50/2SULIT

1449/1

NAMA: _______________________________________________ TINGKATAN: ______________

FINAL YEAR EXAMINATIONPAPER 1 Time: One hour fifteen minutes

This question paper consists of 40 questions. Answer all the questions. Each question is followed by four options A, B, C and D. For each question, choose one answer only. Non-programmable scientific calculator is allowed.

1Round off 74 107 to three significant figures.

A70 000C74 100

B74 000D74 110

2Express 0.00073 in standard form.

A7.3 104C7.3 101

B7.3 101D7.3 104

3

=

A6 104C6 102

B6 102D6 104

4Express 7.468 105 as a single number.

A7 468C746 800

B74 680D7 468 000

58.5 103 + 640 =

A1.49 102C1.49 103

B9.14 102D9.14 103

6The area of a rectangular wall is 47.5 m2. If the breadth of the wall is 250 cm, find the length of the wall in cm.

A1.9 102C1.9 104

B1.9 103D1.9 105

7(6p + 5)(p 4) =

A6p2 24p 20B6p2 19p + 20

C6p2 29p + 20

D6p2 19p 20

89m(4m 3n) (5m n)2 =

A11m2 17mn n2

B11m2 37mn + n2

C34m2 17mn n2

D34m2 37mn + n2

9Expressas a single fraction in its simplest form.

A

C

B

D

10One of the factors of (8 18x2) is

A4 9xC1 xB2 3xD2 9x

117x2 6x(5 x) =

Ax2 30xCx2 30xB13x2 + 30xD13x2 30x

12Given that 4(x 2) = 5 5(x + 2), find the value of x.

A C3

B

D3

13Factorisex2 x.

A

C

B

D

14Given n() = 15, n(P) = 10, n(P Q) = 6 and n (P Q)' = 3, find n(Q).

A5C7

B6D8

15The Venn diagram in Diagram 1 shows the elements of set X, set Y and set Z.

Diagram 1

It is given that the universal set = X Y Z and n(X') = n(X Z). What is the value of p?

A1C3

B2D4

16It is given that the universal set

={x : 3 x < 21, x is an integer},

set A={4, 8, 12, 16, 20},

set B={x : x is a multiple of 3} and

set C={x : x is a factor of 30}.

Find the elements of the set A (B C)'.

A12C4, 8, 12, 16, 20

B3, 6D3, 6, 12, 15

17The Venn diagram in Diagram 2 shows universal set , set J and set K.

Diagram 2

The region of J' K' is equivalent to the region

AJ' KC(J K)'

BJ KD(J K)'

18Premise 1:If x is a factor of 9, then x

is a factor of 36.

Premise 2:5 is not a factor of 36.

What is the conclusion for the premise above?

A5 is a factor of 9.

B9 is a factor of 36.

C5 is not a factor of 9.

D9 is not a factor of 36.

19Diagram 3 shows a straight line PQ cross the origin, O.

Diagram 3

Find the gradient of the line PQ.

A C

B D

20Find the x-intercept of the straight line 4x + 8y + 3 = 0.

A0C

B D

21Which of the following graphs represents x 3y = 6?

A

B

C

D

22Table 1 is a frequency table showing the score of mathematics test of a class of students.

ScoreFrequency

80 848

85 8911

90 947

95 994

Table 1

Calculate the mean score of the students.

A86.17C90.17

B88.17D91.17

23A box contains 12 red marbles and 8 green marbles. Jonathan puts another 4 red marbles and 6 green marbles into the box. Find the probability of choosing a green marble.

A

C

B

D

24Table 2 shows the number of boys and girls in two classes. A student is chosen at random from the classes.

Class 4AClass 4B

Boy2423

Girl2128

Table 2

Find the probability that a boy from class 4A is chosen.

A

C

B

D

25The probability of Samad hitting a target in a shooting session is. If Samad tries for 45 times, how many times does Samad fail to hit the target?A15C25

B20D30

26A number is choosen at random from set P = {4, 8, 12, 16, 20, 24, 28, 32}. Find the probability that a perfect square number is chosen.

A

C

B

D

27Diagram 4 shows a circle with centre O. ABC and ADE are tangents to the circle at B and D respectively.

Diagram 4

Find the value of x.

A34C56B44D68

28Diagram 5 shows a circle with centre O. PQR is tangent to the circle at Q.

Diagram 5

Given that SQR = 106 and TPQ = 38, find the value of y.

A37C52B48D64

29In Diagram 6, JKL is a tangent to the circle with centre O at K. JNO and LMO are straight lines.

Diagram 6

Given that KLO = 45 and NPM = 54, find KJN.

A27C45B36D63

30Diagram 7 shows PQR and PST are tangents to a circle with centre O.

Diagram 7

Given that PSQ = 63, find the value of z.

A27C63B54D72

31Diagram 8 show two circles with centres O and C respectively. WX is a common tangent to the circles. OYZC is a straight line.

Diagram 8

Find the length of YZ in cm.

A2.56C3.37

B3.00D4.00

32Diagram 9 shows a line PQ passes through the origin, O.

Diagram 9

Find the value of cos .

A C

B D

33Which of the following graphs shows y = cos for 0 180?

A

B

C

D

34In Diagram 10, JKL is a straight line.

Diagram 10

Given that KL = 12 cm and ML = 5 cm, find the value of sin y.

A

C

B D

35Diagram 11 shows two right-angled triangles, ABC and CDE.

Diagram 11

Given that cos p =and tan q =, find the length of EB in cm.

A4.00C8.00

B7.62D9.38

36Diagram 12 shows a right-angled triangle PQS and R is the midpoint of straight line QS.

Diagram 12

Given that sin = , find the value of cos x.

A0.6839C0.9375

B0.7293D1.3713

37Diagram 13 shows two vertical poles PQ and RS on a horizontal plane.

Diagram 13

The angle of depression of P from R is 30. Find the height of RS in m.

A2.89C7.89

B5.00D10.00

38Diagram 14 shows a vertical flagpole, JK. KL is a horizontal plane. A boy is standing 3 m away from the flagpole.

Diagram 14

Calculate the angle of elevation of J from the boy.

A1549'C3948'B2849'D3325'39Diagram 15 shows a right-angled triangular prism with a horizontal rectangular base JKLM.

Diagram 15

Name the angle between line LP and the plane JKLM.

ALJMBMQP

CPLM

DLPM

40Diagram 16 shows a cube.

Diagram 16

Calculate the angle between plane AGC and plane ABCD.

A3513'C5444'B45D90PAPER 2 Time: Two hours and thirty minutes

This question paper consists of two sections: Section A and Section B. Answer all the questions in Section A and four questions from Section B. Write your answers in the spaces provided in the question paper. Show your working. It may help you to get mark. Non-programmable scientific calculator.

Section A

[52 marks]

Answer all the questions in this section.

1Solve the following quadratic equation.

10x2 + 15x 10 = 11 14x

[4 marks]

Answer:

2Diagram 1 shows a trapezium, PQRS.

Diagram 1

Given that area of PQRS = 51 cm2, find the value of x.

[4 marks]

Answer:

3The Venn diagram in Diagram 2 shows the elements of universal set , set A , set B and set C.

Diagram 2 (a)State the elements for (A B)'.

(b)Shade the area represented by A (B C)'.

[4 marks]

Answer:

(a)

(b)

4Given ={x : 2 x < 20, x is an integer},

P={x : x is a multiple of 2}.

Q={x : x is a factor of 30},

R={x : x is a perfect square}.

Find

(a)Q R(b)(P Q) R(c)(P R)' Q

[5 marks]Answer:

(a)

(b)

(c)

5(a)State whether the following sentence is a statement.

3 is a prime number.

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

The sum of all the interior angles of ABCD is 360.

(c)

3= 2(1) + 1

5= 2(2) + 1

7= 2(3) + 1

Based on the information above, make a general conclusion by induction regarding the sequence 3, 5, 7, ...

[5 marks]

Answer:

(a)

(b)

(c)

6(a)Complete each of the following statements with the

quantifier all or some so that it will become a true

statement.

(i)______ prime numbers can only be divided by 1 and itself.

(ii)______ factors of 30 are factors of 20.

(b)Complete the following argument.

Premise 1:All triangles have 3 edges.

Premise 2:

Conclusion:PQR has 3 edges.

(c)Write two implications for the following statement.

(x 2)(x + 5) = 0, if and only if x = 2 or x = 5.

[6 marks]

Answer:

(a)(i)

(ii)

(b)

(c)

7Diagram 3 shows two parallel lines, EF and GH.

Diagram 3

Find

(a)the coordinates of G,

(b)the equation of the line EF.

[5 marks]

Answer:

(a)

(b)

8Table 1 shows the marks of a group of students in a mathematics test. If a student is chosen at random, the probability of the student scored 85 marks is.

Marks80859095100

Number of students7x1163

Table 1 (a)Calculate the value of x.

(b)Find the probability of picking a student who obtained less than 90 marks.

[5 marks]

Answer:

(a)

(b)

9Diagram 4 shows a circle with centre O. PQR is tangent to the circle at Q.

Diagram 4

Given that VTQ = 30 and USQ = 64, find the value of

(a)x

(b)y(c)z

[6 marks]

Answer:

(a)

(b)

(c)

10Diagram 5 shows two boys looking at a vertical pole PQ. Boy A with 1.68 m height standing 5 m apart from the pole whereas boy B with 1.72 m height standing 3 m apart from the pole.

Diagram 5

The angle of elevation of P from boy A is 1930'. Find

(a)the height of PQ in m,

(b)the angle of depression of boy B from P.

[5 marks]

Answer:

(a)

(b)

11Diagram 6 shows a prism with isosceles triangle UQR as its uniform cross-section and PQRS is a horizontal base. X and Y are the midpoints of QR and PS respectively.

Diagram 6

Identify and calculate the angle between planes QTR and PQRS.

[3 marks]

Answer:Section B

[48 marks]

Answer any four questions from this section.

12(a)Factorise each of the following quadratic expresions

completely.

(i)27x2 + 9x(ii)4x2 4x 3

(iii)

= 10p

[6 marks](b)The Venn diagram in Diagram 7 shows the number of elements in sets X, Y and Z where = X Y Z and n() = 50.

Diagram 7

Find

(i)value of x,

(ii)n[X' (Y Z)]

(iii)n(X Z')

[6 marks]

Answer:

(a)(i)

(ii)

(iii)

(b)(i)

(ii)

(iii)

13Diagram 8 shows a trapezium, EFG. EF and OG are parallel lines.

Diagram 8 Rajah 8

Find

(a)the value of p,

[5 marks] (b)the equation of line EF,

[4 marks] (c)the x-intercept of line EF.

[3 marks]

Answer:

(a)

(b)

(c)

14Diagram 9 shows a common tangent PQR to the two circles with centre O and C at P and Q respectively.

Diagram 9

Given that OP = 5 cm, CQ = 7 cm and POT = 100, find

(a)the value of x,

[3 marks] (b)the length of TU in cm,

[3 marks] (c)perimeter of PQCO in cm,

[3 marks] (d)the area, in cm2, of the shaded region. (Use = )

[3 marks]

Answer:

(a)

(b)

(c)

(d)

15(a)In Diagram 10, JKL and LMN are tangents to the circle

with centre O at K and M respectively. KOP is a straight

line.

Diagram 10

Given that KM = 17 cm and MP = 8 cm, find

(i)x,(ii)y,(iii)z.

[7 marks](b)Diagram 11 shows a ladder PQ leaning on a vertical wall RS.

Diagram 11

The angle of elevation of Q from P is 50. Find

(i)the length of the ladder in m,

(ii)the angle of depression of P from R.

[5 marks]

Answer:

(a)(i)

(ii)

(iii)

(b)(i)

(ii)

16Table 1 shows the height of 50 Form 4 students.

Height (cm)Frequency

150 1544

155 1598

160 16413

165 16911

170 1749

175 1795

Table 1 (a)Calculate the estimated mean of the height of the students.

[3 marks] (b)Construct a cumulative frequency table for the data.

[2 marks] (c)For this part of the question, use graph paper.

By using a scale of 2 cm to represent 5 cm on the horizontal axis and 2 cm to represent 5 students on the vertical axis, draw an ogive for the data in (b).[4 marks] (d)From the orgive in (c), find

(i)the first quartile,

(ii)the third quartile,

(iii)the interquartile range.

[3 marks]

Answer:

(a)

(b)

(c)Refer graph

(d)(i)

(ii)

(iii)

6

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