Analysis of Additional Mathematic ( 2004 - 2007 ) Maths/Times/2008/Add Maths...SPM 2008 [ 3756/1 ] [...

SPM2008

[ 3756/1 ] [ 3756/2 ]

Additional MathematicAnalisisMata Pelajaran

99

JAW

APA

N b

oleh

did

apat

i di la

man

web

http

://w

ww

.tim

es.m

y

SOALAN ULANGKAJI SPM 2008

NO TOPICSPAPER 1 PAPER 2

2004 2005 2006 2007 2004 2005 2006 20071 1,2,3 1,2,3 1,2 1,2,3 - - 2 -2 4 4,5 3 4 - - - -3 5,6 6 4,5 5,6 - - - -4 - - - - 1 1 1 15 7,8 7,8,9 6,7,8 7,8 - - - -6 14,15 14 12 13,14 2 9 9 27 - 23 24 22 4 4 6 58 19 18 16 18 9 10 10 99 20,21 19,20 17,18,

1919,20 5b,10a 2a,8a - 4(a),(b)

10 - - - - 13 12 13 1511 - - - - 12 13 15 1312 9,10,

11,1210,11,

129,10 9,10,

116 3 3 6

13 13 13 11 12 7 7 7 714 22 21 20,21 21 5a,10b 2b,8b,

8c8 4(c),10

15 16,17 15,16 13,14 15,16 8 6 5 816 18 17 15 17 3 5 4 317 23 22 22 23 - - - -18 24 24 23 24 - - - -19 25 25 25 25 11 11 11 1120 - - - - 15 15 12 1221 - - - - 14 14 14 14

TOTAL 25 25 25 25 15 15 15 15

FunctionsQuadratic EquationsQuadratic FunctionsSimultaneous EquationsIndices and LogarithmsCoordinate GeometryStatisticsCircular MeasureDifferentiation

Solution of TrianglesIndex NumberProgressions

Linear LawIntegration

VectorsTrigonometric FunctionsPermutations and CombinationsProbabilityProbability DistributionsMotion Along A straight LineLinear Programming

Analysis of Additional Mathematic( 2004 - 2007 )

http://edu.joshuatly.com http://www.joshuatly.com

SULIT

3472/1 SULITLihat sebelah

SOALAN ULANGKAJI SPM 2008100JA

WA

PAN

bol

eh d

idap

ati d

i lam

an w

eb h

ttp:/

/ww

w.ti

mes

.my

TIMES HIGHER EDUCATION

SOALAN ULANGKAJI SPM 2008ADDITIONAL MATHEMATICS

Paper 1Nov./Dis2 hour

DO NOT OPEN UNTILL INTSRUCTED TO

1. Answer all the questions

2. Think thoroughly before answering any of the questions. If you need to change your answer, erase the answer properly and thoroughly before remarking the question sheet.

This question paper contains 5 printed pages and 0 non printed pages


SULIT


101

JAW

APA

N b

oleh

did

apat

i di la

man

web

http

://w

ww

.tim

es.m

y


Answer all question ( 80 marks )

1. Diagram 1 shows a graph that represents the relation between x and y. State(a) the type of relation between x and y(b) whether the relation is a function. [ 3 marks ]

x

y

0

DIAGRAM 1

2. Given an arithmetic progression 20 , 5 , - 10 , - 25, ……..,- 145.Find the number of terms of the progression. [ 2 marks ]

3. The ninth term and the sixth term of a geometric progression are 1792 and 224 respectively. If all the terms are positive, find

(a) the common ratio.(b) the first term [ 3 marks ]

4. The equations of two straight lines are x + 3y = 2 and y=kx + 7k . Given that the two lines are perpendicular to each other, find the value of k. [ 2 marks ]

6. Given that cos y = and y is an obtuse angle , find the value of sin ( 90º – y ) [ 2 marks ]5

3−

7. Find the values of p given the quadratic equation has two real and equal roots. [ 3 marks ]xp

x2

19 2 =+

8. The roots of a quadratic equation are -5 and , form the equation in the form ax² + bx + c = 0 , where a, b and c are constants. [ 2 marks ]4

3

9. There are 4 red marbles, 7 blue marbles and 5 yellow marbles in a box. Two marbles are drawn at random from the box, one after the other, without replacement. Calculate the probability that

(a) both balls are of the same colour (b) both balls are not blue [ 4 marks ]

5. The graph of a function y = (x+h) (x-k) intersect the x - axis at x = -4 and x = 6 where h and k are positive constants.

a) state the values of h and kb) find the equation of the axis of symmetry [ 3 marks ]


SULIT



WA

PAN

bol

eh d

idap

ati d

i lam

an w

eb h

ttp:/

/ww

w.ti

mes

.my

10. Diagram 2 shows the sectors of two circles OPQ and ORS with centres at O. Given that OP = 3PR and POQ = 0.8 radian, find the perimeter of the shaded region.

[ 3 marks ]

∠

DIAGRAM 2

S

R

P

O

Q

θ

11. A curve passes through point ( -1,1 ) and has a gradient function x ² ( x ² - 1 ) x + 1 Find the equation of the curve. [ 3 marks ]

12. Solve the equation [ 3 marks ])32(loglog25log +=+ xx kkk

13. Solve the equation [ 3 marks ]( ) 01234 2

1

=+−+

yy

14. Colour Number of pens Yellow x – 1 Green x Orange 16

Table 1

Table 1 shows the number of pens in a box. The probability of picking a green pen at random is . Calculate the total number of pens in the box. [ 3 marks ]11

3

15. Diagram 3 shows seven cards.

J E N A R I S

DIAGRAM 3

How many different arrangements can be obtained if the arrangement must begin with a vowel ? [ 3 marks ]

16. A committee of 8 members has to be formed from 10 teachers and 4 students.Calculate the number of ways this can be done if (a) 5 teachers are committee members (b) not more than 2 students are committe [ 4 marks ]

2 cm


SULIT


103

JAW

APA

N b

oleh

did

apat

i di la

man

web

http

://w

ww

.tim

es.m

y


16)(.8)(3

0

3

0

−=+= ∫∫ dxkxfifkofvaluetheFinddxxf

18. Given P ( -3,4) and Q (6,-7) . Find

(a) PQ (b) the unit vector for PQ [ 3 marks ]

19. Find the equation of the normal to the curve y = - 1 + 5x + 3x ² at the point (1,2). [ 4 marks ]

20. Given that sin 30 º = h and cos 40 º = k, express cos 70 º in terms of h and k . [ 4 marks ]

21 Given the function and the composite function f g(x) = 4x. Find

(a) g(x)(b) the value of x when gf(x) = 6 [ 4 marks ]

17. Given that dx of if dx [ 3 marks ]

0,12

)( ≠= xx

xfx

12


SULIT



WA

PAN

bol

eh d

idap

ati d

i lam

an w

eb h

ttp:/

/ww

w.ti

mes

.my

22. Seven numbers, k , 4, 5 , 7, 2k, 12 and 12 have a mean of h . When the number 9 is added to the set of data, the new

mean is h. Find the value of k and of h. [ 4 marks ]2829

23. X is a random variable of a normal distribution with a mean of 6.4 and a standard deviation of 1.4 . Find (a) the Z score if X = 8.5(b) P ( 6.4 ≤ X ≤ 8.5 ) [ 4 marks ]

24. Diagram 4 shows a straight line graph of against x². Given where m and n are constants. Calculate the value of m and of n.nx

y

m+= 22

y

1

y

1

x²

(-1,0)

(2,6)

DIAGRAM 4

25. Solve the equation 3 cos² x + sin x - 1 = 0 for 0º ≤ x ≤ 360º [ 4 marks ]

END OF QUESTION PAPER


SULIT


105

JAW

APA

N b

oleh

did

apat

i di la

man

web

http

://w

ww

.tim

es.m

y


TIMES HIGHER EDUCATION

SOALAN ULANGKAJI SPM 2008ADDITIONAL MATHEMATICS

Paper 2Nov./Dis

DO NOT OPEN UNTILL INTSRUCTED TO

1. Answer all the questions

2. Think thoroughly before answering any of the questions. If you need to change your answer, erase the answer properly and thoroughly before remarking the question sheet.

This question paper contains 8 printed pages and 0 non printed pages


SULIT



WA

PAN

bol

eh d

idap

ati d

i lam

an w

eb h

ttp:/

/ww

w.ti

mes

.my

Section A( 40 marks )

Answer all questions in this section.

1. Solve the simultaneous equations:

x – 2y = 5 , [ 7 marks ]763

−=−x

y

y

x

2. Diagram 1 shows a rectangle PQRS. The coordinates of P and Q are (-2,1) and (4,4) respectively.Given that the equation of PR is y – x = 3, find

(a) the coordinates of point S (b) the equation of SQ (c) the area of the rectangle PQRS [ 6 marks ]

DIAGRAM 1

3. Given that px² – x is a gradient function for a curve such that p is a constant. y = 4x – 5 is a tangent equation at point (1,-1) to the curve. Find

(a) the value of p (b) the curve equation (c) the normal equation of the curve at point (1,-1) [ 6 marks ]

4. (a) Given the functions f(x) = 3x + k and f – 1 (x) = 2hx , where h and k are constants. Find the value of h and k. q [ 3 marks ]

(b) Given the functions f(x) = 4x - 3 and g(x) = , Find

(i) f – 1

(1) (ii) g f – 1

(13) [ 4 marks ]

3

52 +hx

0,6

≠xx

P

SQ

R

0x

y


SULIT


107

JAW

APA

N b

oleh

did

apat

i di la

man

web

http

://w

ww

.tim

es.m

y


5 (a) The sum of the first n terms of the geometric progression 64,32,16,8,4……. is 127.5 . Find (i) the common ratio (ii) the value of n [ 3 marks ]

(b) A rope with a length of 200cm is cut into 25 sections whose lengths are in arithmetic progression. Given that the sum of the lengths of 3 smallest section is 4.2 cm , find

(i) the length of the largest section (ii) the sum of the last three largest section [ 4 marks ]

6. (a) The mass of students in a school is normally distributed with mean 52.5 kg and variance 10 kg² . Find the probability that a student chosen at random has a mass of less than 45 kg.

(b) A box contains blue and green balls. 40 % of the balls are blue in colour.

(i) If 6 balls are selected at random, find the probability that at least one ball is blue in colour. (ii) The variance for blue balls is 12. Find the number of balls in the box. [ 7 marks ]


SULIT



WA

PAN

bol

eh d

idap

ati d

i lam

an w

eb h

ttp:/

/ww

w.ti

mes

.my

Section B( 40 marks )

Answer four questions from this section

7. Use the graph paper to answer this question.Table 1 shows the values of two variables , x and y , obtained from an experiment. The variables of x and y are related by the

equation , where p and q are constants.12=−

x

q

y

p

x 1.5 2.0 2.5 3.0 5.0y 0.55 0.94 1.45 2.02 4.76

(a) Plot against by using a scale of 2 cm to 0.05 unit on the – axis and 2 cm to 0.2 units on the -axis. Hence,

draw the line of best fit. [ 5 marks ] (b) Use the graph from (a) to find the value of (i) p (ii) q [ 5 marks ]

y

1x²1

x²1

y

1

8. (a) Given cos x = - and 0º < x < 180º , find the value of (i) sec x + cot x (ii) tan ( x – 135º ) [ 4 marks ]

(b) (i) Sketch the graph of y = 1 – sin 2x for 0 ≤ x ≤ 2∏ [ 3 marks ] (ii) Hence, by drawing a suitable straight line on the same axes, find the number of solutions that satisfying the equation x = 2 ∏ sin 2x for 0 ≤ x ≤ 2∏ [ 3 marks ]

53

Table 2 shows the distribution of marks of 60 students in a test.

(a) Without drawing the ogive, estimate (i) median (ii) interquartile range [ 3 marks ]

(b) Compute the (i) mean (ii) standard deviation for the marks of the students. [ 7 marks ]

9. Marks Frequency41 - 45 346 - 50 851 - 55 756 - 60 1561 - 65 1366 - 70 871 - 75 6

Table 1

Table 2


SULIT


109

JAW

APA

N b

oleh

did

apat

i di la

man

web

http

://w

ww

.tim

es.m

y


10. Diagram 2 shows two circles with centres, P and Q . AB is the common tangent to the two circles at points C and D respectively. If the radii of the two circles are 7 cm and 4 cm respectively, find (a) RQD , in radian (b) the perimeter , in cm , of the shaded region (c) the area , in cm², of the shaded region [ 10 marks ]

∠

4 x

11. Diagram 3 shows a pentagon ABEDC. Given AB = 4x , AC = 6y and CD = 8x.(a) Express in terms of x and/or y (i) CB (ii) DA [ 4 marks ]

(b) If BE = nBC and AE = mAD , express AE (i) in terms of n, x and y (ii) in terms of m , x and y hence, find the value of m and of n. [ 6 marks ]

→ → → →

→ → →

→→

→

A C D B

DIAGRAM 2P

RQ

6 y

BA

C D

E

8 x


SULIT



WA

PAN

bol

eh d

idap

ati d

i lam

an w

eb h

ttp:/

/ww

w.ti

mes

.my

Section C( 20 marks )

Answer two questions from this section .

12. Use the graph paper to answer this question.

Given that x and y are two positive integres with the following conditions.

I : The maximum value of x is 40

II : The sum of x and y is not more than 100

III : The difference between y and twice the value of x is 25 or less

(a) Write the inequalities other than x > 0 , y > 0 for each of the above. [ 2 marks ]

(b) By using a scale of 2 cm to 20 unit on both axes, construct a graph and shade the region as `` F`` that satisfies all the inequalities. [ 3 marks ]

(c) Based on your graph, answer all the questions

(i) Find the maximum value of y when x = 40

(ii) Find the maximum value of k when k = x + 2y

(iii) Find the minimum value of x when y = 40 [ 5 marks ]


SULIT


111

JAW

APA

N b

oleh

did

apat

i di la

man

web

http

://w

ww

.tim

es.m

y


14. (a) Diagram 4 shows a triangle KLM. Given KL = 6.8 cm, ∠LKM = 48º and ∠LMK = 25º. Find

(i) the length of KM (ii) the area of ∆ KLM [ 4 marks ]

(b) Diagram 5 shows a cyclic quadrilateral UVWT. Given that , ∠TUV = 140º , UV = 4 cm , UT = 8 cm , and WT = 10 cm. Find (i) the length of VT (ii) ∠TVW (iii) the area of quadrilateral UVWT [ 6 marks ]

K

DIAGRAM 4

L

M48º 25º

DIAGRAM 5

V

U

W

T

140º

13. A particle moves along a straight line and passes through a fixed point O. Its displacement, s meters, from O at time t seconds alter passing through O is given by s = 2t³ – 3 t² . Find

(a) the initial acceleration

(b) the velocity when t = 4

(c) the time when the particle is instantaneously at rest

(d) the time when the particle reaches at velocity of 12 cms–1 [ 10 marks ]


SULIT



WA

PAN

bol

eh d

idap

ati d

i lam

an w

eb h

ttp:/

/ww

w.ti

mes

.my

15. (a) The price indices of a pair of shirts of a particular brand P in the years 2005 and 2003 based on the year 2001 are 156 and 144 respectively. (i) Calculate the price index of a pair of shirts of brand P for the year 2005 based on the year 2003. [ 3 marks ] (ii) If a pair of shirts of brand P is priced at RM250 in the year 2003, calculate its corresponding price in the year 2001. [ 2 marks ]

(b)

Item Price in 1998 (RM) Price in 2000(RM)

Price Index in 2000 based on 1998

Weightage

K 3.00 3.60 120 4L X 2.50 125 2M 4.00 4.40 110 1N 2.50 4.00 Y 5

Table 3 shows the prices of four commodities K, L, M and N in year 1998 and 2000, the price index in year 2000 was based on 1998. Calculate

(i) the value of x and of y [ 2 marks ]

(ii) the composite index number of the cost of the item production of the four commodities in year 2000 is based on year 1998. [ 3 marks ]

Table 1

END OF QUESTION PAPER


Analysis of Additional Mathematic ( 2004 - 2007 ) Maths/Times/2008/Add Maths...SPM 2008 [ 3756/1 ] [...

Documents

Transcript of Analysis of Additional Mathematic ( 2004 - 2007 ) Maths/Times/2008/Add Maths...SPM 2008 [ 3756/1 ] [...