spm mat trial 15 1

8/2/2019 Spm Mat Trial 15 1

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Portal Pendidikan Utusan 2008 © Hak Cipta TerpeliharaUtusan Melayu (M) Berhad, Kuala Lumpur 1

SPM MATHEMATICS

SET 1

PAPER 1

Answer all questions .

1. Round off 73 900 correct to two significant figures.

A 74B 740C 73 000D 74 000

2. Express 0.00804 in standard form

A 8.04× 10

2

B 8.04 × 103

C 8.04 × 10 –3

D 8.04 × 10 –5

3. 5.3 × 10 –6 − 7.37 × 10 –7 =

A 4.563× 10 –6

B 4.563 × 10 –7

C 2.07 × 10 –6

D 2.07 × 10 –7

4. Express 235 as a number in base eight.

A 158 B 278

C 518 D 728

5. 10012 + 1112 =

A 10002B 11102

C 111112

D 100002




6. In Diagram 1 shows three congruent rectangles.

6 cm

2 cm

DIAGRAM 1

Calculate the total area, in m2, of the whole diagram.

A 1.8× 10 –5

B 1.8 × 10 –4

C 1.8 × 10 –3

D 1.8 × 105

7. Diagram 2 shows a pentagon ABCEF. ABF is an isosceles triangle andDEF is a straight line.

DIAGRAM 2

The value of x + y = A °75

B °115

C °125

D °135

50o

65o

125o

xo

yo

A

B

C

D

E

F x

o




8. In Diagram 3, the value of x is.

DIAGRAM 3

A 65B 70C 80

D 105

9. Diagram 4 shows an observer and a tower standing on horizontalground. The angle of elevation of the top of the tower Q, from theobserver P is 350.

Q

P

56 m

DIAGRAM 4

Calculate the height, in m, of the tower.

A 33.62B 40.71C 44.37D 45.87

1.5 m

x°

75°

115°

145°




10. In Diagram 5, PQR is a tangent to the circle centre O, at point Q.

DIAGRAM 5

Given that OTP is a straight line. Find the value of θ.

A 120B 135C 150D 165

11 In Diagram 6, MLK is a straight line.

J

x0

y0

M L K

DIAGRAM 6

Given sin x0 =

13

5, then tan y

o =

A5

12− B

12

5− C

12

5D

5

12

S

P Q

T

θ°

O

30°




12 Diagram 7 shows a right prism with a horizontal base RSTU. Theprism has a uniform cross section in the form of trapezium PQRS.

W V

P Q

T U

S R

DIAGRAM 7

Name the angle between the plane WSR and the plane RSTU.

A ∠ WRT

B ∠ WRUC ∠ WSR

D ∠ WST

13 Given that tan x0 = −1.1918 and 00 ≤ x

0 ≤ 3600, find the values of x.

A 130 and 230

B 130 and 310

C 140 and 220

D 230 and 310

14 In Diagram 8, P, Q and R are three points on a horizontal plane. R liesto the east of P. The bearing of Q from P is 0720.

Q

P R

DIAGRAM 8

The bearing of R from Q is

A 1620 B 1980 C 2880 D 3420




15 Given that 5 − 2 ( p + 2) = p, then p =

A3

1−

B 3

1

C −3D 3

16 (2 x − 3)2 − 2( x − 5) =

A 4 x2 − 2 x − 14

B 4 x2 − 2 x + 14

C 4 x2 − 14 x − 19

D 4 x2 − 14 x + 19

17 Given that pr

=−3

4 2

, then r =

A p3

4

B 23 − p

C 43 − p

D p34 −

18ab

b

a 10

4

2

1 −− =

Aab

b

5

)1(2 −

B

ab

ba

5

3 −

Cab

a

5

23 +

Dab

b

5

23 −




19 Simplify ( )2

17316 p p ×−

A 24 p B 216 p

C 54 p D 516 p

20 Find the value of 3

)2(922

1

2

3

×

A 6B 12C 18D 36

21 In Diagram 9, Q is an image of P under a rotation of 900 anti clockwise.

Q

P

DIAGRAM 9State the coordinates of the centre of rotation.

A (5, 5) B (5, 6) C (6, 1) D (6, 2)

22 Diagram 10 shows the point M and the line y = x. Transformation Prepresents a reflection in the line y = x.

y

M

DIAGRAM 10

2 4 6

- 2

- 2

2

4

6

x

2 4 6 8

2

4

6

8

y

x0

0

y = x




State the coordinates of the image of point M under the transformation P.

A (1,−1) B (1, 3) C (3, 1) D (5, 3)

23 In Diagram 11, triangle PST is the image of triangle PQR under theenlargement at centre P.

DIAGRAM 11

Find the scale factor of the enlargement.

A2

1B

3

1C 2 D 3

24 List all the integers x which satisfy both the inequalities x < 6 and

2x + 3 ≥ 8.

A 2, 3, 4B 3, 4, 5C 2, 3, 4, 5D 3, 4, 5, 6

y

2 3 4

2

1

4

6

8

x5

1

3

5

7

P Q

R

S

T

0




25 Which one of the following graphs represents y = tan x ?

A

B

C

D

90°45°0

y

x

y

180°90°0

y

x

y

270°90°0

y

x

y

360°180°0

y

x

y




26 Which one of the following graphs represents x

y2

−= ?

A B

C D

-2

2

-2

-2

y y

x

x

x

x

y y

0 0

0 0




27 Diagram 12 shows the graph of y = x3 + 2.

P

DIAGRAM 12

Which one of the following is the coordinates of P?

A (1, 5)B (2, 8)C (3, 29)D (8, 26)

28 In Diagram 13 the gradient of the line PQ is4

3− .

P(0, 6)

Q

DIAGRAM 13

The x-intercept for the line PQ is

A −8

B −4C 6D 8

y

x

2

O

y

x0




29 Given that ξ = x : 20 < x < 30, x is an integer,

set K = x : x are numbers such as x < 26and set L = x : x is a prime number. Find n(K ∩ L) .

A 1

B 2C 3D 4

30 Diagram 14 shows a Venn diagram with the universal set ξ, set P and setQ. Set R is not shown in the diagram. Set R is a subset of set P.

ξ

P . 1 . 3 Q

. 2 . 4 . 5. 6 . 7

. 8

DIAGRAM 14

Set R is

A {1, 2, 3}B {2, 4, 6}C {3, 5, 7}D {3, 5, 7, 8}

31 Given that the universal set ξ = { x : 11 ≤ x ≤ 24, x is an integer},set P = { x : x is a prime number}set Q = { x : x is a number such that the product of its digits areodd numbers}

List all the elements of set P ∪ Q.

A {11, 13, 17, 19}B {13, 15, 17, 19, 23}C {11, 13, 15, 17, 19, 23}D {11, 13, 15, 17, 19, 21, 23}




32 In the diagram 15, O is the centre of the earth and NGS is the Greenwichmeridian.

DIAGRAM 15

L, M and B are three towns on the surface of the earth.Given that ∠MOB = 40°, the longitude of town L is

A 40 °EB 140 °EC 140 °WD 140 °S

33 Table 1 shows the score obtained by a group of students in a quiz.

Score 0 1 2 3 4

Number of students

3 5 7 x 9

TABLE 1

If the median score is 2, the possible value of x could be

A 5 B 6 C 7 D 8




34 Diagram 16 shows a straight line PQ on a Cartesian plane.

The gradient of PQ is

A −4

B −3C 3

D 12

35 From the following equation of the straight lines, the equation of thestraight line which parallel with the x- axis is

A 2= x

B y x =

C x y −=

D 2= y

36 Table 2 shows the number of marbles with different colours in a box.

Colour Yellow Red Green

Number of

marbles

6 8 11

TABLE 2

If a marble is drawn at random from the box, state the probability thatthe marble drawn is green in colour.

A11

1B

14

1C

25

11D

25

1

30

12

y

x

P

Q

DIAGRAM 16




37 A class consists of 33 students. There are 10 Malay students and the restare Chinese and Indians. If a student is chosen at random from the class,

the probability of choosing an Indian student is3

1. How many Chinese

students are there in the class?

A 11 B 12 C 21 D 22

38. A bag contains 16 white balls and a few blue balls which are of the same

size. The probability of a white ball chosen at random is5

2. Another 4

balls are being added into the bag. If a ball is chosen at random,calculate the probability of choosing a white ball.

A 5

3

B 2

1

C 11

4

D 11

5

DIAGRAM 17

39 Diagram 17 is a pie chart showing the results of a test. Given that thenumber of students who obtained Grade B is 60, find the number of students who got grade C .

A 48B 36C 24

D 12

40 Given that ⎟⎟ ⎠

⎞⎜⎜⎝

⎛ =⎟⎟

⎠

⎞⎜⎜⎝

⎛ −+⎟⎟

⎠

⎞⎜⎜⎝

⎛ 7

5

5

22

3

9

k . Find the value of k .

A −3 B −2 C −1 D 2




ANSWERS

1 D 21 A

2 C 22 C

3 A 23 D

4 A 24 B

5 D 25 B

6 C 26 C

7 C 27 C

8 B 28 D

9 A 29 C

10 C 30 B

11 A 31 D

12 D 32 C

13 B 33 A

14 A 34 A

15 B 35 D

16 D 36 C

17 D 37 B

18 D 38 D

19 A 39 D

20 C 40 C

spm mat trial 15 1

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