add maths paper 1
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PROGRAM DIDIK CEMERLANG AKADEMIK
SPM
MODEL SPM QUE 1 )
ORGA
JABATAN PELAJARA
ADDITIONALMATHEMATICS
MODU
http://maths
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NISED BY:
LE 19N NEGERI PULAU PINANG
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Additional Mathematics ( Paper 1) SPM
Jabatan Pelajaran Pulau Pinang 2
3472/1 NO. KAD PENGENALANAdditionalMathematicsPaper 1 ANGKA GILIRAN
2 Hours
JABATAN PELAJARAN NEGERI PULAU PINANG
ADDITIONAL MATHEMATICS
Paper 1
Two Hours
JANGAN BUKA KERTAS SOALAN INISEHINGGA DIBERITAHU
1. Tuliskan angka giliran dan nombor kadpengenalan anda pada ruang yangdisediakan.
2. Calon dikehendaki membaca arahandi halaman 2.
Kod PemeriksaQuestions Marks Actual Marks
1 22 33 34 35 36 37 38 39 310 211 412 413 414 215 216 317 418 419 420 421 322 423 324 325 4
Total
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Additional Mathematics ( Paper 1) SPM
Jabatan Pelajaran Pulau Pinang 3
INFORMATION FOR CANDIDATES
1. This question paper consists of 25 questions.
2. Answer all questions.
3. Give only one answer for each question.
4. Write your answer clearly in the spaces provided in the question paper.
5. Show your working . It may help you to get marks .
6. If you wish to change your answer , cross out the work that you have done. Then write down the
new answer.
7. The diagrams in the questions provided are not drawn to scale unless stated.
8. The marks allocated for each question and sub-figure mathematical tables is provided .
9. You may use a non-programmable scientific calculator .
10.A booklet of four-figure mathematical tables is provided.
11.You may use a non programmable scientific calculator.
12.This question paper must be handed in at the end of examination.
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Additional Mathematics ( Paper 1) SPM
Jabatan Pelajaran Pulau Pinang 4
Answer all questions
1 . Diagram 1, the function h maps x to y and the function k maps y to z.
DIAGRAM 1
Determine
(a) hk 1 ( 4),
(b) kh 1 ( 2). [2 marks]
Answer : (a) ___________
(b) ___________
2. The function p1 is defined as p1 (x) =x
x43 , x 4.
Find
(a) p(x),
(b) p(5). [3 marks]
Answer : (a) ___________
(b) ___________
x y z
4
3
2
hk
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Additional Mathematics ( Paper 1) SPM
Jabatan Pelajaran Pulau Pina
3. The following information refers to the functions h and g.
Find f (x). [3 marks]
Answer : ___________
4. The straight line y = t intercept with the curve y = 3 + 5x 4x2 at the two points A and B .
Find the range of values of t . [3 marks]
Jawapan : ___________
5. Solve the quadratic equation5
23
12 2
xx Give your answer correct to three decimal
places . [3 marks]
g (x) = 4 3 x
fg (x) = 2 x + 5
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Answer : x = ___________
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Additional Mathematics ( Paper 1) SPM
Jabatan Pelajaran Pulau Pinang 6
6. Diagram 2 shows the graph of a quadratic functions g(x) = 4 2(x + h)2 where h is constant.
DIAGRAM 2
The curve y = g(x) has maximum point (3, k) , where k is a constant .State
(a) the value of h,
(b) the value of k,.
(c) the equation of the axis of symmetry .[3 marks]
Answer : (a) h = ___________
(b) k = ___________
(c) ___________
7. Solve the equation .)4)(8(
164 13
xx
x [3 marks]
Answer : x = ___________
y = g(x)
(3,k)
x
y
O
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Additional Mathematics ( Paper 1) SPM
Jabatan Pelajaran Pulau Pinang 7
8. Solve the equation log2 (x 1) + 2 = 2 log2 x [3 marks]
Answer : x = ___________
9. Given that log2 x = p and log2 y = r, express
2
3
232log
yx in term p and r.
[3 marks]
Answer : ___________
10. The sum of the first n term of an arithmetric progression is given by Sn= 5n 3. Find the
fifth term . [2 marks]
Answer : ___________http://mathsmozac.blogspot.com
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Additional Mathematics ( Paper 1) SPM
Jabatan Pelajaran Pulau Pinang 8
11. The first three terms of an arithmetic progression are 21 , 1, 2 ,
Find
(a) the common ratio ,
(b) the sum of the first 10 terms after the 5th term .
[ 4 marks]
Answer : (a) ___________
(b) ___________
12. The sum of the first n terms of an arithmetric progression 47, 44, 41, is 1325. Find
(a) the common difference of the progression ,
(b) the value of n. [4 marks]
Answer : (a) ______________
(b) n = ___________
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Additional Mathematics ( Paper 1) SPM
Jabatan Pelajara
13. Diagram 3 shows a straight line graph of log10 y againts log10 x.
The variables x and y are related by equation y = p x q, where p and q are contants .
(a) Calc
(b) Find
14. The follow
parallel to e
Express p
log10 y
log10 x
2
4 O
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ulate the value of p and q,n Pulau Pinang 9
the value of y if x = 10. [4 marks]
Answer : (a) p = ___________
q = ___________
(b) y =___________
ing information refers to the equations of two straight lines , AB and CD , which
ach other.
in terms q. [2 marks]
Answer : p =___________
AB : 2y = p x + q
CD : 3y = (q + 1) x + 2
Where p and q are constants
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Additional Mathematics ( Paper 1) SPM
Jabatan Pelajaran Pulau Pinang 10
15. Given that B point is (8, 5) and O is origin.
(a) ExpressOB in terms of
~i and
~j .
(b) Find the unit vector in the direction ofOB . [2 marks]
Answer : (a) ___________
(b) ___________
16. Given thatOA = 2
~i + 3
~j ,
OB = 10
~i + 6
~j and R is a point on AB such that AR :
AB = 2 : 3. Find
(a)AB ,
(b)OR . [3 marks]
Answer : (a) ___________
(b) ___________
17. Solved the equation 3cot
1 22 xsekx
for 0 x 360.
[4 marks]
Answer : x = ___________http://mathsmozac.blogspot.com
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Additional Mathematics ( Paper 1) SPM
Jabatan Pelajaran P
18. Diagram 4 shows the sector OPQ, centre O with a radius of 5 cm . Line PR is perpendicular tothe line OQ and QR = 1 cm.
[4 marks]
Find ( a ) POR in radians ,
( b ) the perimeter of the shaded region .
Answer : ( a ) .
( b ) .
19. Given that 2)25(4)( xxxf , find )(" xf [4 marks]
RAJAH 4
Q
P O
R
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Answer : ___________
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Additional Mathematics ( Paper 1) SPM
Jabatan Pelajaran Pulau Pinang 12
20. Given that x = t + 3t 2 and y = 2t 1
(a) finddydx in term of t.
(b) If y decreases from 4.0 to 3.98, Find the corresponding small change in t .
[4 marks]
Answer : (a) ___________
(b) ___________
21. Given that 2321
xxy and )(4 xf
dxdy
with )(xf is a function in x .
Calculate the value of dxxf )(32
2 . [3 marks]
Answer : ___________
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Additional Mathematics ( Paper 1) SPM
Jabatan Pelajaran Pulau Pinang 13
22. A chess team consists that of 5 students . The team will be chosen from a group of 6 boys
and 4 girls . Calculate the number of teams that can be formed such that each team consists
of
(a) 4 boys,
(b) Not more than 2 girls.[4 marks]
Answer : (a) ___________
(b) ___________
23. The mean of five numbers is m. The sum of the squares of the numbers is 720 and the
standard deviation is 9h2. Express m in term of h.
[3 marks]
Answer: m = ___________
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Additional Mathematics ( Paper 1) SPM
Jabatan Pelajaran Pulau Pinang 14
24. Ali has 6 accessories of the item which consists of P, Q, R, S, T and U. He wants to arrange
4 of the items in a row . Find the probability that
(a) the arrangment is TUPS ,
(b) the arrangment does not incule P item
[3 marks]
Answer : (a) ___________
(b) ___________
25. X is a random variable of normal distribution with a mean of 10 and a variance 9 , find the
value of r such that P ( X < r ) = 0 . 9 7 5.
[4 marks]
Answer : ___________
END OF QUESTION PAPER
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Additional Mathematics ( Paper 1) SPM
Jabatan Pelajaran Pulau Pinang 15
Answers
1. ( a ) h k 1 ( 4) = 2
( b ) k h 1 ( 2) = 4
2 . ( a ) p 1 ( x ) =x
x43
p 1 ( y ) = yy43
x =y
y43
x ( 4 y ) = 3 y
4 x x y = 3 y
y ( x + 3 ) = 4 x
y =3
4xx
p ( x ) =3
4xx , x 3,
( b ) 35)5(4)5(
p
=25
3 . g ( x ) = 4 3 x
y = 4 3 x
3 x = 4 y
x =3
4 y
g 1(x) =3
4 x
f ( x ) = f g g 1 ( x ) = f g
34 x
= 2 53
4
x
=3
223 x
4 . y = t , y = 3 + 5 x 4 x 2
3 + 5 x 4 x 2 = t
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Additional Mathematics ( Paper 1) SPM
Jabatan Pelajaran Pulau Pinang 16
4 x 2 5 x + t 3 = 0
Intercept at two points , use b 2 4 a c > 0
( 5 ) 2 4 ( 4 ) ( t 3 ) > 0
1 6 t < 7 3
t