Mathematics : Intermediate 2 : Paper 2 : Units 1,2,3 : Item Bank
part
marks
3
Syllabus Code
1.1
Calc. Code
Grade
(CN,CR,NC) (C, B, A)
CR
C
Source
2001 q1
The population of a city is increasing at a steady rate of 2.4% per annum.
The present population is 528,000.
Wat is the expected population in 4 years time?
Give your answer to the nearest thousand.
3
Give 1 mark for each •
Notes
1
For an answer without working, award 3/3
•1
1.024
•2
528 , 000 ¥ 1.024 4 or equiv.
•3
581, 000
3 marks
12
Mathematics : Intermediate 2 : Paper 2 : Units 1,2,3 : Item Bank
part
marks
Syllabus Code
(a)
4
2.4
(b)
2
2.4
Calc. Code
Grade
(CN,CR,NC) (C, B, A)
CR
C
CR
Source
2001 q2
C
Two groups of six students are given the same test.
(a)
The marks of group A are:
73
47
59
71
48
62
Use an appropriate formula to calculate the mean and the standard deviation.
Show clearly all your working.
(b)
4
In group B, the mean is 60 and the standard deviation is 29.8.
Compare the results of the two groups.
2
Give 1 mark for each •
Notes
•1
60
•2
Sx2 = 22208 and ( Sx) = 129600
•3
•4
1
2
129600
6
5
22208 11.0
4 marks
•5
6
•
both have same mean
greater spread in B
2 marks
Alternative for •2 and •3
•2
3
•
Sx2 = 22208 and ( Sx) = 129600
2
129600
6
5
22208 -
13
For an answer without working, award 0/4
Mathematics : Intermediate 2 : Paper 2 : Units 1,2,3 : Item Bank
part
marks
Syllabus Code
(a)
2
2.3
(b)
(c)
1
1
2.3
2.3
Calc. Code
Grade
(CN,CR,NC) (C, B, A)
CN
C
CN
CN
Source
2001 q3
C
C
The contents of twenty matchboxes were counted.
44
44
46
45
47
48
47
41
48
45
45
44
42
43
44
46
46
43
49
45
(a)
Construct a dot plot for the data.
(b)
Describe the shape of the distribution.
(c)
What would you expect the “average contents per matchbox” to be?
2
Give 1 mark for each •
•1
start dot plot(scale & 1 point)
•2
complete dot plot
Notes
1
–
2 marks
3
•
symmetrical
1 mark
4
•
45
1 mark
14
1
1
Mathematics : Intermediate 2 : Paper 2 : Units 1,2,3 : Item Bank
part
marks
Syllabus Code
5
2.1
Calc. Code
Grade
Source
(CN,CR,NC) (C, B, A)
CR
A/B
2001 q4
N
Gordon and Brian leave a hostel at the same time.
Gordon
Gordon walks on a bearing of 045∞ at a speed of 4.4 kilometres per hour.
Brian walks on a bearing of 100∞ at a speed of 4.8 kilometres per hour.
If they both walk at steady speeds, how far apart will they be after 2 hours?
Hostel
5
Brian
Give 1 mark for each •
•1
8.8 * & 9.6
•2
–GHB = 55∞
Notes
1
For an answer without working, award 0/5
2
3
3
start to use cosine rule
4
•
GB2 = 8.8 2 + 9.6 2 - 2.8 ◊ 8.9 ◊ 6 cos 55∞
•5
8.5km
•
Values at •1 and •2 may be indicated on a diagram
A scale drawing may be used. mark out of 5 (must
include a statement about scale used).
5 marks
15
Mathematics : Intermediate 2 : Paper 2 : Units 1,2,3 : Item Bank
part
marks
Syllabus Code
(a)
2
3.2
(b)
(c)
2
1
3.2
3.2
Calc. Code
CN
CN
Source
2001 q5
C
C
y
The equation of the parabola shown is y = ( x - 2)2 - 9 .
(a)
Grade
(CN,CR,NC) (C, B, A)
CN
C
State the coordinates of the minimum turning point of the parabola.
x
(b)
Find the coordinates of C.
(c)
A is the point (–1,0). State the coordinates of B.
Give 1 mark for each •
Notes
1
In (a) and (b)
( x) = 2
For an answer without working, award 2/2
2
( y) = -9
3
y = (0 - 2) - 9
4
(0 , -5)
•
2 marks
•
•
2
2 marks
5
•
( 5, 0)
1 mark
16
2
1
C
•1
2
B
A O
Mathematics : Intermediate 2 : Paper 2 : Units 1,2,3 : Item Bank
part
marks
Syllabus Code
(a)
3
1.2
(b)
4
1.2
Calc. Code
Grade
(CN,CR,NC) (C, B, A)
CR
C
CR
Source
2001 q6
A/B
A drinks container is in the shape of a cylinder with radius 20
centimetres and height 50 centimetres.
(a)
50 cm
Calculate the volume of the drinks container
Give your answer in cubic centimetres, correct to 2
significant figures.
(b)
20 cm
3 cm
3
The liquid from the full container can fill 800 cups, in
the shape of cones, each of radius 3 centimetres.
What will be the height of liquid in each cup?
4
Give 1 mark for each •
•1
p.20 2 .50
•2
62831.8
3
•
Notes
1
–
63 , 000 cm3
3 marks
4
•
•5
•6
•7
vol of cylinder ∏ 800
1
.p.3 2 .h
3
1
.p.3 2 .h = 78.75
3
8.3 cm
4 marks
17
Mathematics : Intermediate 2 : Paper 2 : Units 1,2,3 : Item Bank
part
marks
Syllabus Code
3
1.4
Calc. Code
Grade
(CN,CR,NC) (C, B, A)
CN
A/B
Source
2001 q7
Multiply out the brackets and collect like terms.
(
)
( x + 4 ) 2 x2 + 3 x - 1
3
Give 1 mark for each •
Notes
1
–
•1
at least 3 terms correct inc. 2 x3
•2
2 x3 + 3 x2 - x + 8 x2 + 12 x - 4
•3
2 x3 + 11x2 + 11x - 4
3 marks
18
Mathematics : Intermediate 2 : Paper 2 : Units 1,2,3 : Item Bank
part marks
Syllabus Code
5
Calc. Code
Grade
(CN,CR,NC) (C, B, A)
CR
A/B
2.1
Source
2001 q8
A
A regular pentagon ABCDE is drawn in a circle, centre O,
with radius 10 centimetres.
Calculate the area of the regular pentagon.
10 cm
E
B
O
D
Give 1 mark for each •
•1
evidence of split into 5 triangles
•2
72∞
1
.10.10 sin 72∞
2
•3
•4
47.55cm
•5
238 cm2
Notes
1
2
5 marks
19
–
C
5
Mathematics : Intermediate 2 : Paper 2 : Units 1,2,3 : Item Bank
part marks
(a)
(b)
2
4
Syllabus Code
3.1
3.2
Calc. Code
Grade
(CN,CR,NC) (C, B, A)
CN
CR
A/B
A/B
Source
2001 q9
-1
2
Express a ÊË 2 a 2 + a ˆ¯ in its simplest form.
(a)
2
2
Solve the quadratic equation 3 x + 3 x - 7 = 0 using an appropriate formula.
Give your answers correct to 1 decimal place.
(b)
Give 1 mark for each •
3
1
2a 2
2
2a 2 + a 3
•
•
Notes
1
For an answer without working, award 0/4
or a 3
3
2 marks
3
•
use quadratic formula
•
-3 ± 3 2 - 4.3.( -7 )
6
D = 93
•6
1.1 and - 2.1
4
•
5
4 marks
20
4
Mathematics : Intermediate 2 : Paper 2 : Units 1,2,3 : Item Bank
part marks
Syllabus Code
5
Calc. Code
Grade
(CN,CR,NC) (C, B, A)
CR
A/B
1.5
Source
2001 q10
The diagram shows a mirror which has been designed
for a new hotel.
O
The shape consists of a sector of a circle and a kite
140∞
AOCB.
A
C
• The circle, centre O, has a radius of 50 centimetres.
• Angle AOC = 140∞
• AB and CB are tangents to the circle at A and C
respectively.
B
Find the perimeter of the mirror.
Give 1 mark for each •
•1
•2
•3
•4
•5
Notes
1
–
220
.p.100
360
192 cm
evidence of arc + 2 lengths
AB
or equiv.
tan 70∞ =
50
467 cm
5 marks
21
5
Mathematics : Intermediate 2 : Paper 2 : Units 1,2,3 : Item Bank
part marks
Syllabus Code
(a)
3
3.3
(b)
2
3.3
(a)
Solve the equation 4 tan x∞ + 5 = 0 ,
(b)
Show that tan x∞ cos x∞ = sin x∞ .
0 £ x £ 360 .
•2
5
or equiv.
4
( x) = 128.7
•3
( x) = 308.7
Notes
1
–
tan x∞ = -
3 marks
•4
•5
Grade
CN
Source
2001 q11
A/B
3
2
Give 1 mark for each •
•1
Calc. Code
(CN,CR,NC) (C, B, A)
CR
C
sin x
= tan x
cos x
sin x
2 marks
22