentences
below.

• an arc
O
• a chord
• a sector

The shaded area is called ...............................................................................................

This area is bounded by two radii and .......................................................................

4 1.8 ÷ 0.03 =

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

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

–4–
5 Sergio said ‘If I toss 2 coins, I can get 2 heads, or 2 tails, or a head and a tail.
1
Therefore the probability that I get 2 heads is – ’.
3
Sergio is incorrect. Write a brief reason why he is incorrect.

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

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

6 In a survey, students are asked how many mobile phone calls they have made
that day. The results are shown in the cumulative frequency histogram and
polygon below.

60

50
Cumulative frequency

40

30

20

10

0
0 1 2 3
Calls

Use the graph to find the median number of calls made.

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

7 Which number in the box is:

smaller than 870

486 888
AND greater than 540
AND even 639

AND divisible by 3? 762 572

The number is ..................................................................................................................

–5–
8 Tides alternate between low and high. The time between low tide and high tide
at Brown’s Beach is 6 hours and 10 minutes. There is a low tide at 7:13 am.

When will the next low tide occur?

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

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

9 Calculate the sum

2 + 4 + 16 + 18 + 2 + 4 + 16 + 18 + 2 + 4 + 16 + 18
.............................................................................................................................................
.............................................................................................................................................

10 If 12 × 167 = 2004
then 24 × = 2004

The value of is ...........................................................................................................

11 Arrange these scores into a stem-and-leaf plot.

14, 17, 20, 22, 23, 23, 24, 33

Stem Leaf

1
2

12 In Question 11, the mean of the scores is 22. Change any one of the scores to make
the mean 23.

Old score New score

changes to

–6–
13 This diagram shows a trapezium.

10 cm

NOT TO
4 cm SCALE

13 cm

Calculate the perimeter of the trapezium.

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

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

14 Khadija thought of a number. She doubled the number, then subtracted five. The
result was 63.

What was the number Khadija thought of?

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

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

15 Write a number in the box so that the expression

+3
_________
8
has a value between 1 and 2.

16 A sequence is formed by adding the two previous numbers together. Fill in the
two missing numbers in this sequence.

4, ................, ................, 22

17 Write 2−3 as a fraction.

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

–7–
18 What is the greatest number of 60 cent chocolates I can buy with $10?

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

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

19 Adele sells cosmetics. She is paid by commission.

Briefly explain the meaning of commission.

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

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

20 By measuring appropriate lengths, calculate the area of this triangle in square

centimetres. Show all your measurements on the diagram.

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

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

–8–
21 Write the next line of this pattern.

1 × 2 × 3 × 4 + 1 = 52
2 × 3 × 4 × 5 + 1 = 112
3 × 4 × 5 × 6 + 1 = 192
4 × 5 × 6 × 7 + 1 = 292

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

22
C

4m° NOT TO
SCALE

A 2m° 3m° B

Triangle ABC has angles 2m°, 3m° and 4m° as shown.

Use an equation, or a calculation, to show that m = 20.

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

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

23 Complete the next line in the pattern.

3 × 102 = 300

3 × 101 = 30

3 × 100 = 3

3 × 10–1 = 0.3

3 × =

–9–
24 $500 is invested for 2 years at 10% per annum, compounded annually.

Calculate the total interest earned.

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

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

25 More than one triangle can be constructed with sides 6 cm and 8 cm and an angle
of 40°. ΔXYZ is one example.

6 cm

40°
X Z
8 cm

Construct a triangle that is NOT congruent to ΔXYZ, and that has sides 6 cm and
8 cm and an angle of 40°.

End of Section 1

– 10 –
© Board of Studies NSW 2006
 2006 School Certificate Specimen Test
Mathematics

Section 2

75 marks
Time allowed for this section is 1 hour
and 30 minutes

This section has TWO parts

Part A – Questions 26–80 55 marks

Part B – Questions 81–84 20 marks

Calculators may be used in this section

Do not commence Section 2 until you are

instructed to do so

Print run
Part A

Questions 26–80 55 marks

Use the Section 2 – Part A Answer Sheet for Questions 26–80.

Instructions for answering multiple-choice questions

■ For Questions 26–75, select the alternative A, B, C or D that best answers the
question. 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 incorrect
answer and fill in the new answer.
A B C D

■ 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 as follows.

correct

A B C D

– 12 –
26 Simplify 22 × 23.

(A) 25 (B) 26 (C) 45 (D) 46

27 In scientific notation, 0.0043 is written as

(A) 4.3 × 102 (B) 4.3 × 103 (C) 4.3 × 10−2 (D) 4.3 × 10−3

28

I II

In which of the solids is the cross-section a triangle?

(A) I only (B) II only
(C) Both I and II (D) Neither I nor II

29 Abdul wrote the following lines of working to solve the following equation:

5x + 7 = 16

Line 1 5x = 16 − 7

Line 2 5x = 9

9
Line 3 x =–
5
4
Line 4 x = 1–
9

In which line did he make an error?

(A) Line 1 (B) Line 2 (C) Line 3 (D) Line 4

– 13 –
30 Maureen was born on 26 November 1990. What was her age on 26 August 2004?

(A) 13 years 8 months (B) 13 years 9 months

(C) 14 years 8 months (D) 14 years 9 months

31 Michelle drew a circle inside a rectangle. She drew a diameter of the circle and
extended it. When she extended the diameter, it was a diagonal of the rectangle.

Which of the following could be Michelle’s drawing?

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

32 Which of the following scales would be the most appropriate to make a scale
drawing of a police car on a piece of paper the same size as this page?

(A) 1 : 25 (B) 1 : 100 (C) 1 : 250 (D) 1 : 1000

33 The possible three-child families are

BBB, BBG, BGB, BGG, GBB, GBG, GGB, GGG

where B = boy, G = girl.

What is the probability that in a three-child family there will be AT LEAST ONE
girl?

3 4 6 7
(A) – (B) – (C) – (D) –
8 8 8 8

34 Expand and simplify 3(t − 1) − t + 1

(A) 2t + 4 (B) 2t − 4 (C) 2t − 2 (D) 2t

– 14 –
35 For this triangle, what is the value of sin θ ?

NOT TO
13 12
SCALE

5 12 12 13
(A) – (B) – (C) – (D) –
13 5 13 12

36 Which of the following could represent the probability of an event that is LIKELY
to occur?

1 2 1 4
(A) – (B) – (C) – (D) –
9 5 2 5

37 Peta sells cars. She earns $270 per week plus 5% commission on her total weekly
sales over $40 000.

What is the value of her sales in a week when she earns $860?

(A) $11 800

(B) $17 200
(C) $51 800
(D) $57 200

– 15 –
38 Alice is going to use this pattern to pave her courtyard.

20 cm

10 cm

NOT TO
SCALE

She is going to pave an area of 12 m2. How many 20 cm × 10 cm pavers will she
need?

(A) 75 (B) 150 (C) 240 (D) 600

39 Darren has $x in his bank account, and he saves $y every week. How much will
be in his account after n weeks?

(A) x + yn (B) xn + yn (C) xn + y (D) x + y + n

40 Helena’s home repayments increased from $962.22 to $984.24 per fortnight.

How much extra will Helena repay each year?

(A) $264.24 (B) $528.48 (C) $572.52 (D) $1145.04

41 Using a protractor, find the size of x.

(A) 70° (B) 110° (C) 250° (D) 290°

– 16 –
42 The diagram shows the price of oranges in four shops.

Shop 1 Shop 2 Shop 3 Shop 4

In which shop are oranges cheapest per kilogram?

(A) Shop 1 (B) Shop 2 (C) Shop 3 (D) Shop 4

43 Simplify 3a2 × 4a3

2a

(A) 6a3 (B) 6a4 (C) 6a5 (D) 6a6

44 Gertrude normally works four-hour shifts. She is paid $8.50 per hour normal
time, and $12.50 per hour for any time she works over four hours.

Gertrude works a shift from 9:15 am to 2:15 pm. What is her total pay?

(A) $42.50 (B) $46.50 (C) $62.50 (D) $71.50

– 17 –
45 EFGH is a parallelogram. MH is perpendicular to EF.

H G

E M F

Which of the following lengths are sufficient information to find the area of EFGH?

(A) The lengths of HG and EH only

(B) The lengths of HG and MH only
(C) The lengths of the diagonals EG and HF only
(D) The lengths of EH and MH only

46 What is the area of this shape?

NOT TO
13 cm SCALE
22 cm

15 cm

25 cm

(A) 417 cm2 (B) 459 cm2 (C) 507 cm2 (D) 639 cm2

47 Using trigonometry, calculate the size of the smallest angle in this triangle,
correct to the nearest degree.

5 NOT TO
3
SCALE

(A) 31° (B) 37° (C) 41° (D) 49°

– 18 –
48 The diagram shows part of a number line. Which point is closest to 3.15?

P Q R S
2.7 3.7

(A) P (B) Q (C) R (D) S

49 When he climbed a 60 m tree, Ross climbed 140 rungs on his ladder. He plans to
climb a 75 m tree.

How many rungs will be on the ladder?

(A) 155 (B) 175 (C) 200 (D) 215

50 The diagram is the net of a rectangular prism, drawn to a scale 1 : 2.

SCALE 1 : 2

What is the volume of the prism?

(A) 27 cm3 (B) 54 cm3 (C) 108 cm3 (D) 432 cm3

– 19 –
51 Barbara wrote each letter of her name on separate cards.

She placed the cards face down on a table. She is going to turn over two cards at
the same time.

In how many ways can she turn over two cards that have the same letter on
them?

(A) 3 (B) 4 (C) 5 (D) 10

52 x + 10

2x

What is the perimeter of this rectangle?

(A) 3x + 10 (B) 4x + 20

(C) 5x + 10 (D) 6x + 20

53 The balances show relationships between the masses of three types of object.

Which of the following shows the three objects arranged from heaviest
to lightest?

(A) , , (B) , ,

(C) , , (D) , ,

– 20 –
 1
54 Which one of the following containers could hold – litre of water without
overflowing? 2

(A) (B)

5 cm
10 cm 4 cm
20 cm
4 cm
10 cm

(C) (D)

8 cm
15 cm
8 cm
8 cm

5 cm
5 cm

55 The graph shows the number of errors made by a class of students in a Year 10
Mathematics test.

Errors made by students

18
15
Frequency

12
9
6
3
0
5 6 7 8
Number of errors

How many students are in the class?

(A) 4 (B) 15 (C) 23 (D) 33

– 21 –
56
x°

y° 110°

What are the values of x and y?

(A) x = 40, y = 70 (B) x = 55, y = 55

(C) x = 50, y = 60 (D) x = 70, y = 40

57 A discount voucher offered 25% discount, up to a maximum discount of $15.

Daniel bought goods to the value of $80, and Naomi bought goods to the value
of $40. They each had a discount voucher.

How much more money did Daniel pay than Naomi?

(A) $5 (B) $10 (C) $30 (D) $35

58

c b

The shaded design is made from four of the small triangles.

What is the perimeter of the design?

(A) 4c + 4b + 4a (B) 4c + 4b – 4a

(C) 4a – 4b + 4c (D) 4a2 + 4b2 + 4c2

– 22 –
59 In the diagram, lengths BC, CD and BD are equal and ∠BEA is a right angle.

D
B NOT TO
SCALE

x
A E

What is the size of x?

(A) 30° (B) 35° (C) 45° (D) 60°

60 David earns $7.67 an hour for an 8 hour shift. John earns $6.97 an hour and
receives a $5.60 meal allowance for an 8 hour shift.

Which of the following statements about their earnings for an 8 hour shift
is correct ?

(A) They receive the same amount.

(B) David receives $5.60 more than John.
(C) John receives $4.90 more than David.
(D) John receives $11.20 more than David.

– 23 –
61 Rod completed this table to draw the graph of y = x2 + 2 .

x −2 −1 0 1 2

y 6 3 2 3 6

Which graph should he draw?

(A) y (B) y

x x
O O

(C) y (D) y

x x
O O

62 The table shows the frequencies for a set of scores.

Score Tally Frequency f×x

x f
1 10 10
2 6 12
3 2 6
4 1 4
5 3 15

What is the mean of this set of scores?

22 47 47 47
(A) – (B) – (C) – (D) –
5 5 15 22

– 24 –
63 Michael won $240. He donated one third of his winnings to charity. He divided
the remainder between his savings account and his investment account in the
ratio 3 : 5.

How much did he deposit in his savings account?

(A) $30 (B) $60 (C) $90 (D) $100

1
64 The time in Maitland is – hour ahead of the time in Broken Hill. The time in
1 2
Albany is 1– hours behind the time in Broken Hill.
2

When the time in Maitland is 13:30, what is the time in Albany?

(A) 11:30 (B) 12:30 (C) 14:30 (D) 15:30

65 The annual membership fee at Jerry’s golf club is $345, and it costs $15 to play
each game. Jerry’s golf budget for 2006 is $900.

How many games of golf will Jerry be able to play at his club in 2006?

(A) 23 (B) 37 (C) 60 (D) 83

66 P
NOT TO
α In ΔPQR, sides PQ and RQ
SCALE
are equal, and side PR is
shorter than side PQ.
θ β
R Q

Which statement is true?

(A) α = θ (B) α=β

(C) θ = β (D) α, β and θ are all equal

– 25 –
67 Class interval Cumulative frequency
1–3 4
4–6 12
7–9 18
10–12 23
13–15 26

What is the modal class for this set of data?

(A) 4–6 (B) 7–9 (C) 10–12 (D) 13–15

68 Kevin and Jim are playing a game using a spinner. A player wins when the
spinner stops on his colour. Kevin always chooses white, and Jim always
chooses green.

Which spinner should Kevin choose so that he has the greatest chance of beating
Jim?

(A) (B)
White Blue
White Green

Green White

Blue White
White Green

(C) (D)
Red

White Green White

Blue

Green
White Blue

– 26 –
69 Madi covered the front page of this examination paper with $2 coins. She placed
as many coins on the page as possible without overlapping.

ACTUAL SIZE

What is the approximate value of the coins?

(A) $140–$218 (B) $220–$276

(C) $278–$330 (D) $332–$380

70 Ervino took his family for dinner. The cost of each meal was: Ervino, $24;
Chris, $18; Rebecca, $20; and Ben, $22. Ervino paid the total bill, using two of
these discount vouchers.

1
2 Price Main Meal
Buy any main meal and
1
2
receive a second main meal
for 12 price (up to equal value)

What is the lowest total amount he could be required to pay?

(A) $61 (B) $62 (C) $64 (D) $65

71 Aisha is looking at a map of caves.

Jimbo cave is 90 m below ground level.

Lateral cave is 50 m higher than Cathedral cave.
Jimbo cave is 20 m lower than Lateral cave.

How far below ground level is Cathedral cave?

(A) 60 m (B) 120 m (C) 140 m (D) 160 m

– 27 –
72 What is the area of rectangle ABCD?

A E B

6 cm 8 cm

D C
10 cm

(A) 24 cm2 (B) 48 cm2 (C) 50 cm2 (D) 60 cm2

73 In a group of 19 boys, all play either tennis or rugby, and some play both. 14 boys
play tennis and 8 play rugby.

One of the boys is selected at random. What is the probability that he plays
tennis but not rugby?

5 6 11 14
(A) – (B) – (C) – (D) –
19 19 19 19

74 The formula for the perimeter of a rectangle is

P = 2  + 2b.

What is the value of b when  = 5 and P = 40?

(A) 15 (B) 25 (C) 30 (D) 35

– 28 –
75 A teacher recorded the number of days that her students were absent.

Number of students
6

0
0 1 2 3 4
Number of days absent

A student is chosen at random.

The probability that this student had 3 days absent is

(A) 3 (B) 7 (C) 3 (D) 7

20 20 7 8

– 29 –
Section 2 (continued)

Instructions for answering Questions 76–80

■ Questions 76–80 contain options a, b, c and d. Each option may be Correct or

Incorrect. In each question, one, two, three or four options may be Correct.

■ For Questions 76–80, fill in the response ovals on the Section 2 – Part A
Answer Sheet to indicate whether options a, b, c and d are Correct or
Incorrect. You must fill in either the Correct or the Incorrect response oval for
each 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 and
fill in your new answer.

Correct Incorrect
a.

■ If you change your mind and have crossed out what you consider to be the
right answer, then indicate your intended answer by writing the word
‘answer’ and drawing an arrow as follows.

answer
Correct Incorrect

a.

– 30 –
76 The number of goals scored by Jim’s soccer team in eight matches is:

2, 2, 2, 3, 3, 4, 4, 5.

In its ninth game the team scored six goals.

Indicate whether each of the following is Correct or Incorrect.

a. The mean increased.

b. The mode increased.
c. The median increased.
d. The range increased.

77 Fatima is making a pattern of rectangles, using matches.

Indicate whether each of the following is Correct or Incorrect.

a. The number of matches Fatima needs is three times the number of

rectangles plus one.
b. The number of matches Fatima needs is four more than three times the
number of rectangles.
c. The number of matches Fatima needs is four times the number of
rectangles minus one.
d. The number of matches Fatima needs is twice the number of rectangles
plus one more than the number of rectangles.

78 The minute hand of a clock is between 3 and 4 and the hour hand is between
7 and 8.

Indicate whether each of the following is Correct or Incorrect.

a. The time on a digital watch could be 3:39.

b. The time on a digital watch could be 7:18.
c. The time on a digital watch could be 8:17.
d. The time on a digital watch could be 19:16.

– 31 –
79 A bag contains red, black and yellow marbles. There are more red than black
marbles, and there are more black than yellow marbles.

There are 3 yellow marbles and 10 red marbles. Chris draws a marble at random.

Indicate whether each of the following is Correct or Incorrect.

3
a. The probability of drawing a yellow marble could be .
17
7
b. The probability of drawing a black marble could be .
21
10
c. The probability of drawing a red marble could be .
22
10
d. The probability of drawing a red marble could be .
23

80 The perimeter of a rectangle is 24 cm.

Indicate whether each of the following is Correct or Incorrect.

a. The area of the rectangle could be 11 cm2.

b. The area of the rectangle could be 27 cm2.
c. The area of the rectangle could be 35 cm2.
d. The area of the rectangle could be 40 cm2.

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– 33 –
 BLANK PAGE

– 34 –
© Board of Studies NSW 2006
 2006 School Certificate Specimen Test
Mathematics Centre Number

Section 2 (continued)
Student Number
Part B

Questions 81–84 20 marks

Answer the questions in the spaces provided.

Question 81 (5 marks)

Please turn over

– 35 –
Print run
 Marks
Question 81 (5 marks)

(a) Ted needs to choose a spinner for a game. 1

Ted makes the statement:

‘Spinner A and Spinner B are equally likely to stop on an odd number.’

1 5 7 2

8 2 9 5

6 7 8 3

Spinner A Spinner B

Explain briefly why Ted’s statement is incorrect.

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

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

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

(b) Ted decides to conduct a trial to test his statement. 1

He spins each spinner 10 times and records his results in the table, as
shown.

Spinner A Spinner B
Odd 6 5
Even 4 5
Total 10 10

Why would Ted’s trial NOT be an appropriate test of his statement?

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

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Question 81 continues on page 37

– 36 –
 Marks
Question 81 (continued)

(c) Julie chooses a different spinner. It has 5 sectors of equal size numbered 3
1, 2, 3, 4 and 5, as shown.

5 1

4 2
3

Julie’s teacher asked her to spin the arrow 100 times and record the
number of times the arrow stopped on an odd number and the number
of times it stopped on an even number.

Julie’s results are shown in the table.

Odd 22
Even 78
Total 100

Why do you think Julie’s teacher said: ‘I am surprised by these results.’?

What results would you expect? Give mathematical reasons to justify

your answer.

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

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End of Question 81

– 37 –
 Marks
Question 82 (5 marks)

A boat at sea is 100 metres from the base of a cliff. From the boat the angle of
elevation of the top of the cliff is 22°.

NOT TO
SCALE

22°
100 m

(a) Calculate the height of the cliff. Give your answer in metres correct to 2
one decimal place.

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

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

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

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

(b) On the diagram above, mark the angle of depression of the boat from the 1
top of the cliff.

(c) The boat drifts to a position halfway towards the cliff. 2

On the diagram below, mark the new position of the boat and calculate
the new angle of elevation of the top of the cliff. Give your answer
correct to the nearest degree.

NOT TO
SCALE

22°
100 m

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

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

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– 38 –
 Marks
Question 83 (5 marks)

The diagram shows a number plane. The line y = −2x + 8 crosses the x axis at
C (4,0) and intersects line l at A (–2,12).

A (−2,12)

NOT TO
SCALE

C (4,0)
x
O
l y = −2x + 8

(a) What is the equation of line l? 1

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

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

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

(b) What is the y intercept of the line y = −2x + 8? 1

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

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

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

(c) Show that the point (–3,14) also lies on the line y = −2x + 8. 1

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Question 83 continues on page 40

– 39 –
 Marks
Question 83 (continued)

(d) On the diagram, a circle is to be drawn with diameter AC.

(i) What are the coordinates of the centre of this circle? 1

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

(ii) Calculate the radius of this circle. 1

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End of Question 83

– 40 –
 Marks
Question 84 (5 marks)

A square and a right-angled triangle are joined to form a pentagon, as shown.

14.8 cm

8 cm
NOT TO
10 cm SCALE

6 cm

(a) Calculate the area of this pentagon. Show all working. 2

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...............................................................................................................................
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Question 84 continues on page 42

– 41 –
 Marks
Question 84 (continued)

(b) Another pentagon is formed from a square and a right-angled triangle.

Measurements on this pentagon are given using pronumerals a, b, x
and y, as shown.

a
NOT TO
x SCALE

(i) Explain why an expression for the area of this pentagon is 2

1
– ab + a2 + b2.
2

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

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

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

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

(ii) Write an expression for the area of this pentagon in terms of x and y. 1

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End of test

– 42 –
© Board of Studies NSW 2006
 Mathematics
2006 School Certificate Specimen Test Mapping Grid
For each item in the test, the grid shows the marks allocated, the syllabus content and syllabus
outcomes it relates to, and the bands on the performance scale it is targeting. The range of bands
shown indicates the performance candidates may be able to demonstrate in their responses. That
is, if an item is shown as targeting Bands 3–5, it indicates that candidates who demonstrate
performance equivalent to the Band 3 descriptions should be able to score some marks on the
item, while those who perform at Band 5 or above could reasonably be expected to gain high
marks. In the case of one-mark items, candidates who demonstrate performance at or above the
bands shown generally could be expected to answer the item correctly.

Working Targeted
Content
Question Marks Strand Topic Mathematically Performance
Outcomes
Outcomes Bands
Section 1
1 1 Number Integers NS4.2 4.2 2–3
2 1 Number Fractions, Decimals and NS4.3 4.2 3–4
Percentages
3 1 Space and Properties of Geometrical SGS4.3 4.3 2–3
Geometry Figures
4 1 Number Fractions, Decimals and NS4.3 4.2 3–4
Percentages
5 1 Number Probability NS5.1.3 5.1.3 3–4
6 1 Data Data Representation and DS5.1.1 5.1.3 2–3
Analysis
7 1 Number Operations with Whole NS4.1 5.1.2 2–3
Numbers
8 1 Measurement Time MS4.3 4.2 3–4
9 1 Number Operations with Whole NS4.1 5.1.4 2–3
Numbers
10 1 Number Operations with Whole NS4.1 5.1.4 2–3
Numbers
11 1 Data Data Representation DS4.1 4.3 2–3
12 1 Data Data Analysis and DS4.2 5.1.2 5–6
Evaluation
13 1 Measurement Perimeter and Area MS5.1.1 5.1.2 3–4
14 1 Patterns and Algebraic Techniques PAS4.4 5.1.2 2–3
Algebra
15 1 Number Fractions, Decimals and NS4.3 5.1.2 3–4
Percentages
16 1 Patterns and Number Patterns PAS4.4 5.1.2 4–5
Algebra
17 1 Number Rational Numbers NS5.1.1 5.1.2 3–4
18 1 Number Consumer Arithmetic NS5.1.2 5.1.2 3–4
19 1 Number Consumer Arithmetic NS5.1.2 5.1.3 3–4
20 1 Measurement Perimeter and Area MS4.1 5.1.2 5–6
21 1 Patterns and Number Patterns PAS4.2 4.1 3–4
Algebra
22 1 Patterns and Algebraic Techniques PAS4.4 5.1.2 3–4
Algebra
23 1 Number Rational Numbers NS5.1.1 5.1.4 3–4
24 1 Number Consumer Arithmetic NS5.1.2 5.1.3 3–4
25 1 Space and Properties of Geometrical SGS4.3 5.1.4 5–6
Geometry Figures
 Working Targeted
Content
Question Marks Strand Topic Mathematically Performance
Outcomes
Outcomes Bands
Section 2 Part A
26 1 Number Rational Numbers NS5.1.1 5.1.2 3–4
27 1 Number Rational Numbers NS5.1.1 5.1.3 2–3
28 1 Space and Properties of Solids SGS4.1 4.4 2–3
Geometry
29 1 Patterns and Algebraic Techniques PAS4.4 5.1.4 2–3
Algebra
30 1 Measurement Time MS4.3 4.3 3–4
31 1 Space and Properties of Two SGS4.3 4.3 2–3
Geometry Dimensional Figures
32 1 Number Fractions, Decimals and NS4.3 4.2 4–5
Percentages
33 1 Number Probability NS5.1.3 5.1.2 2–3
34 1 Patterns and Algebraic Techniques PAS4.4 4.2 3–4
Algebra
35 1 Measurement Trigonometry MS5.1.2 5.1.3 2–3
36 1 Number Probability NS4.4 4.3 2–3
37 1 Number Consumer Arithmetic NS5.1.2 5.1.2 4–5
38 1 Measurement Perimeter and Area MS4.1 5.1.2 4–5
39 1 Patterns and Algebraic Techniques PAS4.3 5.1.2 2–3
Algebra
40 1 Number Consumer Arithmetic NS5.1.2 5.1.2 3–4
41 1 Space and Angles SGS4.2 4.2 2–3
Geometry
42 1 Number Consumer Arithmetic NS5.1.2 5.1.2 3–4
43 1 Patterns and Algebraic Techniques PAS5.1.1 5.1.2 3–4
Algebra
44 1 Number Consumer Arithmetic NS5.1.2 5.1.2 2–3
45 1 Measurement Perimeter and Area MS4.1 5.1.2 3–4
46 1 Measurement Perimeter and Area MS5.1.1 4.2 2–3
47 1 Measurement Trigonometry MS5.1.2 5.1.4 3–4
48 1 Number Fractions, Decimals and NS4.3 5.1.2 3–4
Percentages
49 1 Number Fractions, Decimals and NS4.3 5.1.2 2–3
Percentages
50 1 Measurement Surface Area and Volume MS4.2 5.1.2 4–5
51 1 Number Probability NS5.1.3 5.1.2 3–4
52 1 Patterns and Algebraic Techniques PAS4.3 4.2 3–4
Algebra
53 1 Patterns and Algebraic Techniques PAS4.4 5.1.4 2–3
Algebra
54 1 Measurement Surface Area and Volume MS4.2 5.1.2 3–4
55 1 Data Data Representation DS4.1 5.1.3 2–3
56 1 Space and Properties of Geometrical SGS4.3 4.2 3–4
Geometry Figures
57 1 Number Consumer Arithmetic NS5.1.2 5.1.2 4–5
58 1 Number Consumer Arithmetic NS5.1.2 5.1.2 3–4
59 1 Space and Properties of Geometrical SGS4.3 4.2 3–4
Geometry Figures
60 1 Number Consumer Arithmetic NS5.1.2 5.1.2 3–4
61 1 Patterns and Coordinate Geometry PAS5.1.2 5.1.2 2–3
Algebra
 Working Targeted
Content
Question Marks Strand Topic Mathematically Performance
Outcomes
Outcomes Bands
62 1 Data Data Analysis and DS4.2 5.1.2 4–5
Evaluation
63 1 Number Fractions, Decimals and NS4.3 5.1.2 3–4
Percentages
64 1 Measurement Time MS4.3 5.1.2 2–3
65 1 Number Consumer Arithmetic NS5.1.2 5.1.2 2–3
66 1 Space and Properties of Geometrical SGS4.3 5.1.2 3–4
Geometry Figures
67 1 Data Data Represention and DS5.1.1 5.1.3 2–3
Analysis
68 1 Number Probability NS5.1.3 5.1.2 4–5
69 1 Measurement Perimeter and Area MS4.1 5.1.2 4–5
70 1 Measurement Perimeter and Area MS5.1.1 5.1.2 4–5
71 1 Number Integers NS4.2 5.1.2 3–4
72 1 Measurement Perimeter and Area MS4.1 5.1.2 4–5
73 1 Number Probability NS5.1.3 5.1.2 4–5
74 1 Patterns and Algebraic Techniques PAS4.4 5.1.2 2–3
Algebra
75 1 Number Probability NS5.1.3 5.1.2 3–4
76 1 Data Data Analysis and DS4.2 5.1.2, 5.1.4 43–5
Evaluation
77 1 Patterns and Number Patterns PAS4.2 5.1.2, 5.1.4 3–5
Algebra
78 1 Measurement Time MS3.5 5.1.2, 5.1. 2–4
79 1 Number Probability NS5.1.3 5.1.2, 5.1.4 4–6
80 1 Measurement Perimeter and Area MS4.1 5.1.2, 5.1.4 5–6
Section 2 Part B
81(a) 1 Number Probability NS5.1.3 5.1.2, 5.1.3, 2–3
5.1.4
81(b) 1 Number Probability NS5.1.3 5.1.2, 5.1.3, 2–4
5.1.4
81(c) 3 Number Probability NS5.1.3 5.1.2, 5.1.3, 2–5
5.1.4
82(a) 2 Measurement Trigonometry MS5.1.2 5.1.2, 5.1.4 3–5
82(b) 1 Measurement Trigonometry MS5.1.2 5.1.2, 5.1.4 2–3
82(c) 2 Measurement Trigonometry MS5.1.2 5.1.2, 5.1.4 4–6
83(a) 1 Patterns and Coordinate Geometry PAS5.1.2 5.1.2 4–5
Algebra
83(b) 1 Patterns and Coordinate Geometry PAS5.1.2 5.1.3 3–4
Algebra
83(c) 1 Patterns and Coordinate Geometry PAS5.1.2 5.1.4 4–5
Algebra
83(d)(i) 1 Patterns and Coordinate Geometry PAS5.1.2 5.1.2, 5.1.4 5–6
Algebra
83(d)(ii) 1 Patterns and Coordinate Geometry PAS5.1.2 5.1.2, 5.1.4 5–6
Algebra
84(a) 2 Measurement Perimeter and Area MS5.1.1 5.1.2, 5.1.4 2–4
84(b)(i) 2 Measurement Perimeter and Area MS5.1.1 5.1.2, 5.1.4 4–6
84(b)(ii) 1 Measurement Perimeter and Area MS5.1.1 5.1.2, 5.1.4 5–6