Sulit1449/2 Nama………………………………………Mathematics Paper 2 Kelas………………..September 2013

SMJK PEREMPUAN CHINA PULAU PINANGPEPERIKSAAN PERCUBAAN SPM TAHUN 2013

MATHEMATICS FORM 5Paper 2

Two hours thirty minutes

Jangan buka kertas soalan ini sehingga diberitahu

1.Tulis nama dan kelas anda pada ruang yang disediakan

2.Kertas soalan iniadalah dalam bahasa Inggeris

3.Calondikehendaki membaca arahan di bawah.

Kertas soalan ini mengandungi 15 halaman bercetak.1. This question paper consists of two sections: Section A and Section B.

2. Answer all questions in Section A and four questions from Section B.

3. Write your answers clearly in the spaces provided in the question paper.

4. Show your working. It may help you to get marks.

5. The diagram in the questions provided are not drawn to scale unless stated.

6. You may use a non-programmable scientific calculator.

Section Question Full Marks Marks Obtained

A

1 42 43 44 35 56 67 58 59 710 311 6

B

12 1213 1214 1215 1216 12

TOTAL 100

MATHEMATICAL FORMULA

Section A Answer all questions in this section (52 marks)

1.Solve the quadratic equation

2 x2+3 x−x+6

=2 (4 marks)

Answer:

2.The diagram1 shows a solid formed by combining a cone and a cylinder.The diameter of the cylinder and the diameter of the base of the cone are both 7cm. The volume of the solid is 231cm3.

Calculate the height in cm of the cone. (Use π=227 )

(4 marks) Answer:

3.Calculate the value of p and q that satisfy the simultaneous linear equations. (4 marks)

12

p−2 q=13

3 p+4 q=−2 Answer:

Diagram 1

4.On the graph in the answer space, state the three inequalities which define the shaded region in the graph below (3 marks)

Answer:

________________________ _______________________ ________________________

5.(a) Complete the following statement using the quantifier “all” or “some” to

make it a false statement. __________multiple of 3 are odd numbers. (b) Write down Premise 2 to complete the following argument. Premise 1 : All subsets of P are subsets of Q. Premise 2:___________________________________________ Conclusion : R is a subset of Q.

(c) Write down two implications based on the following sentence 2 x+3=7 if and only if x=2 Implication 1:______________________________________ Implication 2:_______________________________________(d) State whether the following sentence is a statement or non statement. 4 is a factor of 10 (5 marks)Answer:(a) _________________________________

(b) Premise 2:_____________________________________

(c) Implication1:___________________________________ Implication 2:__________________________________

(d)_____________________________________________

6.Nine cards bearing the letters of the word

are placed in the box and two cards are drawn at random, one at a time. Calculate the probability that (a)The first card is not an E. (b)The first card is an E and the second card is a R. (c)both cards bear the same letter. (6 marks)

Answer: (a) (b)

(c)

7. Diagram 2 shows the speed time graph of a lorry and a car for a period of 60 seconds. The graph ABCD represents the movement of the lorry and the graph PQ represents the movement of the car.

(5 marks) a) State the maximum speed of the lorry. b) Calculate the value of t , if the rate of change of speed of the lorry in the first

t seconds is 1.75 m s−2.c) The difference in distance travelled by the lorry and the car during 60seconds

is 78m.Find the uniform speed of the car.Answer

Diagram 2

P ER E RE S E V

(a) (b)

(c)8. In the diagram 3,O is the origin.JK, KL and LM are straight lines.JK is parallel

to LM and KL is parallel to the x-axis. Given that the equation is LM is 2 y=x+4

Find (a) the equation of KL  (b) the equation of JK and (c) state its y-intercept (6 marks) Answer: (a)

(b)

(c)

Diagram 3

9. It is given that matrix M=[4 7n 6] and matrix N =

13 [ p −7

−3 4 ] such that

MN=[1 00 1] ( 7 marks)

(a) Find the value of p and n. (b) using matrix method, find the value of m and n that

satisfy the following simultaneous linear equations. 4 m+7 y=7 3 m+6 n=10

Answer:a)

b)

10. Diagram 4 shows a cuboid with a rectangular base ABCD. Given HG¿ 13 JG.

(a) Name the angle between line BH and the plane DCGJ.(b) Calculate the angle between line BH and the plane DCGJ.

(3marks) Answer: (a)

(b)

11. In diagram 5 shows two semicircles AOBCE and OBCD with the centre O and B respectively. BFC is a sector with the centre B. AOBC is a straight line and OA=2OB.BC=3.5cm. ∠FBC = ∠AOE = 60°

Using π =227 , calculate

(a) the perimeter, in cm, of the whole diagram.(b) the area, in cm2, of the shaded region. .

Answer: (6 marks)

(a)

(b)

Diagram 4

Diagram 5

Section B(48 marks)

Answer four questions from this section.12(a) Complete table 1 in the answer space for the equation y=6+2x−x3

Answer: (a) y=6+2x−x3

(3 marks)(b) For this part of the question, use the graph paper provided. You may use a

flexible curve ruler. By using a scale of 2cm to 1 unit on the x- axis and 2cm to 10 units on y-axis, draw the graph of

y=6+2 x−x3 for - 4 ≤ x ≤ 4 Answer:

(b)Refer graph (c)From your graph, find the value of y when x= - 2.4 Answer: y =_________(1 mark)

(d) Draw a suitable straight line on your graph to find the value of x which satisfy the equation x3+9=12 x for - 4 ≤ x ≤ 4 State these values of x. Answer x =_______________________________ (4 marks)

x -4 -3 -2 -1 0 1 2 3 4y 62 10 6 7 2 -50

13(a) Transformation T is a translation ( 5−2)

Transformation R is a reflection in the line y = 1 State the coordinates of the image of the point K under the following transformations.

i) T 2 ii) TR (4 marks)

Answer (refer diagram 6.1) i)

ii)

Diagram 6.1

13 b) Diagram 6.2 shows pentagon ABCDE, FGHJK and SGPQR drawn on a

Cartesian plane. SGPQR is the image of ABCDE under the combined transformation VU. Describe in full

(i)The transformation U(ii)The transformation V

(iii)Given that the shaded region represents a region of area 330m2,calculate the area in m2,of the region represented by FGHJK ( 8 marks)

Diagram 6.2Answer:

( b)(i) U:__________________________________________________ __________________________________________________

(ii) V:____________________________________________________ _____________________________________________________

(iii)

14. Diagram 7.1 shows a solid right prism with a rectangular base ABCD. BCHGK is the uniform cross section of the prism. The rectangle FJKG is an inclined plane. EFGH is a horizontal plane. The edges AJ, BK, CH and DE are verticals. AB = DC = FG = EH = JK = 6 cm, AD = BC= 4 cm, FE = GH = CH = DE = 5cm and AJ = BK = 3 cm.

Draw in full size, (a) the elevation of the solid onto a vertical plane parallel to BC as viewed from X, (3 marks)

Answer:a)

Diagram 7.1

(b) A solid right prism with rectangular base LMNC and right–angled triangle MLQ as its uniform cross section is joined to the solid in diagram 7.1 at the vertical plane LCPQ. The composite sold is as shown in diagram 7.2. The base ABLMNCD is on a horizontal plane. LC = MN = 2cm, LM = CN = 3cm, LQ = CP = 4cm.

Draw to full scale (i) the elevation of the Composite solid on a Vertical plane parallel to AB as viewed from Y .

(4 marks) (ii)the plan of the composite

solid. (5 marks)

Answer bi):

b ii)

Diagram 7.2

Diagram 7.2

15) The table below shows the frequency distribution of mass, in kg, of a group of 50 tourists.

Mass(kg) Frequency35-39 040-44 445-49 750-54 1455-59 1260-64 865-69 470-74 1

(a) State the modal class Answer:____________ (1 mark)(b) Calculate the estimated mean of the mass of the group of tourists.(3 marks)

Answer:

(c) Construct a cumulative frequency table for the above data. (2 marks)Upper boundary

39.5 44.5

Cumulative frequency

0

(d)For this part of the question use the graph paper provided By using a scale of 2cm to 5kg on the horizontal axis and 2cm to 5 tourists on the vertical axis, draw an ogive for the data (4 marks)(e)From the ogive find the interquartile range . (2 marks)Answer (e)

16. P (75° S ,82°W ), Q(75¿¿° S ,18° E)¿, K, L are four points on the surface of the earth . K is due north of P and LP is the diameter of the earth. a)State the latitude and longtitude of L. (2 marks) b) Given the distance from P to K measured along the meridian is 6300 nautical miles. Calculate the latitude of K. (3 marks) c)Calculate the shortest distance from K to L measured along the surface of the earth. (3 marks) d)An aeroplane took off from Q at 0720 and flew due west to P and then flew due north to K. The average speed for the whole flight was 650 knots.Find the time it arrived at K. (4 marks)

Prepared by: P.G.Ooi Checked by: Approved by