smc addmath mocks 2008

8/9/2019 SMC Addmath Mocks 2008

1/8

SULIT

3472

Additional Mathematics

Aug / Sept

2008

3 jam

LEMBAGA PEPERIKSAAN MALAYSIA

SRI MURUGAN CENTRE MALAYSIA

PEPERIKSAAN MOCKS SPM 2008

ADDITIONAL MATHEMATICS

Three Hours

Instructions :

1. This question paper consists of three sections: Section A, Section B andSection C.

2. Answerallquestions in Section A, four questions from Section B andtwo questions from Section C.

3. Give onlyone answer / solution to each question.

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

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

6. The marks allocated for each question and sub-part of a question are shown in brackets.

7. A list of formule is provided.

8. You may use a non-programmable scientific calculator or a booklet of four-figure mathematical tables.

This question paper consists of 8 pages


2/8

347

[Lihat sebela

SULI

2

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

ALGEBRA

1

2 4

2

b b acx

a8

loglog

log

c

a

c

bb

a

2

m n m n

a a a 9 Tn = a + (n

1) d

3m n m na a a 10 Sn =

2

n[ 2a + (n1) ]

4 (am)

n= a

mn 11 Tn = ar

n1

5 log a mn =log am + log a n 12 Sn =( 1) (1 )

, 11 1

n na r a r r

r r

6 log log loga a am

m nn

13 , 11

aS r

r

7 log logn

a am n m

CALCULUS

1 y = uv,dv du

u vdx dx

3u

yv

,2

du dvv u

dx dx

v

2dy dy du

dx du dx4 Area under a curve =

b b

a a ydx xdy

5 Volume generated = 2 2b b

a a y dx x dy

STATISTICS

1x

xN

ORfx

xf

7 ( ) , 1n r n r rP X r C p q p q

2

2( )x x

N=

2

2( )

xx

N8

!

( )!

n

r

nP

n r

3

1

2

m

N F

m L Cf

9!

( )! !

n

r

nC

n r r

41 1

1

W II

W10

XZ

51

2

QI

Q11 Mean, = np

6 ( ) ( ) ( ) ( )P A B P A P B P A B 12 npq


3/8

347

[Lihat sebela

SULI

3

GEOMETRY

1 Distance =2 2

2 1 2 1( ) ( ) x x y y 52 2

r x y

2 Midpoint = 1 2 1 2,2 2

x x y y6

2 2

xi y jr

x y

3 A point dividing a segment of a line

1 2 1 2, ,nx mx ny my

x ym n m n

4 Area of triangle =1 2 2 3 3 1 2 1 3 2 2 3

1( ) ( )

2x y x y x y x y x y x y

TRIGONOMETRY

1 Arc length, s j

2 Area of sector =21

2j

3sin sin sin

a b c

a b c

4 a2

= b2+ c

22bc cos A

5 Area of triangle = 1 sin2

ab C


4/8

347

[Lihat sebela

SULI

4

Section A[60 marks]

Answerallquestions from this section

1. The ordered pairs {(A, 1), (A, 2), (B,1), (B,3), (C, 4), (C, 2)} show the association of grades and aggregates.

State

(a) the images of B

(b) the objects of 2

[2 mark

2. The function w is defined as5

( ) , 22

w x xx

(a) w-1(x)

(b) w-1(4)

[3 mark

3. The quadratic equationx(x + 2) = mx - 4 has two distinct real roots. Find the range of values ofm.

[3 mark

4. Given that1

3and -2 are the roots ofa quadratic equation, write the equation in the form ofax

2+ bx + c = 0,

where a, b, and c are constants.[3 mark

5. Find the range ofx ifx(x -13) -42.

[3 mark

6. Diagram 1 shows the graph of a quadratic functionf(x) = 3(x +p)2 + 2, wherep is a constant. The curvey =f(x)

has the minimum point (2, q), where q is a constant.

Diagram 1State

(a) the value ofp

(b) the value ofq

(c) the equation of the axis of symmetry

[3 mark

7. Find the solutions of log a 524 log a 3 + log a 9 = 2.

[3 mark

8. Solve the equation 813x

= 276x+1

.

[3 mark

9. A flower arrangement will be done from 6 yellow roses and 9 pink roses. How many combinations can

obtained if an arrangement that consists of ten flowers must

(a) have equal number of both colours.

(b) have not more than 3 yellow roses

[4 mark


5/8

347

[Lihat sebela

SULI

5

10. Hafiza has seven t-shirts ; 2 are blue, 3 are red and 2 are yellow. She also has 8 skirts ; 3 are green, 2 are red an

3 are yellow. She selects a T-shirt and a skirt at random. Calculate the probability that the t-shirt and skirt select

are from the same colour.

[3 mark

11. Solve the simultaneous equations 4x +y = -8 andx2 +xy

2= 2 .

[5 mark

12. Use the graph paper to solve this question.

Marks Number of Students

30-39 3

40-49 19

50-59 30

60-69 6

70-79 2

Table 1

Table 1 above shows the distribution of marks of 60 students in a test.

(a) Draw a histogram and estimate the mode. [4 mark

(b) Without drawing the ogive, compute the median mark. [3 marks

13. (a) Find the angles between 00 and 360 0 that satisfy 6 cosx = 1 + 2 secx . [3 mark

(b) Sketch the graph of3

3cos2

y x for 0 x 2 . [3 mark

14. In the diagram 2 below, ABC = 900 and the equation of the straight lineBCis 2y +x + 6 = 0.

Diagram 2

(a) Find

(i) the equation of straight lineAB(ii) the coordinates ofB

[4 mark

(b) A point P moves such that its distance from pointA is always 5 units. Find the equation of the locus ofP.[2 mark

15. (a) The first term of an arithemetic progression is 10 and the 10th terms is twice the fourth term. Find the sum of

13 terms.

[4 mark

(b) Write the recurring decimal 0.37373737 .. as a single fraction in its lowest terms.

[2 mark


6/8

347

[Lihat sebela

SULI

6

Section B[40 marks]

Answerfour questions from this section

16. The diagram 3 below shows a sectorROS of a circle with centre O.

Diagram 3

Point Tlies on OS, point Ulies on OR and TUis perpendicular to OR. The length ofOTis 9cm and

5 ROS radian Given that OT: OS = 3 : 5, calculate (Use = 3.142)

(a) the length, in cm, ofTS [2 mark

(b) the perimeter, in cm, of the shaded region [4 mark

(c) the area, in cm2

, of the shaded region [4 mark

17. The following table 2 shows the values of the variablesx and V, that are related by the equation V2

= kxn, where

and n are constants.

X 2 3 5 8 10 12

V 3.6 5.0 7.8 11.2 13.8 16.2

Table 2(a) Draw the graph of log10 Vagainst log10x [5 mark

(b) From the graph, find

(i) the value ofkand ofn.

(ii) the value ofx when V= 4.47

[5 mark

18 (a)Given thatABCD is a parallelogram, 2 6 BC i j

and 3 3CD i j

, find

(i) AC

(ii) the unit vector in the direction of AC

[4 mark

(b) PQRS is a parallelogram, 3 3PQ i j

,7

2PR hi j

and 6PS i k j

, where h and kare

constants.(i) Find the value ofh and k.

(ii) Hence, calculate the length of the diagonal PR.

[6 mark19 (a) It is found that 5 bottles of milk produced by a factory are defective. Calculate

(i) the probality that at least 3 bottles are defective in a sample of 10 bottles. [2 mark

(ii) the number of bottles that have to be chosen so that the probability that there is at least 1 defective bottle

less than 0.65. [3 mark

(b) The masses of schoolbags of primary school students follow a normal distributions with a mean 14 and a

standard deviation of 14 kg and a standart deviation of 2 kg.

(i) Find the probality that the mass of a schoolbag chosen at random will be less than 17 kg. [2 mark

(ii) If 20 out of 140 schoolbags have masses of more than m kg, find the value ofm. [3 mark


7/8

347

[Lihat sebela

SULI

7

20 (a) The diagram 4 shows a shaded region enclosed by the curvey =x2-6x+ 9 and the straight line PQ.

Diagram 4

Find(i) the coordinates of the points P and Q. [2 mark

(ii) the area of the shaded region. [3 mark

(b) A conical container with a diameter of 50 cm, and a height of 30 cm. Water is poured into the container at aconstant rate of 2000 cm3s-1.

Diagram5From the diagram 5,calculate the rate of change of the radius of the water level at the instant when the radius

the water level is 5cm. (Use = 3.142; volume of cone =21

3r h ) [5 mark

Section C[20 marks]

Answertwo questions from this section

21. The diagram 6 shows a quadrilateralABCD. The area of ABD is 16 cm2 and ABD is obtuse.

Diagram 6Find,

(a) ABD [3 mark(b) the length ofAD [2 mark

(c) the area of BCD [5 mark

y =x2

-6x+ 9


8/8

347

[Lihat sebela

SULI

8

22. The table 3 below shows the cost priceof the ingredients needed to prepare nasi lemak, in the year 1998 and 2004

Ingredients Cost price per unit (RM)

1998

Cost price per unit (RM)

2004

Weigtages

Egg 0.20 0.22 1

Rice 2.00 2.42 2

Chilli 20.00 22.00 5

Coconut 1.60 1.80 6Anchovy 24.00 28.00 8

Groundnuts 2.50 2.60 4

Table 3

From the table,

(a) calculate the price index of each ingredients for the year 2004. [4 mark

(b) If the weightage of each ingredients is proportional to the monthly expenses needed, calculate the composite

index for the year 2004 taking the year 1998 as the base year. [4 mark(c) selling price of a packet of nasi lemak in the year 2004, if it was sold at price of RM 1.60 in the year 1998.

[2 mark

23. A particle moves in a straight line, Its displacement, s m, from a fixed point O, tseconds after passing through O

is given by3 29

183 2

t ts t.

(a) Find the initial velocity of the particle. [3 mark

(b) The particle comes to instantaneous rest at point P and point Q. Find the distance ofPQ. [4 mark

(c) Find the range of values oftwhen the particle moves to the right. (Assume that the motion of the particle to

the right is positive.) [3 mark

24. A principal of a school plans to buyx basketball andy footballs for a new academic year, subject to the followinconstraints :

(I) : The total number of balls bought should not be more than 80

(II) : The number of footballs bought should not be more than 4 times the number of basketballs bought.

(III) : The number of footballs bought should exceed the number of basketballs bought by at least 10.

(a) Write three inequalities, apart fromx 0 andy 0, which satisfy the above constraints. [3 mark

(b) Hence, using a scale of 2cm to 10 units on both axes, construct and shade the feasibe regionR which satisfies

all the above constraints. [4 mark

(c)Using your graph, find

(i) the range of the number of footballs bought if the number of basketballs is 30.

(ii) the maximum allocation needed if the cost prices of a basketball and a football are RM60 and RM80

respectively.

[3 mark

END OF QUESTION PAPER

smc addmath mocks 2008

Documents