Maths Ppsmi 2006 F4 P2

Panel Pakar Runding GC MMMT
Form Four
1449/2
Mathematics Name : …………………………………
Paper 2
October Form : …………………………………
2006
1
2 hours
2
JABATAN PELAJARAN NEGERI
NEGERI SEMBILAN DARUL KHUSUS

PPSMI ASSESSMENT
2006
For examiner’s use only
MATHEMATICS
Total Marks
Section Question
Paper 2 Marks Obtained
1 3
Two hours and thirty minutes 2 4
DO NOT OPEN THIS QUESTION PAPER 3 4
UNTIL YOU ARE TOLD TO DO SO 4 6
1 This question paper consists of two sections, 5 4
Section A and Section B. Answer all questions in
Section A and four questions in Section B. A 6 5
7 5
2 Write your answers clearly in the spaces provided
in the question paper. 8 4
3 Write in blue / black pen. You may use a pencil for 9 5
diagrams or graphs. 10 6
4 The marks allocated are given in brackets at the 11 6
end of each question or part question.
12 12
5 Diagrams in the question paper are not drawn to 13 12
scale unless stated.
B 14 12
6 Show all your working. Omission of essential
working will result in loss of marks. 15 12
16 12
7 You are allowed to use non-programmable
calculators.
Total
9 This question paper must be handed in at
the end of the examination.

This question paper has 26 printed pages
[Turn Over

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2 Panel Pakar Runding GC MMMT
The following formulae may be helpful in answering the questions. The symbols given are the ones
commonly used.

RELATIONS
1 am × an = am+n

2 am ÷ an = am−n

3 (am) n = amn

1 ⎛ d − b⎞
4 A −1 = ⎜ ⎟
ad − bc ⎜ − c a ⎟
⎝ ⎠

n (A)
5 P(A) =
n (S)

6 P(A’) = 1 − P(A)

7 Distance = ( x1 − x 2 ) 2 + ( y1 − y 2 ) 2

8 Midpoint
⎛ x + x 2 y1 + y 2 ⎞
(x, y ) = ⎜ 1 , ⎟
⎝ 2 2 ⎠

dis tan ce travelled
9 Average speed =
time taken

sum of data
10 Mean =
number of data

sum of (class mark × frequency)
11 Mean =
sum of frequencies

12 Phythagoras Theorem
c2 = a2 + b2

y 2 − y1
13 m=
x 2 − x1

y − int ercept
14 m= −
x − int ercept

PPSMI/Maths/F4/P2 https://panelmathsaddmathswordpress.com/

SHAPE AND SPACE
1
1 Area of trapezium = × sum of parallel sides × height
2

2 Circumference of circle = πd = 2πr

3 Area of circle = πr2

4 Curved surface area of cylinder = 2πrh

5 Surface area of sphere = 4πr2

6 Volume of right prism = cross sectional area × length

7 Volume of cylinder = πr2h

1 2
8 Volume of cone = πr h
3
4
9 Volume of sphere = πr3
3
1
10 Volume of right pyramid = × base area × height
3
11 Sum of interior angles of a polygon = ( n − 2) × 180°

arc length angle subtended at centre
12 =
circumference of circle 360 o

area of sec tor angle subtended at centre
13 =
area of circle 360 o

PA '
14 Scale factor, k =
PA

15 Area of image = k2 × area of object


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For Section A
Examiner’s
Use
[52 marks]

Answer all questions in this section.

1. The Venn diagrams in the answer space shows sets P, Q and R.
On the diagram provided in the answer spaces, shade

(a) the set P’ ∩ Q’

(b) the set (Q ∩ R)’ ∩ P
[3 marks]

Answer:

(a)
ξ
P Q
R

(b)

ξ
P
R
Q

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2. Diagram 1 shows a solid formed when a cylinder is taken out from the pyramid. For
The base of the pyramid is a square. Examiner’s
Use

15 cm

DIAGRAM 1

The height of the cylinder is 9 cm and the diameter is 7 cm.
The height of the pyramid is 21 cm.

22
By using π = , calculate the volume, in cm3, of the solid.
7
[4 marks]

Answer:

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For 3. Calculate the values of m and n that satisfy the following simultaneous linear
Examiner’s equations:
Use
2m + n = 3
4m − 3n = 11

[4 marks]

Answer:

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4. Diagram 2 shows two sectors OPJQ and OSR with the same centre O. For
Examiner’s
Use
S
J

P 60°
Q
O R

DIAGRAM 2

OR = 21cm and OQ = 14cm.
22
Using π = , calculate
7

(a) the perimeter, in cm, of the whole diagram,

(b) the area, in cm2 , of the shaded region.
[6 marks]
Answer:

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For 5. Solve the equation x(2x – 5) + 3 = 0
Examiner’s [4 marks]
Use

Answer:

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6. (a) Is the sentence below a statement or non-statement? For
Examiner’s
Use
“ 3 + 5 = 1 + 9 ”.

(b) Write down two implications based on the following sentence.

“ 4k < 20 if and only if k < 5”

(c) Complete the premise in the following argument :

Premise I : If n + 1 is an even number then n is an odd number.
Premise II : n is not an odd number.
Conclusion :

[4 marks]
Answer:

(a)

(b) Implication 1:

Implication 2:

(c) Conclusion:

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For 7. In Diagram 3, the graph shows the straight lines JK, JL and RS.
Examiner’s
Use
y

S(13,20)
K

J L

x
O R

DIAGRAM 3

J is on the y-axis and R is on the x-axis. JL is parallel to the x-axis and JK is
parallel to RS. The equation of JK is 2y = 6x + 8.

(a) State the equation of the straight line JL.

(b) Find the equation of the straight line RS.

(c) State the x-intercept of the straight line RS.
[6 marks]
Answer:

(a)

(b)

(c)

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8. Diagram 4 shows a cube with DCGH as the horizontal base. For
Examiner’s
A B Use

E F

6 cm
D C
3 cm
H 4 cm G

DIAGRAM 4
[4 marks]
Calculate the angle between the line AG and the plane DCGH.

Answer:

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For 9. (a) While on vacation in Cherating, Samuri decides to buy 6 postcards for
Examiner’s Jamil, 3 postcards for Mala and 2 postcards for Teck Sin. All the
Use
postcards are kept in a bag.
If a postcard is taken at random from the bag, find the probability that
the postcard is for Jamil.

(b) In a class, 12 pupils are from Perak.
If a pupil is chosen at random from the class, the probability of choosing a
1
pupil from Perak is .
3
Find the number of pupils in the class.
[5 marks]
Answer:
(a)

(b)

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10. In Diagram 5 , O is the origin. For
Examiners’s
y Use

P(9,15)
Q(3,10)

x
R O
DIAGRAM 5

OP is parallel to RQ.

Find

(a) the gradient of RQ,

(b) the equation of the straight line RQ,

(c) the x-intercept of RQ.
[6 marks]
Answer:

(a)

(b)

(c)

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For 11. (a) Complete the following mathematical statements in the using the
Examiner’s
Use
symbols < or > to form
(i) a true statement
2×3 2+3

(ii) a false statement
(2 +3)2 22 + 32

(b) Complete the premise in the following argument:

Premise 1 : All pentagons have five sides.
Premise 2 : ________________________
Conclusion : PQRST has five sides.

(c)
0 = 3(0)2
3 = 3(1)2
12 = 3(2)2
27 = 3(3)2

Based on the information above, make a general conclusion by induction
regarding the number sequence 0 , 3 , 12 , 27 , . . .
[6 marks]
Answer:

(a) (i)
2×3 2+3

(ii)
(2 +3)2 22 + 32

(b) Premise 2 :

(c)

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Section B For
[48 marks] Examiner’s
Use

Answer four questions in this section.

12. (a) In Diagram 6, OABC is a parallelogram. O is the origin.
y B

A(1,4)

C(5,2)

O x
DIAGRAM 6
Find
(i) the gradient of OA
(ii) the equation of the straight line BC
(iii) the y-intercept of the line AB.
[5 marks]
(b) Diagram 7 shows a pyramid JKLMN.
N

5 cm

K

J L

M
DIAGRAM 7

The base JKLM is a square. MN = 13 cm.
(i) Calculate the angle between the line NL and the base JKLM.
(ii) Calculate the angle between the plane NLM and the base JKLM.
[7 marks]

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For Answer:
Examiner’s
Use
12. (a) (i)

(ii)

(iii)

(b) (i)

(ii)

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13. (a) Diagram 8 shows some number cards. For
Examiner’s
Use
2 3 5 6 8 9 11 12

DIAGRAM 8

All the cards are put inside a box. A card is drawn at random from the box.

(i) List its sample space.
(ii) List the elements of the event of getting even number
(iii) Find the probability of getting an odd number
(iv) A boy adds 2 even numbered cards to the box. A card is then drawn at
random from the box. Find the probability of getting an even number.
[6 marks]

(b) In Diagram 9, JK and PQ are arcs of two different circles with centre O.
K

Q T
J

P 150°

O R

DIAGRAM 9

ORTQ is a square. OJ = 28 cm and P is a centre of OJ.
22
Using π = , calculate
7
(i) the perimeter, in cm, of the whole diagram.
(ii) the area, in cm2, of the shaded region.
[6 marks]

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For Answer:
Examiner’s
Use
13. (a) (i)

(ii)

(iii)

(iv)

(b) (i)

(ii)

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For
Examiner’s
14. (a) Solve the equation 3n − 4 = 11n.
2
Use
[4 marks]
1 2
(b) Solve the equation 20 + x = x +8.
2
[4 marks]
(c) Diagram 10 shows a solid formed by joining a half cone
and a half cylinder.

10 cm

DIAGRAM 10

The diameters of the cylinder and the base of the cone are both 14 cm.
The height of the cone is 5 cm.
22
Using π = , calculate the volume, in cm3 , of the solid.
7
[4 marks]

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For 14. (a)
Examiner’s
Use

(b)

(c)

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15. Diagram 11 shows the ages, in years, of 30 participants in a game on a family day. For
Examiner’s
Use
3 11 13 14 18 12
23 24 7 13 22 13
19 27 6 16 24 29
13 25 8 11 20 17
14 17 18 16 9 16

DIAGRAM 11

a) Based on the data in the diagram above, complete the following table in the
answer space.

Age Frequency Midpoint Upper boundary

1 - 5
6 - 10
11 - 15
16 - 20
21 - 25
26 - 30

[4 marks]

b) Based on the table in (a), calculate the estimated mean age of the participants.

[3 marks]

c) By using a scale of 2 cm to 5 years on x-axis and 2 cm to 1 participant on the
y-axis, draw a histogram for the data.
[4 marks]

d) From the histogram, find the percentage of participants who are more than
15 years old.
[1 mark]

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For
Examiner’s Answer:
Use

15. (a)
Age Frequency Midpoint Upper
(Years) Boundary
1−5
6 − 10
11 − 15
16 − 20
21 − 25
26 − 30

(b)

(c) Refer to page 23

(d)

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For
Examiner’s 16. Table 1 shows the distribution of the ages of 200 participants in a big walk event.
Use

Age ( years) Frequency

15 - 19 10

20 - 24 20

25 - 29 50

30 - 34 60

35 - 34 36

40 - 44 18

45 - 49 6

TABLE 1

(a) Using the data in Table 1, complete the table provided in the answer space.

[4 marks]

(b) Calculate the estimated mean age of the participants.

[3 marks]

(c) By using a scale of 2 cm to 5 years on the x-axis and 2 cm to 20 participants on

the y-axis , draw an ogive for the data.
[5 marks]

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Answer: For
Examiner’s
Use
(a)
Age (years) Frequency Cumulative Upper
Frequency Boundary

15 − 19 10

20 − 24 20

25 − 29 50

30 − 34 60

35 − 39 36

40 − 44 18

45 − 49 6

(b)

(c) Refer to page 26

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Maths Ppsmi 2006 F4 P2

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