Directions for Section 2
2003
SCHOOL
CERTIFICATE
TEST
•
You have 90 minutes to answer Section 2 Part A and
Section 2 Part B
•
Calculators may be used in Section 2
Directions for Part A
•
Allow about 60 minutes to answer Part A
•
All questions in this part are multiple choice
•
Each question has only ONE correct answer
•
Complete your answers to Questions 26–75 on the answer
sheet provided
11 November
MATHEMATICS
SECTION 2
Part A
50 marks
S3
–9–
2003 SCT • MATHEMATICS • SECTION 2 • PART A
Complete your answers to Questions 26–75 on the Section 2 Part A—Answer Sheet
26
27
28
2
Chan shaded – of a diagram. Which diagram could be the one Chan shaded?
3
(A)
(B)
(C)
(D)
Which one of the following is NOT equal to 2a?
(A) a + a
(B)
(C) 3a − a
(D) 2a2 − a
It is a quarter to eight in the evening.
Which digital watch shows the correct time?
(A)
(B)
(C)
(D)
– 10 –
a×2
2003 SCT • MATHEMATICS • SECTION 2 • PART A
29
Consider the following data:
7, 8, 9, 9, 15, 18, 19, 20 .
Which of the following statements is true?
30
(A) Median = 12
(B)
Mean = 12
(C) Mode = 12
(D) Range = 12
At a tennis tournament drinks are sold in containers the size and shape of a
standard tennis ball.
Estimate the amount of drink that a container could hold when full.
(A) 50 mL
31
(B)
150 mL
(C) 600 mL
(D) 750 mL
The population of Shanghai is given as 16 million to the nearest million.
The population could be
32
(A) 15 090 000
(B)
15 700 000
(C) 16 500 000
(D) 160 000 000
A formula for calculating the number of days, n, that fresh milk will keep at
different temperatures, t°, above freezing, is
n=
6
.
t+1
How much longer will milk keep at 1° than at 5°?
(A) 1 day
33
(B)
2 days
(C) 3 days
(D) 4 days
Richard sailed due south for 40 km. Then he sailed due east for 40 km to a reef.
What is the true bearing of the reef from Richard’s starting point?
(A) 045°
(B)
090°
(C) 135°
– 11 –
(D) 225°
2003 SCT • MATHEMATICS • SECTION 2 • PART A
34
In which diagram does triangle XYZ have an area of 12 m2?
The diagrams are NOT TO SCALE.
(A)
(B)
X
X
4m
Y
1.5 m
Z
1.5 m
3m
Y
W
(C)
4m
Z
4m
(D)
X
X
4m
Y
35
W
3m
Z
3m
6m
Y
W
4m
Z
4m
W
In the year 1350 AD, a knife was found in China. At that time it was estimated to be
150 years old.
Dynasty
Time period
Song
960–1280 AD
Yuan
1280–1368 AD
Ming
1368–1644 AD
Qing
1644–1911 AD
During the time period of which dynasty was the knife probably made?
(A) Song
(B)
Yuan
(C) Ming
– 12 –
(D) Qing
2003 SCT • MATHEMATICS • SECTION 2 • PART A
36
Jarrod is investigating a quadrilateral. He measures an angle between the
diagonals to be 85°.
Which one of these shapes could the quadrilateral be?
(A) Kite
37
(B)
Rectangle
(C) Rhombus
(D) Square
A group of Year 10 students have part-time jobs. Their mean hourly rate of pay
is $6.50.
Which of the following statements MUST be true?
(A) The difference between the highest and lowest hourly rate is $6.50.
(B)
There are more students earning $6.50 per hour than any other amount.
(C) Half the students earn more than $6.50 per hour and half earn less than
$6.50 per hour.
(D) The total of all student hourly rates divided by the total number of students
is $6.50.
38
What is the size of the angle between the hands of a clock at half past eight?
(A) 60°
39
(B)
65°
(C) 75°
(D) 80°
Which of the following shapes has only ONE axis of symmetry?
(A)
(B)
(C)
(D)
– 13 –
2003 SCT • MATHEMATICS • SECTION 2 • PART A
40
Danni is comparing the daily timetables of four different schools.
Which of the following gives students the most lesson time per day?
(A) 8 lessons of 40 minutes
(B)
6 lessons of 54 minutes
(C) 5 lessons of 1 hour and 3 minutes
(D) 4 lessons of 1 hour and 16 minutes
41
Each letter of the word ISOSCELES is written on a card and placed in a hat. One
card is then chosen at random.
O
S
C
E
L
E
S
I
S
The chance of choosing an E is
(A) double the chance of choosing an O.
(B)
half the chance of choosing a C.
(C) the same chance as choosing an S.
(D) less than the chance of choosing an L.
42
The goal of a new business is to make an average profit of $4000 per month. It
made a loss of $2400 in the first month.
How much profit does the business need to make in the second month to achieve
its goal?
(A) $1600
(B)
$5600
(C) $6400
– 14 –
(D) $10 400
2003 SCT • MATHEMATICS • SECTION 2 • PART A
43
Two rectangles measuring 10 cm by 6 cm are overlapped to form an L-shape, as
shown in the diagram.
NOT TO
SCALE
What is the area of the figure?
(A) 64 cm2
44
(B)
84 cm2
(C) 96 cm2
(D) 104 cm2
During an eclipse of the sun, a circular shadow with a diameter of 40 km was cast
on Earth.
What was the approximate area of the shadow?
(A) 63 km2
(B)
126 km2
(C) 1257 km2
x°
66°
100° x°
NOT TO
SCALE
(D) 5027 km2
45
Calculate the value of x.
(A) 52
(B)
66
(C) 97
(D) 104
46
NOT TO
SCALE
8 cm
10 cm
Which expression gives the volume of the cylinder?
(A) π × 42 × 10
(B)
(C) π × 82 × 10
(D) π × 102 × 8
– 15 –
π × 52 × 8
2003 SCT • MATHEMATICS • SECTION 2 • PART A
47
There are four players in the school tennis team. The coach has to choose two of
these players to represent the school.
How many different groups of two players can the coach choose?
(A) 2
48
(B)
6
(C) 12
(D) 16
Kim made errors when solving the equation 3x − 15 = −2 + 10.
Here is Kim’s working:
3x − 15 = −2 + 10
Line I
3x − 15 = −8
Line II
3x = 7
3
x =–
7
Line III
In which lines were the errors made?
49
(A) Lines I and II
(B)
Lines I and III
(C) Lines II and III
(D) Lines I, II and III
Sharyn is making a cube from this net.
Which of the following cubes CANNOT be made from the net?
(A)
(B)
(C)
– 16 –
(D)
2003 SCT • MATHEMATICS • SECTION 2 • PART A
50
A cardboard carton weighs 240 g. It is packed with 12 bottles of drink, each
weighing 1.3 kg.
What is the total weight of the carton and bottles?
(A) 15.6 kg
51
(B)
(C) 15.888 kg
(D) 18 kg
(C) −0.2 < −0.6
(D) 0.12 < 0.01
Which statement is correct?
(A) 0.19 < 0.2
52
15.84 kg
(B)
0.6 < 0.62
Sue was standing in a queue at the video store. She noticed that there were
three more people ahead of her than behind her. There were 16 people in the
queue in total.
What was Sue’s position in the queue?
(A) 6th
53
(B)
7th
(C) 9th
(D) 10th
The following triangles are NOT drawn to scale. When drawn to scale, which
triangle must contain a right angle?
(A)
(B)
9
5
9
8
25
16
(C)
(D)
15
31
9
18
41
40
– 17 –
2003 SCT • MATHEMATICS • SECTION 2 • PART A
54
Which of the following could be a travel graph?
(A)
(B)
km
km
Time
(C)
Time
(D)
km
km
Time
Time
55
In the following figures, all angles are 90°.
10
5
I
10
5
10
II
5
III
Which figures have the same perimeter?
(A) I and II
(B)
(C) II and III
(D) I, II and III
– 18 –
I and III
NOT TO
SCALE
2003 SCT • MATHEMATICS • SECTION 2 • PART A
56
My first bite of a chocolate bar removed 10% of the bar. My second bite was the
same size as my first.
Approximately what percentage of the remaining bar did I eat with my second
bite?
(A) 9%
57
(B)
10%
(C) 11%
(D) 20%
Sophia tossed a fair coin ten times, with 3 heads and 7 tails appearing.
What is the probability that the next toss will be a head?
(A)
58
1
2
(B)
3
7
(C)
Which of the following is equivalent to
(A)
4+3
9+3
(B)
42
– 19 –
(D)
4×3
9×3
(D)
4
11
4
?
9
(C)
92
3
10
4
9
2003 SCT • MATHEMATICS • SECTION 2 • PART A
59
The diagrams in this question are NOT TO SCALE.
P
12
6
Q
R
9
Which of these triangles is congruent to ∆PQR?
(A)
(B)
24
12
12
18
6
(C)
(D)
12
9
6
6
– 20 –
2003 SCT • MATHEMATICS • SECTION 2 • PART A
60
A boat sailed 24 kilometres in 90 minutes.
What was the average speed of the boat?
(A) 12 km/h
61
(B)
16 km/h
(C) 18 km/h
(D) 36 km/h
Water was poured into a container at a constant rate. The graph shows the height
of the water level as time passed.
Water
level
Time
Into which container was the water poured?
(A)
62
(B)
(C)
(D)
Ivan sends 3 text messages on his mobile telephone for every 4 text messages he
receives. Ivan received 240 text messages last year.
In total, how many messages did he send and receive last year?
(A) 180
(B)
320
(C) 420
– 21 –
(D) 560
2003 SCT • MATHEMATICS • SECTION 2 • PART A
63
A garden has been designed using two identical semicircles of radius 3 m, as
shown in the diagram.
3m
What is the perimeter of the garden?
(A) 18.8 m
64
(B)
(C) 24.8 m
(D) 28.3 m
Which of the following sets of numbers is arranged in order from smallest to
largest?
(A) −3, −4, 75%,
(C) −3, −4,
65
21.8 m
4
3
(B)
4
, 75%
3
−4, −3, 75%,
(D) −4, −3,
4
3
4
, 75%
3
Omar’s motorbike is described as ‘500 cc’ because it has an engine capacity of
500 cm3.
Which of the following represents the same capacity?
(A) 5000 mm3
66
(B)
(C) 0.5 m3
5L
(D) 0.5 L
The value of two dozen cricket balls is $183.60.
What is the value of 7 of these cricket balls?
(A) $7.65
(B)
$15.30
(C) $53.55
– 22 –
(D) $107.10
2003 SCT • MATHEMATICS • SECTION 2 • PART A
67
For which of the following graphs are the values of x two more than the values
of y?
y
(A)
4
4
3
3
2
2
1
1
−3 −2 −1
−3
68
1
2
3
−2 −1
x
−1
−1
−2
−2
−3
−3
−4
−4
y
(C)
y
(B)
4
3
3
2
2
1
1
1
2
3
−2 −1
x
−1
−1
−2
−2
−3
−3
−4
−4
The normal price of a radio is $65.
Which expression gives its price with a 15% discount?
(A) $65 × 0.85
(B)
(C) $65 − 0.15
(D) $65 × 0.15
– 23 –
2
3
x
1
2
3
x
y
(D)
4
−2 −1
1
$65 + $65 × 0.15
2003 SCT • MATHEMATICS • SECTION 2 • PART A
69
A
D
NOT TO
SCALE
6 cm
9 cm
B
E
5 cm
C
F
∆ABC is similar to ∆FED. The corresponding sides of ∆FED are twice as long as
the corresponding sides of ∆ABC.
What is the length of side EF?
(A) 3 cm
70
(B)
6 cm
(C) 10 cm
(D) 12 cm
Peter is asked to complete the following statement:
4
An event with a probability of – ___________ .
5
Which alternative should Peter choose to complete the statement?
71
(A) is unlikely to happen
(B)
is likely to happen
(C) is certain to happen
(D) has a 50/50 chance of happening
P is the centre of a circle. Q and R are on the circumference.
P
Q
R
Which is NOT shown in the diagram?
(A) Sector
(B)
(C) Diameter
(D) Arc
– 24 –
Radius
2003 SCT • MATHEMATICS • SECTION 2 • PART A
72
...
This pattern of triangles, made with matchsticks, was continued until there were
30 triangles.
How many matchsticks were used?
(A) 61
73
(B)
63
(C) 65
(D) 90
A piece of cotton 100 metres long has been wound tightly onto a cotton reel. The
cotton reel has a diameter of 3 cm.
Approximately how many times was the cotton wound around the reel?
(A) 350
74
(B)
500
(C) 1000
(D) 1500
A tetrahedron is used as a die in a game. The four sides are numbered 1, 2, 4
and 8. When the die is rolled, the three visible sides are added together.
Which of the following totals is possible?
(A) 7
(B)
8
(C) 9
– 25 –
(D) 10
2003 SCT • MATHEMATICS • SECTION 2 • PART A
75
A
NOT TO
SCALE
B
E
C
D
In the diagram, AB = BC, AE = ED and CD is twice BE.
Which of the following lengths are NOT sufficient information to find the
perimeter of ∆ACD?
(A) AC and CD
(B)
AB and BE
(C) BE and CD
(D)
AE and CD
End of Section 2 Part A
Go on to Section 2 Part B
– 26 –
2003 SCT • MATHEMATICS • SECTION 2 • PART A
BLANK PAGE
– 27 –
2003 SCT • MATHEMATICS • SECTION 2 • PART A
BLANK PAGE
– 28 –
© Board of Studies NSW 2003
CENTRE NUMBER
STUDENT NUMBER
2003
SCHOOL
CERTIFICATE
TEST
11 November
Directions for Section 2 Part B
•
Allow about 30 minutes to answer Part B
•
Write your answers to Questions 76–84 in this booklet
•
Calculators may be used in Part B
•
Write your Centre Number and Student Number at the top
of this page
MATHEMATICS
SECTION 2
Part B
25 marks
S4
– 29 –
2003 SCT • MATHEMATICS • SECTION 2 • PART B
Questions 76 to 80 are worth 1 mark each. Each question MAY have MORE THAN
ONE correct answer. Fill in the response oval(s) completely.
Question 76
Which of the following has a value of 14?
(A)
42 × 2
4−7
(B)
(A)
60 + 24
4+2
(C)
(B)
90 − 6
3×2
(D)
(C)
21 × 4
12 ÷ 2
(D)
Question 77
Which of these diagrams contains an isosceles triangle?
(A)
(B)
40°
80°
75°
160°
NOT TO SCALE
(C)
(D)
O
72°
36°
O is the centre
of the circle
(A)
(B)
(C)
– 30 –
(D)
2003 SCT • MATHEMATICS • SECTION 2 • PART B
Question 78
A frame in the shape of a rectangular prism is made from 24 cm of wire. Each side
length is a whole number of centimetres.
Which of the following volumes is possible?
(A) 4 cm3
(B)
(A)
(B)
6 cm3
(C) 8 cm3
(D) 12 cm3
(C)
(D)
Question 79
This solid contains 8 blocks. It was viewed from the top, the front, the back and the sides.
Which of the following could be seen?
(A)
(B)
(C)
(D)
(A)
(B)
(C)
(D)
Question 80
Brad put $110 into an envelope. He used SIX notes and NO coins. The envelope could
contain
(A) exactly 1 twenty-dollar note.
(B)
(C) exactly 3 twenty-dollar notes.
(D) exactly 4 twenty-dollar notes.
(A)
(C)
(B)
exactly 2 twenty-dollar notes.
(D)
End of questions that may require you to fill in more than one correct answer
Please turn over
– 31 –
2003 SCT • MATHEMATICS • SECTION 2 • PART B
Marks
Question 81 (5 marks)
P
T
Q
PQRS is a rectangle.
T is the midpoint of PQ.
PT = TQ = 8 cm and TS = 10 cm.
The perimeter of PQRS is 44 cm.
NOT TO
SCALE
S
(a)
R
What type of quadrilateral is TQRS?
1
...............................................................................................................................
...............................................................................................................................
(b)
Calculate the perimeter of TQRS. All working MUST be shown.
...............................................................................................................................
...............................................................................................................................
...............................................................................................................................
...............................................................................................................................
...............................................................................................................................
...............................................................................................................................
...............................................................................................................................
...............................................................................................................................
...............................................................................................................................
...............................................................................................................................
– 32 –
2
2003 SCT • MATHEMATICS • SECTION 2 • PART B
Marks
Question 81 (continued)
A transformation has been used to move triangle PTS to the new position QTV
as shown.
V
P
T
Q
S
(c)
NOT TO
SCALE
R
What transformation has been performed?
1
...............................................................................................................................
...............................................................................................................................
(d)
What is the ratio of the area of triangle QTV to the area of triangle RSV?
...............................................................................................................................
...............................................................................................................................
– 33 –
1
2003 SCT • MATHEMATICS • SECTION 2 • PART B
Marks
Question 82 (5 marks)
Joanne recorded the time it took customers to receive their orders from both a
pizza restaurant and a Chinese takeaway shop. All times were recorded to the
nearest minute.
(a)
Joanne showed the time for 22 customers to receive their pizza in this
stem-and-leaf plot.
(i)
0
8899
1
001455578
2
335566
3
145
What is the median length of time customers waited for pizzas?
1
...................................................................................................................
...................................................................................................................
(ii)
The manager of the pizza restaurant wants to make a free pizza
offer.
Manager’s FREE
pizza offer
If you have to wait
minutes
or more your pizza is FREE!
Based on Joanne’s data, what number could the manager put in
the
to give between 5% and 10% of customers a free pizza?
...................................................................................................................
...................................................................................................................
...................................................................................................................
– 34 –
1
2003 SCT • MATHEMATICS • SECTION 2 • PART B
Marks
Question 82 (continued)
(b)
Joanne recorded the following 15 waiting times for meals from the
Chinese takeaway shop. All times are in minutes.
9
28
6
12
3
4
4
7
19
10
16
4
22
14
8
She arranged the customer waiting times in categories.
(i)
1
Complete the frequency table.
Tally
Frequency
Less than 5 minutes
From 5 minutes to 15 minutes
More than 15 minutes
Total = 15
(ii)
Joanne then started to show the data in this sector graph.
1
Less than
5 minutes
Accurately complete the sector graph. Label the sectors.
(iii)
George can wait only 15 minutes for a takeaway meal.
Based on Joanne’s data, should he choose pizza or the Chinese
food? Give one reason for your answer.
...................................................................................................................
...................................................................................................................
– 35 –
1
2003 SCT • MATHEMATICS • SECTION 2 • PART B
Marks
Question 83 (5 marks)
(a)
Jim wishes to make a kite with dimensions, in centimetres, as shown.
x
16
30
NOT TO
SCALE
30
50
(i)
1
Calculate the area of the kite.
...................................................................................................................
...................................................................................................................
(ii)
Use a calculation to show that x = 34.
1
...................................................................................................................
...................................................................................................................
...................................................................................................................
...................................................................................................................
(b)
Jim uses a large piece of green paper to make the kite, allowing overlaps
on each side. The shaded rectangle has an area of 170 cm2.
w
16
30
30
50
Calculate the width (w) of the rectangle.
...............................................................................................................................
...............................................................................................................................
– 36 –
1
2003 SCT • MATHEMATICS • SECTION 2 • PART B
Marks
Question 83 (continued)
2
ng
(
80
m
)
(c)
Str
i
h
NOT TO
SCALE
55°
Ground
Jim has 80 m of string with which to fly the kite. When the string makes
an angle of 55° with the ground, he attaches it to a point on the ground.
Using a scale drawing with a scale 1 : 500, calculate the height (h) of the
kite above the ground. Start your diagram on the ground level shown
below.
Ground level
– 37 –
2003 SCT • MATHEMATICS • SECTION 2 • PART B
Marks
Question 84 (5 marks)
The first 13 numbers of the Fibonacci Sequence are
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233.
(a)
1
What is the next number in the Fibonacci Sequence?
...............................................................................................................................
...............................................................................................................................
(b)
1
Consider this pattern:
12 + 12 = 1 × 2
1 2 + 12 + 22 = 2 × 3
1 2 + 1 2 + 22 + 3 2 = 3 × 5
1 2 + 1 2 + 2 2 + 32 + 5 2 = 5 × 8
1 2 + 1 2 + 22 + 32 + . . . +
2
=
× 144
What number in the Fibonacci Sequence is represented by
?
...............................................................................................................................
...............................................................................................................................
(c)
1
Write the next line of this pattern:
1×5+1 = 2×3
2×8−1 = 3×5
3 × 13 + 1 = 5 × 8
5 × 21 − 1 = 8 × 13
...............................................................................................................................
...............................................................................................................................
– 38 –
2003 SCT • MATHEMATICS • SECTION 2 • PART B
Marks
Question 84 (continued)
(d)
F and S are two consecutive numbers in the Fibonacci Sequence. S is
larger than F.
1
Write an algebraic expression for the number immediately before F in the
Fibonacci Sequence.
...............................................................................................................................
...............................................................................................................................
(e)
Given the Fibonacci Sequence 1, 1, 2, 3, 5, 8, 13, 21, 34 . . .
Consider this pattern:
1+1+2 = 4
1+1+2+3 = 7
1 + 1 + 2 + 3 + 5 = 12
1 + 1 + 2 + 3 + 5 + 8 = 20
You are asked to find the sum of the first 50 numbers in the Fibonacci
Sequence without adding them up.
Explain how you could use another number in the sequence to do this.
...............................................................................................................................
...............................................................................................................................
End of test
– 39 –
1
2003 SCT • MATHEMATICS • SECTION 2 • PART B
BLANK PAGE
– 40 –
© Board of Studies NSW 2003