Mrsm Maths P1 2005

SULIT 1449/1 Matematik Kertas 1 September 2005

1449/1

1¼ jam

MAKTAB RENDAH SAINS MARA

PEPERIKSAAN PERCUBAAN SIJIL PELAJARAN MALAYSIA 2005

MATEMATIK Kertas 1 Satu jam lima belas minit

1 4 4 9 1

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU 1.

Kertas soalan ini adalah dalam dwibahasa

2.

Soalan di halaman kiri adalah dalam bahasa Melayu. Soalan di halaman kanan adalah yang sepadan dalam bahasa Inggeris

3.

Calon dikehendaki membaca maklumat di halaman 2 atau halaman 3.

Kertas soalan ini mengandungi 39 halaman bercetak dan 1 halaman tidak bercetak

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©2005 Hak Cipta Bahagian Pendidikan & Latihan (Menengah) MARA

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INFORMATION FOR CANDIDATES 1. This question paper consists of 40 questions. 2. Answer all questions. 3. Answer each question by blackening the correct space on the answer sheet. 4. Blacken only one space for each question. 5. If you wish to change your answer, erase the blackened mark that you have made. Then blacken the space for the new answer. 6. The diagrams in the questions provided are not drawn to scale unless stated. 7. A list of formulae is provided on pages 4 to 7. 8. A booklet of four-figure mathematical tables is provided. 9. You may use a non-programmable scientific calculator.

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The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used. RELATIONS

1

a ×a

2

a m ÷ a n = a m–n

3

(a m)n = a mn

4

A–1 =

5

P(A) =

6

P(A' ) = 1 − P(A)

7

Distance = ( x1 − x2 ) 2 + ( y1 − y2 ) 2

8

Midpoint

m

n

= a

m+n

1 ⎛ d − b⎞ ⎜ ⎟ ad − bc ⎜⎝ − c a ⎟⎠

n ( A) n (S )

x + x y +y ( x , y ) = ⎛⎜ 1 2 , 1 2 ⎞⎟ ⎝

2

2

⎠

9

Average speed = distance travelled

10

Mean =

sum of data number of data

11

Mean =

Sum of (class mark × frequency) sum of frequencies

12

Pythagoras Theorem

time taken

c2 = a2 + b2 y2 − y1 x2 − x1

13

m=

14

m= −

y − intercept x − intercept

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SHAPE AND SPACE 1 × sum of parallel sides × height 2

1

Area of trapezium =

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

8

Volume of cone

=

1 2 πr h 3

9

Volume of sphere

=

4 3 πr 3

=

1 × base area × height 3

10 Volume of right pyramid

11 Sum of interior angles of a polygon = (n – 2) × 180°

12

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

13

angle subtended at centre area of sector = area of circle 360o

14 Scale factor , k =

PA' PA

15 Area of image = k 2 × area of object

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Answer all questions. 1

Round off 0.0062057 correct to three significant figures. A B C D

2

3.64 × 10 A B C D

3

4.5 × 10 − 8 – 5 + 2.1×10 − 2

=

6.35 x 10 −8 3.55 x 10 −7 3.64 x 10 −7 2.10 x 10 −2

4.412 x 10 6 4.412 x 10 3 4.412 x 10 −3 4.412 x 10 −9

Which of the following is equivalent to 62 8 ? A B C D

5

−7

In the year 2002, 205 122 ships stopped at Lumut Port with cargoes weighing up to a total of 905 million tonnes. Calculate the mean mass of cargoes, in tonnes, shipped in. A B C D

4

0.006 0.00620 0.00621 0.01

5110 2205 1100102 1111102

1101012 − 11102 = A B C D

1000012 1110102 1110112 1001112

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In Diagram 1, ABC is an equilateral triangle. A x° 43°

106° C B

DIAGRAM 1 The value of x is A B C D

7

31o 77o 91o 134o

In Diagram 2, PQRXST and RUVWX are regular polygons. PTY and VWY are straight lines. V W

U R

X

Q

S m° P

Y

T DIAGRAM 2

Find the value of m A B C D

24o 36o 48o 72o

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In Diagram 3, QSR is a circle with centre O. PQ and PR are tangents to the circle at Q and R. Q P 36° x° O S R DIAGRAM 3 POS is a straight line. Given that ∠OPQ = 36o, the value of x is A B C D

9

216o 234o 244o 252o

In Diagram 4, P and Q are two points on a horizontal ground. Nest A

Nest B

P

15 meter

Q

DIAGRAM 4 A tree is at a point P. The angles of depression of point Q from the nest A and the nest B are 21o and 14o respectively. Calculate the distance, in metres, between the two nests. A B C D

1.406 1.747 1.842 2.018

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In Diagram 5, TRW and PQR are straight lines.

10

P y Q

26 cm T

R

29 cm

21 cm

W

DIAGRAM 5 Q is the mid point of PR . Find the value of tan y. A B C D

12 5 12 − 13 5 − 12 5 − 13 −

Diagram 6 shows graphs of y = cos x and y = sin x .

11

y

1

y = cos x y = sin x

q

0

o

x

360

─1 DIAGRAM 6 Find the value of q . A B C D

90o 135o 180o 225o

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Diagram 7 shows a cube with a horizontal base ABCD. F

G

M E

H C

B

D

A

DIAGRAM 7 M is the midpoint of EF.

Calculate the angle between the line MA and the plane CDEF. A B C D

13

19.47o 41.81o 48.19o 70.53o

In Diagram 8, points M, P, Q and R are on a horizontal plane. Q

R

P

50o DIAGRAM 8 M

M is due south of R. Given that MP = MQ and the bearing of P from M is 250o. Find the bearing of Q from M. A B C D

330o 300o 250o 150o

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P(50º N , 125º W ), Q and R are three points on the earth’s surface with PQ = QR = RP measured along the great circle. Q is due south of P. The position of R is A B C D

15

19

(10º N , 55º E ) ( 20º N, 55º E ) ( 10º N , 125ºE ) ( 20º N , 125º E) ⎛h⎞

Transformation T represents translation ⎜⎜ ⎟⎟ . Point ( 3 , ─1 ) is the image of point k ⎝ ⎠

(1 , 6 ) under transformation T. T is A

⎛− 7⎞ ⎜⎜ ⎟⎟ ⎝ 2 ⎠

B

⎛ 7 ⎞ ⎜⎜ ⎟⎟ ⎝ − 2⎠

C

⎛ − 2⎞ ⎜⎜ ⎟⎟ ⎝ 7 ⎠

D

⎛ 2 ⎞ ⎜⎜ ⎟⎟ ⎝− 7⎠

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SULIT 16

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Diagram 9 shows ∆ PQR is the image of ∆ XYZ under a rotation of 90o clockwise. y 4 3 2 1 -4 -3

P

Y Z X

0

x

1 2 3 4

Q R -2 -3

DIAGRAM 9 State the coordinates of the centre of rotation. A B C D

17

( 3 , −2 ) (0,3) (−1 , 2 ) (−2 , 1 )

Diagram 10 shows the triangle KLM. Point L is the image of point K under a certain reflection. y

D C B

M

L

K

9 8 7 6 5 4 3 2 1

-9 -8 -7 -6 -5 -4 -3 -2 -1 0 -1 A -2

x

DIAGRAM 10 Which of the points A, B, C and D is the image of M under the same reflection?

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SULIT 18

23

2ae – bd + 2ed – ba = (2e + d)(a – b) (2e + b)(a – d) (2a – b)(e + d) (2e – b)(a + d)

A B C D 19

Given 8p −3 = 5 (p −

B C D

3 3 = − x −1 x −1 2

A B C D 21

1 ), then p = 5

14 15 2 3 2 7 2 − 3

A

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− 3x x2 −1

6 − 3x 2 x2 −1 4 − 3x x2 −1 6 − 3x x2 −1

Given 5y – 4 = 14 – (y + 3), then y = A B C D

2 5 5 2 7 2 15 4

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23

Given

6 + 4n 3(n − 1)

B

6 − 4n 3(n − 1)

C

2 + 4n 3(n − 1)

D

6 3(n − 1)

Simplify (4m−2 n)2 ÷ (m3n −2)3 16m−13n 8 16m −13n 7 4m −13n 8 4m5 n −4

Simplify A B C D

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3m − 4 m + 2 = , then m = n 3

A

A B C D 24

25

3 p −3 (2 p −2 q 4 ) 3 pq

6p−10q11 24p−3q 6 24p−8q11 24p−10q11

Given that m is an integer. Find all the values of m that satisfy both of the inequalities

5 – 2m > −4 and

A

−3 , −2 , −1, 0, 1, 2, 3, 4

B

−1 , 0 , 1 , 2 , 3 , 4

C

0, 1, 2, 3, 4

D

1, 2, 3, 4

m+3 >1 2

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SULIT 26

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Solve the simultaneous linear inequalities 3x + 2 ≤ 4 and 3 – x < 8. 5 The number line that represents the solution is

A

6

–5 B

6 C

–5

6

–5

6

D

27

Given that the matrix equation ( p 1) +

1 (− 4 10) = (4 2

p) .

Find the value of p A B C D 28

4 6 11 12

7⎞ ⎛ 4 1⎞ ⎛ 4 h⎞ ⎛ 4 ⎟⎟ = ⎜⎜ ⎟⎟ − ⎜⎜ ⎟⎟ , find the value of h. Given k ⎜⎜ ⎝ − 3 0⎠ ⎝ 3 1⎠ ⎝ − 9 − 1⎠ A B C D

5 2 –3 –5

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29

⎛ 3⎞ ⎜⎜ ⎟⎟ (2 1) = ⎝ − 1⎠ A B C D

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3⎞ ⎛ 6 ⎜⎜ ⎟⎟ ⎝ − 2 − 1⎠ ⎛6 − 2⎞ ⎜⎜ ⎟⎟ ⎝3 −1⎠ ⎛6⎞ ⎜⎜ ⎟⎟ ⎝ − 1⎠ (9 − 3)

Which of the following graph represents y = A

x3 − 4 ?

B

y

−2

1 2

x

O

y

O

−4

2

x

−4

C

D

y

y

2 2 O

4

x

−4 O

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x

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In Diagram 11, PQ and MN are parallel lines. P (–2,5)

y M

Q (0, 1) x N (4, –1)

DIAGRAM 11 Find the equation of the straight line MN. y = −2x + 7 y = −2x + 9 1 y= − x+1 2 1 y = − x +3 2

A B C D

32 In Diagram 12, ξ is the universal set Error!

ξ

A

B .2

.3

.5

.6

.4 .7

Set of B ∩ A' is

.8

.9

DIAGRAM 12

A { 4, 5, 6, 7, 8 } B { 2, 6, 8, 9 } C { 4, 5, 7 } D { 6, 8 } 33 Diberi bahawa set semesta ξ = { x : 20 ≤ x < 31, x ialah integer }, 1449/1 [Lihat sebelah SULIT Tutor Maths Mr Muruli www.tutormuruli.blogspot.com

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set M = { x : x is a multiple of 5 } and set N = { x : x is a perfect square }. Find n(M ' ∪ N). A B C D 34

Given that ξ = P ∪ Q ∪ R and ξ = { 3, 5, 7, 9, 10, 11, 12, 13 }, P = { odd numbers }, Q = { prime numbers } and R = { two digit numbers }. Set (R ∪ Q) ∩ P is A B C D

35

8 9 10 11

{9} { 3, 5, 7, 9 } { 3, 5, 7, 11, 13 } { 3, 5, 7, 9,11, 13 }

U is inversely proportional to the cube root of W and U = 8 1 when W = . 64

Express U in terms of W. 2

A

U=

B

U=

C

U=

D

U=2 3W

3

W 32

3

W

1 3

W

36 Jadual 1 menunjukkan hubungan antara tiga pembolehubah p, q dan r. 1449/1 [Lihat sebelah SULIT Tutor Maths Mr Muruli www.tutormuruli.blogspot.com

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p

16

72

q

8

−24

r

−6

v

TABLE 1 Given that p ∝ A B C D 37

2

q , calculate the value of v. r

96 12 –12 –96

Table 2 shows the distribution of storm victims from various villages who were given temporary settlement. Location

Kg. Seberang Sungai

Kg. Muara

Kg. Kota

Kg. Paya

Number of victims

60

45

75

20

TABLE 2 One victim is drawn at random. Find the probability that the chosen victim is from Kg. Seberang Sungai or Kg. Kota . 9 80 3 B 100 3 C 8 27 D 40 Satu kajian menunjukkan terdapat kaitan antara tahap penguasaan Bahasa Inggeris dengan pencapaian dalam Matematik. Kebarangkalian seorang pelajar tertentu akan A

38

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3 4 . If he passes English, the probability he passes Mathematics is . However, 5 7 1 if he fails English, the probability he passes Mathematics is . 4 Find the probability a particular student passes Mathematics. is

A B C D

39

3 35 1 7 31 70 23 28

The scores for 8 students in a test are as follows: 32, 38, 49, 46, 32, 11, 44, x If the median score is 41, then the possible value of x is A B C D

36 39 40 44

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Diagram 13 shows a histogram representing the scores of 100 students in a test.

40

Number of the students

50 40 30 20 10 Scores 0

54

64

74

84

DIAGRAM 13 Find the mean score . A B C D

40 64 65 69

END OF QUESTION PAPER

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