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Paper 2

Final Tips For SPM 2011

Section A

1. Calculate the values of p and q that satisfy the following simultaneous linear equations:1

2 2 = 13

3 + 4 = 2

2. Solve the equation 22+5+1 = 23. On the graph provided, shaded the region which satisfies the three inequalities 2 + 8,

and < 8

4. The base JKLM is a horizontal rectangle. Q is the midpoint of JM. The apex V is 8 cm verticallyabove the point Q. Calculate the angle between the line KV and the base JKLM.

= 2 + 8 =

0

V

J

M

K

L

Q10

12

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5. The graph shows that PQ, QR and RS are straight lines. P is on the y-axis. QR is parallel to x-axisand PQ is parallel to RS. The equation of RS is 2 = 4 + 6

a. State the equation of the straight line QRb. Find the equation of the straight line PQ and hence, state its x-intercept.

6. M is a 2 2 matrix where 3 25 4 =

1 00 1

a. Find the matrix Mb. Write the following simultaneous linear equations as a matrix equation.

3 2 = 75 4 = 9

Hence, calculate the values of x and y using matrices.

7. Diagram below shows four cards labelled with letters in box A and numbered cards in box B.A card is picked at random from box A and box B respectively. By listing the sample of all

possible outcomes of the event, find the probability that

Box A Box B

a. A card with a consonant and a card with an odd number are picked.b. A card with a vowel or a card with a number which is factor of 12 are picked.

2

= 4

+ 6

0

5

O RP T 54 6

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8. Diagram below shows the distance-time graph for the journey of Suzana from school to herhouse. On the way, she stopped at a library.

a. Find the time, in minutes, she spent in the library.b. Find the value of d, in km, if the average speed for the whole journey is 11.2 km/h.c. Calculate the speed, in km/h, of Suzana in the last 20 minutes.

9. = = 7cm and = 60using = 22

7, calculate

a. the perimeter, in cm, of the whole diagramb. The area, in cm2, of the shaded region.

10.Diagram below shows a composite solid, formed by the combination of a cone and a cylinder.

The diameter of the cylinder is 10 cm. The diameter of the cone is 7 cm and the height of the

cone is 6 cm.Using22

7 , calculate the volume, in cm

3

, of the solid.

Time / min

0 55

6

15

75

Distance / km

60

O M P

N

R

Q

4 cm

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11.a. Determine whether each of the following statement is true or false.

i. sin 30 = 0.5ii. =

b. sin 30 = 0.5 and = , determine whether the compound statementformed is true or false.

c. Premise 1 : All quadrilaterals has two diagonals.Premise 2 : __________________________________________

Conclusions : PQRS has two diagonals.

d. Make a general conclusion by induction5 = 21 + 31

10 = (2)

2

+ 3(2)

17 = (2)3 + 3(3)

Section B

12.a. Complete the table below for the equation = 4

x 4 2.5 1 0.5 0.5 1 2 3.2 4

y 1 1.6 8 8 4 1.25 1

b. By using the scale of 2 cm to 1 unit on the x-axis and 2 cm to 2 units on the y-axis, drawthe graph of = 4 for 4 4.

c. From your graph, findi. The value of y when = 1.8

ii. The value of x when = 3.4d. Draw the suitable straight line on your graph of find all the values of x which satisfy the

equation4 2 = 3 for 4 4. State these values of x.

13.The date in the diagram below shows the marks obtained by 40 students in their maths exam.40 24 17 30 22 26 35 19

23 28 33 33 39 34 39 28

27 35 45 21 38 22 27 35

30 34 31 37 40 32 14 28

20 32 29 26 32 22 38 44

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a. Using the data in diagram above, and a class interval of 5 marks, completes the followingtable.

Marks Frequency Cumulative frequency

11 15

16 20

b. By using a scale of 2 cm to 5 marks on the x-axis and 2 cm to 5 students on the y axis,draw an ogive based on the data.

c. From your ogive in (b)i. Find the third quartile

ii. Hence, explain briefly the meaning of the third quartile.

14.Diagram below shows four points K, L, M and R on the surface of earth. K lies on the longitude60W. LM is the diameter of the parallel of latitude 45S. R lies 6900 nautical miles due north of

L.

a. Find the position of M.b. Calculate the shortest distance, in nautical miles, from L to M, measured along the

surface of the earth.

c. Find the latitude of R.d. An aeroplane took off from K and flew due west to M along the parallel of latitude with

an average speed of 720 knots. Calculate the time, in hours, taken for the flight.

K

R

S

45

L

50 M

.

N

O0

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15.The diagram below shows a solid right prism with a square base ABCD lying on a horizontalplane. The face EFGBA is the uniform cross-section of the prism. The edges EA, GB, JD and HC

are vertical. The plane EHIJ is horizontal while the plane FGHI is inclined. Draw to full scale, the

plan of the solid.

a. A half-cylinder KLMPND is then joined to the solid in (a) at the plane JIPD such that thebase ABCPND lien on a horizontal plane. The combined solid is as shown in the following

diagram.

b. Draw to full scale,i. the elevation of the combined solid on a vertical plane parallel to BC as viewed

from X,

ii.

the elevation of the combined solid on a vertical plane parallel to CG as viewedfrom Y.

J

3 cm

E

F

I

5 cm

A

B

5 cm

G

C

H

3 cm

6 cm

D

K M

JL

2 cm

3 cmE

FI

5 cm

A

B

5 cm

G

C

P

D NH

3 cm

6 cm

Y

X

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16.

y

51 2 4304 3 2 15 76 8 9 106

1

2

3

4

5

6

7

8

9

10

MN

P L

D

C B

E F

A G

K

H

J

x

Diagram below shows trapeziums ABCD, ABEF, GHJK and LMNP on the

Cartesian plane.

a) Transformation R is a reflection about the line y = 3.Transformation T is the translation

State the coordinates of the image of point Hunder the following transformation :

i) RT

ii) TR

b) ABEFis the image ofABCD under transformation Vand GHJK is the image

ofABEFunder transformation W.

Describe

i) transformationV

ii) a single transformation which is equivalent to transformation WV.

c) LMNP is the image ofABCD under an enlargement.

I) the coordinate of the centre of the enlargement.

ii) Given that the area ofLMNP is 325.8 unit , calculate the area ofABCD.

State2

-2

4( )