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1449/1 1449/1 Mathematics Paper 1 October 2006 1 1 hours 4

Form Four

JABATAN PELAJARAN NEGERI NEGERI SEMBILAN DARUL KHUSUS PPSMI ASSESSMENT 2006 MATHEMATICS Form Four Paper 1 One hour and fifteen minutes

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.

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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

4

A −1 =

5

P(A) =

6

P(A’) = 1 − P(A)

7

Distance =

8

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

9

Average speed =

10

Mean =

sum of data number of data

11

Mean =

sum of (class mark × frequency) sum of frequencies

12

Phythagoras Theorem c2 = a2 + b2

13

m=

14

m= −

1 ⎛ d − b⎞ ⎜ ⎟ ad − bc ⎜⎝ − c a ⎟⎠ n (A) n (S)

( x1 − x 2 ) 2 + ( y1 − y 2 ) 2

distance travelled time taken

y 2 − y1 x 2 − x1 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 =

9 10 11

1 2 πr h 3 4 Volume of sphere = πr3 3 1 × base area × height 3 Sum of interior angles of a polygon = ( n − 2) × 180°

Volume of right pyramid =

12

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

13

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

14

Scale factor, k =

15

Area of image = k2 × area of object

PA ' PA

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Answer all questions.

1.

2.

3.

4.

Round off 5⋅0729 correct to two significant figures. A

5·1

B

5·07

C

5·10

D

5·072

Express 0·0048 in standard form. A

4⋅8 x 10 4

B

4·8 x 10 -3

C

4·8 x 10 -4

D

4·8 x 10 3 -5

8⋅3 × 10

-6

− 9⋅75 × 10 = -6

A

1⋅45 × 10

B

7⋅33 × 10

C

7⋅33 × 10

D

8⋅92 × 10

-5 -6 -5

(m + 4)(2m – 3) = A

2m2 + 5m − 12

B

2 m 2 + 5m + 12

C

2m 2 + 11m − 12

D

2m 2 + 11m + 12

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One of the factors of 9r 2 – 1 is A

3r + 1

B

9r – 1

C

9r +1

D

r–1

Simplify m −2 n 3 × m 7 n 2 A mn11 B m13 n11 C m 2 n8 D

7.

m5n5

Find the value of A

1 2

B

1 4

C

2 3

D

3 2

(2

−4

× 32

) ÷ (2 1 2

−3

)

× 32 .

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6

In Diagram 1, ABDEF is a regular pentagon and ABC is a straight line.

E

xD

D

yD

F

C

B A DIAGRAM 1 The value of x + y is

9.

A

108

B

162

C

168

D

180

Diagram 2 shows part of a regular polygon.

140°

DIAGRAM 2 Find the number of sides. A

5

B

8

C

9

D

10

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7 In Diagram 3, EG is a tangent to the circle FPQR at F. Q

110D P

R

58D

x°

G F

E

DIAGRAM 3 Find the value of x.

11.

A

52

B

55

C

58

D

70

In Diagram 4 , LMN and LQR are tangents to the circle centre O at M and Q. N P

M

β° O o

70

R

Q

α° L

DIAGRAM 4

MP is parallel to LQR . Calculate the value of α + β. A

70

B

90

C

110

D

140

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8 In Diagram 5, PQR is a tangent to the circle QST at Q.

T

S

48D

P

xD

R

Q DIAGRAM 5

RST is a straight line. Find the value of x.

13.

A

18

B

24

C

25

D

48

Diagram 6 shows five points drawn on a Cartesian plane.

y A•

•B

P• C •

•D

M•

O

x

DIAGRAM 6 M is rotated 90 anticlockwise about the centre P. State the image of M. o

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9

Diagram 7 shows two triangles, V and W drawn on square grids. B•

•C

A•

•D

V

W

DIAGRAM 7

W is the image of triangle V under an enlargement. Which of the point, A , B , C or D is the center of the enlargement?

15.

In Diagram 8, PQR is a straight line.

P

θ° 8 cm

S

Q 6 cm

Find the value of cos θ °. A

4 5

B

3 5

C

−

3 5

D

−

4 5

DIAGRAM 8

R

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16.

Given that cos 30° =

A

C

3 o o 1 and tan 30° = . Find 2 cos 330 + tan 150 = 2 3

1 2 3

4 3

B

5 2 3

D

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10

2 3

Which of the following graphs represent y = sin x ? A

C y

y 1

1

180D

0

360D

x

0

90D

180D

90D

180D

x

-1

-1

B

D

y

y

1

0 -1

1

180D

360D

x

0 -1

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x

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11 It is given that sin θ = − 0⋅6821 and 180° ≤ θ ≤ 360°. Find the value of θ. A

43⋅01°

B

136⋅99°

C

223⋅01°

D

313⋅01°

Diagram 9 shows a prism.

F

E M

J

L

K DIAGRAM 9

State the angle between the plane EJM and the base JKLM. A

∠ MJE

B

∠ MJK

C

∠ EJL

D

∠ EJK

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Diagram 10 shows a cube with PQRS as the horizontal base.

20.

X•

H

E

G

F

S

Z •

P

R

Q DIAGRAM 10

X is the midpoint of GH and Z is the midpoint of RS. State the angle between the line PX the plane PQRS.

21.

A

∠ XPR

B

∠ XPS

C

∠ XPZ

D

∠ XPQ

Given 6 − 2 ( f + 1 ) = 5f , find the value of f . 3 A 7 B

4 7

C

7 4

D

8 7

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13 Given 3k + 1 = A

5 14

B

9 14

C

5 2

D

9 2

k + 2 , find the value of k. 5

Diagram 11 shows two vertical poles, EF and PQ on a horizontal ground E

P 10 m

F

20 m

Q

DIAGRAM 11 The angle of depression of peak P from peak E is 50D . Calculate the height, in m, of the pole EF. A

13⋅84

B

23⋅84

C

26⋅78

D

33⋅84

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14 Diagram 12 shows the positions of two spotlights J and L.

Spotlight L Φ

Pole

25 m

φ

Floor

Spotlight J DIAGRAM 12

Spotlight L is on top of the pole.The angle of elevation of spotlight L from spotlight J is 40°. Spotlight L is 25 m above the floor. Calculate the distance , in m , between spotlight J and the pole. A 20⋅98 B 29⋅79 C 32⋅64 D 38⋅89

25.

h h2 − 3 as a single fraction in its simplest form. Express − 4 8h

A

h2 − 3 8h

B

h2 + 3 8h

C

h−3 8

D

h+3 8

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( y + 1)2 − (y 2 − 1) = A 2y B 2y2 + 2y C 2y2 + 2y D 2y2 + 2y + 2

27.

28.

29.

Given that r =

k (2 + r ) , express k in terms of r. k −1

r 2

A

−

B

r 2

C

2r r−2

D

3r r−2

List all the integers x which satisfy both the inequalities 2x + 1 >17 and A

8, 9, 10, 11

B

9, 10, 11

C

9, 10, 11, 12

D

8, 9, 10, 11, 12

Find the solution of the simultaneous inequalities

3 x ≤ 9. 4

1 x < 2 and 1 − 4 x ≤ 7 where x is an 3

integer. A

x ≥ −1

B

x<6

C

−2 ≤ x < 6

D

−1 ≤ x < 6

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16

Table 1 shows the cumulative frequency marks of 40 pupils in a quiz.

Marks

0

1

2

3

4

5

Cumulative frequency

3

8

17

27

34

40

TABLE 1 Find the mode.

31.

A

2

B

3

C

4

D

5

Diagram 13 is a pictograph showing the sale of food sold by students on Canteen Day. Cakes

⊛⊛⊛⊛⊛

Sandwiches

∆∆∆∆∆∆

⊛

represents 4 cakes

∆

represents 10 sandwiches DIAGRAM 13

Calculate the ratio of the total sale of cakes to the total sale of sandwiches based on the price tag below. ⊛

∆

Cakes

Sandwiches

RM 2.00 each

RM 0.50 each

A

1:3

B

3:4

C

4:1

D

4: 3

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17 Diagram 14 is a Venn diagram. ξ

Q

P A

B

D

C

DIAGRAM 14 Which of the region A, B, C, or D represents the set P’ ∩ Q ? 33.

Diagram 15 is a Venn diagram that shows the elements of set P, set Q and set R.

P

Q 5 7

3 4

2 6

R DIAGRAM 15 Find n ( P ∩ Q ∪ R).

34.

A

13

B

18

C

24

D

31

It is given that M = {a, b} . Find all the subsets of M. A

{a} , {b}

B

{a} , {b} , { }

C

{a} , {b} , {a, b} , { }

D

{a} , {b} , {a, b} , {b, a}

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18 In Diagram 16, JK is a straight line.

y J(1,4)

x

O

K(3,−6) DIAGRAM 16 Find the gradient of PQ. A B

36.

1 5 1 − 2 −

C

−2

D

−5

In Diagram 17, PQ is a straight line. y P

O

Q 4

x

DIAGRAM 17 7 Given the gradient of PQ is − , find the y-intercept of PQ. 2 A 2

B

4

C

7

D

14

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19

There are 16 red marbles and 24 blue marbles in a box. A marble is picked at random from the box. Find the probability of picking a red marble. A

2 5

B

3 5

C

1 3

D

2 3

Table 2 shows the distribution of students according to classes.

4 Alpha 4 Beta 4 Delta 4 Gamma 4 Sigma

Class Number of students

38

37

39

36

x

TABLE 2 Given that the probability of choosing a Form 4 Sigma student is A

25

B

30

C

35

D

40

1 . Find the value of x. 6

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39.

40.

20

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Which of the following sentences is a statement? A

7+9

B

a + 2b − c

C

x2+2x=2

D

52>25

“ If m = −8 then m 2 = 64 ”. The antecedent for the implication above is A

m = −8

B

m=8

C

m 2 = −64

D

m 2 = 64

END OF QUESTION PAPER

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