1. ppr maths nbk
1449/1
Mathematics
Paper 1
October
2007
1
1 hours
4 JABATAN PELAJARAN NEGERI
NEGERI SEMBILAN DARUL KHUSUS
PPSMI ASSESSMENT
2007
MATHEMATICS
Form Four
Paper 1
One hour and fifteen minutes
Kertas 2
DO NOT OPEN THIS QUESTION PAPER UNTIL YOU ARE TOLD TO DO SO
1. This question paper consists of 40 questions.
2. Answer all questions.
3. Each question in this paper has four suggested answers marked A , B , C and D.
Choose only one answer for each question and shade the correct space on the answer
sheet provided.
4. Think carefully before answering. If you wish to change your answer, erase properly
and shade your new answer.
This question paper has xx printed pages.
2. 1449/1 2 Form Four
MATHEMATICAL FORMULAE
The following formulae may be helpful in answering the questions. The symbols given are the
ones commonly used.
RELATIONS
1 am × an = am + n 12 Pythagoras Theorem
c2 = a2 + b2
2 am ÷ an = am − n 13 y2 − y1
m=
x2 − x1
3 (am )n = am n 14 y − intercept
m=−
x − intercept
4 1 ⎛ d − b⎞
A−1 = ⎜ ⎟
ad − bc ⎜ − c a ⎟
⎝ ⎠
5 n( A)
P ( A) =
n( S )
6 P ( A' ) = 1 − P( A)
7 Distance = ( x2 − x1 ) 2 + ( y2 − y1 ) 2
8 ⎛ x + x y + y2 ⎞
Midpoint, ( x, y ) = ⎜ 1 2 , 1 ⎟
⎝ 2 2 ⎠
9 distance travelled
Average speed =
time taken
10 sum of data
Mean =
number of data
11 sum of (class marks × frequency)
Mean =
sum of frequencies
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3. 1449/1 3 Form Four
SHAPES AND SPACE
1 1
Area of trapezium = × sum of parallel sides × height
2
2 Circumference of circle = π d = 2 π r
3 Area of circle = π r 2
4 Curved surface area of cylinder = 2 π r h
5 Surface area of sphere = 4 π r 2
6 Volume of right prism = cross sectional area × length
7 Volume of cylinder = π r 2 h
8 1
Volume of cone = π r 2 h
3
9 4
Volume of sphere = π r 3
3
10 1
Volume of right pyramid = × base area × height
3
11 Sum of interior angles of polygon = (n −2)×180°
12 arc length angle subtended at centre
=
circumference of circle 360o
13 area of sector angle subtended at centre
=
area of circle 360o
14 PA'
Scale factor, k =
PA
15 Area of image = k2 × area of object
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4. 1449/1 4 Form Four
1. Round off 0⋅0459 correct to two significant figures.
A 0⋅04
B 0⋅045
C 0⋅046
D 0⋅05
2. Express 0⋅00205 in standard form.
A 2⋅05 × 103
B 2⋅05 × 102
C 2⋅05 × 10−3
D 2⋅05 × 10−2
3. 2⋅38 × 104 − 8⋅41 × 103 =
A 1⋅539 × 104
B 1⋅539 × 103
C 6⋅03 × 104
D 6⋅03 × 103
5.2 × 10 −7
4. =
(4 ×10 )
−2 2
A 3⋅25 × 10−4
B 1⋅3 × 10−3
C 3⋅25 × 10−12
D 1⋅3 × 10−11
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5. 1449/1 5 Form Four
5. The volume of a bottle of mineral water is 512 ml.
The total volume, in litres, of 6 similar bottles of mineral water, correct to three
significant figures is
A 3⋅07
B 30⋅7
C 307
D 3070
6. ( r − 2s )( 5r + s ) =
A 5r2 − 9rs − 2s2
B 5r2 − 9rs + 2s2
C 5r2 + 11rs − 2s2
D 5r2 + 11rs + 2s2
7. 5g ( g − h ) − ( 2g − h )2 =
A g2 − gh − h2
B g2 − 5gh − h2
C g2 − 5gh + h2
D g2 − 9gh + h2
8. It is given that the universal set ξ = { 1 , 2 , 3 , 4 , 5 , 6 , 7 }, set P = { 1 , 3 , 5 , 7 } and
set P ∩ Q = { 5 , 7 }.
If ξ = P ∪ Q , list all the elements of set Q’.
A 1,3
B 2,4,6
C 1,2,3,4,6
D 2,4,5,6,7
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6. 1449/1 6 Form Four
9. Diagram 1 shows a Venn diagram which shows the number of elements of sets J , K
and L.
J K L
5 3 1 4 2
DIAGRAM 1
If the universal set ξ = J ∪ K ∪ L , find n( J’ ∩ L ).
A 3
B 4
C 6
D 7
10. The Venn diagram in Diagram 2 shows the universal set ξ, the elements of sets P , Q
and R.
ξ
P Q
•7 R
•1 •2
•8
•4 •5
•6
•3
DIAGRAM 2
State all the elements of set P’ ∩ R’.
A 2,6
B 2,3,6
C 2,6,8
D 2,3,6,8
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7. 1449/1 7 Form Four
11. Find the y-intercept of the straight line 5x − 3y = 15.
A 5
B 3
C −3
D −5
x y
12. Find the x-intercept of the straight line + = 1.
3 4
1
A
4
1
B
3
C 3
D 4
13. Diagram 3 shows the straight line PQ on a Cartesian plane. DO GRIDS without
coords. y
P(−3,3)
x
O
Q(1,−5)
DIAGRAM 3
Find the gradient of PQ.
A −2
1
B −
2
C 1
D 2
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8. 1449/1 8 Form Four
14. Diagram 4 is a bar chart which shows the score of a Mathematics quiz in class 4
Alpha
Number of students
10
8
6
4
2
Score
1 2 3 4 5
DIAGRAM 4
Find the median score.
A 4
B 3
C 2
D 1
15. Diagram 5 is a pictograph showing the number of books sold in January and
March. The number of books sold in February are not shown.
Month Number of books sold
January
February
March
represents 30 books
DIAGRAM 5
The mean number of books sold for the three months is 150.
Calculate the number of books sold in February.
A 60
B 90
C 142
D 210
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9. 1449/1 9 Form Four
16. Diagram 6 is a pie chart which shows four uniform groups in a certain school.
Police Cadets
Red Crescent Society
150°
75° School Youth Cadets
Scouts
DIAGRAM 6
Calculate the ratio of the number of students in the Red Crescent Society to the
number of students in the Police Cadets.
A 3 : 10
B 10 : 3
C 1:5
D 5:1
17. A box contains similar white balls and green balls.
A ball is picked at random from the box.
5
The probability of picking a green ball is .
9
If there are 36 balls in the box, calculate the number of white balls.
A 16
B 18
C 20
D 32
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10. 1449/1 10 Form Four
18. Diagram 7 shows eight numbered cards.
1 2 3 4 5 6 7 8
DIAGRAM 7
A card is picked at random.
Find the probability that the number shown is a factor of 8.
1
A
8
1
B
4
3
C
8
1
D
2
19. Ameen keeps his 15 blue marbles and 7 red marbles in a box. Later Ameen adds 3
blue marbles and 5 red marbles into the same box.
A marble is chosen at random from the box.
Find the probability of choosing a red marble.
2
A
5
7
B
22
4
C
9
6
D
11
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11. 1449/1 11 Form Four
20. Diagram 8 shows some letter cards.
P L E A S E B E Q U I E T
DIAGRAM 8
A card is picked at random.
Find the probability that a card with letter E is picked?
1
A
13
1
B
4
2
C
5
4
D
13
21. In Diagram 9, LMN is a tangent to the circle at the points M.
N
M
O 56° P
z°
L 120°
Q
DIAGRAM 9
Find the value of z.
A 28
B 38
C 68
D 72
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12. 1449/1 12 Form Four
22. In Diagram 10, PQR is a tangent to the circle QTS at Q.
S
P
x°
Q 105°
65° T U
R
DIAGRAM 10
Find the value of x.
A 30
B 40
C 50
D 60
23. In Diagram 11, EFG is a tangent to the circle at F. JOK is the diameter of the circle.
HJF is a straight line.
H
y° O K
J
30°
E F G
DIAGRAM 11
Find the value of y.
A 105
B 120
C 135
D 150
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13. 1449/1 13 Form Four
24. It is given that cos y°= −0⋅8251 and 90°≤ y°≤ 270°.
Find the value of y.
A 124⋅40
B 145⋅60
C 214⋅40
D 235⋅60
25. In Diagram 12, O is the centre of the unit circle.
y
1
P(0⋅6231,0⋅8816)
−1 θ° 1 x
O
−1
DIAGRAM 12
The value of θ is
A 28⋅16
B 38⋅54
C 51⋅46
D 61⋅83
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14. 1449/1 14 Form Four
26. In Diagram 13, QRS is a straight line.
P
4 y°
Q R S
DIAGRAM 13
4
Given that cos ∠QPR = , find the value of cos y°.
5
3
A
5
4
B
5
3
C −
5
4
D −
5
27. In Diagram 14, LMN and PQ are two vertical poles standing on a horizontal ground.
L
M P
N Q
DIAGRAM 14
The angle of elevation of peak L from peak P is
A ∠LPN
B ∠LQN
C ∠MPL
D ∠MLP
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15. 1449/1 15 Form Four
28. In Diagram 15, EF is a vertical flag pole. GF is horizontal.
E
G 20 m F
DIAGRAM 15
The angle of depression of G from E is 35°.
Calculate the height, in m, of the flag pole EF.
A
B
C
D
29. Diagram 16 shows a right prism with a rectangular base EFGH. The trapezium EFQP
is the uniform cross section of the prism.
S
P R
Q
H
E
G
F
DIAGRAM 16
Identify the angle between the line PG and the base EFGH.
A ∠PGE
B ∠PGF
C ∠PGH
D ∠PGR
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16. 1449/1 16 Form Four
30. Diagram 17 shows a right pyramid with a square base JKLM. The vertex V is
vertically above M.
V
M
J L
K
DIAGRAM 17
Identify the angle between the plane VKL and the base JKLM.
A ∠VKM
B ∠VML
C ∠VLM
D ∠VMK
31. In Diagram 18, PQRST are 5 consecutive vertices of a regular polygon.
P
Q T
30°
R S
DIAGRAM 18
Find the number of sides of the polygon.
A 5
B 6
C 10
D 12
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17. 1449/1 17 Form Four
32. In Diagram 19, PQRSTU is a regular hexagon. UQV and SRV are straight lines.
V
n°
P Q
m°
U R
T S
DIAGRAM 19
Find the value of m + n.
A 108
B 120
C 144
D 180
33. Diagram 20 shows two quadrilaterals, KLMN and EFGH drawn on a square grid.
E
K
P•
N
Q• S• H
R•
L M
F G
DIAGRAM 20
Quadrilateral EFGH is the image of quadrilateral KLMN under an enlargement.
State the centre of enlargement.
A P
B Q
C R
D S
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18. 1449/1 18 Form Four
34. Diagram 21 shows two triangles PQR and RST drawn on a square grid.
P
T
Q S
R
DIAGRAM 21
The triangle RST is the image of the triangle PQR under a clockwise rotation.
State the centre of rotation and the corresponding angle of rotation.
Centre Angle of rotation
A R 90°
B T 90°
C R 270°
D T 270°
35. It is given that 5 − 3(2k + 1) = 2k + 4.
Find the value of k.
5
A −
2
3
B −
2
1
C
5
3
D
4
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19. 1449/1 19 Form Four
h
36. Given that h − r = , express h in terms of r.
r
2r
A
r −1
2r
B
r +1
r2
C
r −1
− r2
D
r +1
3
5
37. Which of the following is equivalent to w ?
5
A w3
3
B w5
C (w) 3
5
D (w) 5
3
(27m n ) × n
1
3 9 3 9
38. Simplify
(m n )
1
−2 4 2
A
B
C
D
39. List all the integers x which satisfy both the inequalities 8 − x ≤ 6 and
3(x − 6) ≤ 12 − 2x.
A 2,3,4,5
B 2,3,4,5,6
C 3,4,5
D 3,4,5,6
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20. 1449/1 20 Form Four
5n
40. The solution for n − 1 ≤ = 4 is
2
A n ≥ −2
B n≥2
C n ≤ −2
D n≤2
END OF QUESTION PAPER
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