3472/1 Name :.. Matematik Tambahan
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1 7/1 Name :.. Matematik Tambahan Kertas 1 Form :.. Ogos 008 Jam SEKOLAH BERASRAMA PENUH BAHAGIAN PENGURUSAN SEKOLAH BERASRAMA PENUH / KLUSTER KEMENTERIAN PELAJARAN MALAYSIA PEPERIKSAAN PERCUBAAN SIJIL PELAJARAN MALAYSIA 008 MATEMATIK TAMBAHAN Kertas 1 Dua jam JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU 1 This question paper consists of 5 questions.. Answer all questions.. Give only one answer for each question.. Write your answers 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-part of a question are shown in brackets. 9. A list of formulae is provided on pages to. 10. A booklet of four-figure mathematical tables is provided.. 11 You may use a non-programmable scientific calculator. 1 This question paper must be handed in at the end of the examination. Question Total Marks TOTAL 80 Marks Obtained Kertas soalan ini mengandungi 15 halaman bercetak 7/ 008 Hak Cipta SBP [Lihat sebelah
2 7/1 The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used. ALGEBRA b b ac log c b 1 x 8 log a b a log c a a m a n a m + n a m a n a m - n (a m ) n a nm 5 log a mn log a m + log a n 6 m log a n log a m - log a n 7 log a m n n log a m 9 T n a + (n-1)d n 10 S n [a + ( n 1) d] 11 T n ar n-1 n n a( r 1) a(1 r ) 1 S n r 1 1 r a 1 S, r <1 1 r, (r 1) CALCULUS 1 y uv, u y, v dy dx dx dy dv u dx + v du v u dx v du dx dv dx, Area under a curve b y dx or a b a x dy dy dx dy du du dx 5 Volume generated b π y dx or a b π x dy a GEOMETRY 1 Distance Midpoint x + (x, y) 1 x r x + y ( x y 1 x ) + ( y1 ) y 1 + y, 5 A point dividing a segment of a line nx1 + mx ny1 + my ( x,y), m + n m + n 6 Area of triangle 1 ( x 1 y + x y + x y ) ( x 1 y1 + x y + x1 y ) rˆ xi + yj x + y 7/1 008 Hak Cipta SBP [ Lihat sebelah
3 7/1 STATISTIC 1 x x σ x N fx f ( x x) N x N _ x w1i 1 I w1 n n! P r ( n r)! n n! C r ( n r)! r! 10 P(A B) P(A)+P(B)- P(A B) σ f ( x x) f fx f x 11 P (X r) r C p q n r n r, p + q 1 1 N F 5 m L + C fm Q1 6 I 100 Q 0 1 Mean µ np 1 σ npq x µ 1 z σ TRIGONOMETRY 1 Arc length, s rθ Area of sector, L sin A + cos A 1 sec A 1 + tan A 5 cosec A 1 + cot A 6 sin A sina cosa 7 cos A cos A sin A cos A sin A 1 r θ 9 sin (A ± B) sina cosb ± cosa sinb 10 cos (A ± B) cosa cosb sina sinb tan A ± tan B 11 tan (A ± B) 1 tan Atan B 1 a sin A b sin B c sin C 1 a b + c - bc cosa 1 1 Area of triangle absin C 8 tan A tan A 1 tan A 7/1 008 Hak Cipta SBP [ Lihat sebelah
4 Blank Page 7/1 008 Hak Cipta SBP [Lihat sebelah
5 7/1 Answer all questions. 1. A function f maps the elements from set P { m,,9,16,5} to set Q { 0,, 8, 15, } as shown below in ordered pairs : { ( m, 0), (, ), (9, 8), (16, 15), (5, ) } (a) Write down the function notation for f. (b) State the value of m. (c) State the codomain. [ marks ] Answer : ( a ).. ( b ) ( c ).... Given that function f : x ax, a 0 and b. f : x 16x b, find the value of a and of [ marks ] 7/1 008 Hak Cipta SBP [ Lihat sebelah5
6 Answer : a. b... k. Given that function f : x, x 0, and x and of k. f : x, x h, find the value of h x h 1 [ markah ] Answer : h... k.... Given m and - are the roots of a quadratic equation x x k 1, find the value of m and of k. [ marks ] 6 7/1 008 Hak Cipta SBP [Lihat sebelah
7 7/1 Answer : m... k Given that quadratic equation x(x p) x has no roots, find the range of values of p. [ marks ] 5 Answer : Diagram 1 shows the graph of a curve f ( x) ( x + p) + q, where p and q are constants. f(x) x f ( x) ( x + p) + q x 8 O Diagram 1 Given the straight line x is the axis of symmetry of the curve and parallel to the y-axis. Find (a) the value of p, (b) the value of q, (c) the turning point of the curve f (x). [ marks] Answer : (a).... 7/1 008 Hak Cipta SBP [ Lihat sebelah7 6
8 (b)... (c) Find the range of the values of x for which x ( x 1) ( x + 5). [ marks] 7 Answer :... x Solve the equation 8 x. [ marks] 8 Answer : Solve the equation log 5 (5 x) 1 log5 x. [ marks] 8 7/1 008 Hak Cipta SBP [Lihat sebelah
9 7/ Given that p log q, express p in terms of q. log 9 7 Answer :... [ marks] 10 Answer : An arithmetic progression has 9 terms. The sum of the first four terms is and the sum of all the odd number terms is 55. Find a) the first term and the common difference, b) the seventh term. [ marks] 8 7/1 008 Hak Cipta SBP [ Lihat sebelah9 11
10 Answer: ( a ) For examiner s use only ( b) For a geometric progression, the sum of the first two terms is 0 and the third term exceeds the first term by 15. Find the common ratio and the first term of the geometric progression. [ marks] 1 Answer: Diagram shows the graph of xy against x. xy (7, ) O x (0, h) Diagram The variables x and y are related by the equation constant. Find the value of h and of k. k y x +, where k is a x [ marks] 10 7/1 008 Hak Cipta SBP [Lihat sebelah
11 7/1 1 Answer : h. k In Diagram below, the equation of straight line LM is x y 6 1. The points L and M lie on the x-axis and y-axis respectively. y 0 L x M Diagram Find the equation of a straight line which is perpendicular to LM and passes through the point M. [ marks] 1 Answer :. 15. In Diagram, OA a and OB b. On the same square grid, draw the line that represents the vector OC a b. [ marks ] B A 7/1 008 OHak Cipta SBP [ Lihat sebelah 11
12 16 15 Diagram 16. Given A(, 5), B(, ) and C( p, q ). Find the values of p and q such that AB BC 9 i 5 j. ~ ~ [ marks] 16 Answer: Solve the equation cos x sin x for 0 x 60. [ marks] 17 Answer: Diagram 5 shows a sector BOC of a circle with centre O. B 1 7/1 008 Hak Cipta SBP [Lihat sebelah
13 7/1 O 0.5 rad Diagram 5 C Given the perimeter of the sector BOC is.5 cm, calculate (a) the radius of the sector (b) the area of the sector. [ marks] 18 Answer: a)... b). 19. Given f ( x), find the value of f (). (5 x) [ marks] 19 Answer: 7/1 008 Hak Cipta SBP [ Lihat sebelah 1
14 0. Find the equation of normal to the curve y x 5x at the point when x 1. [ marks ] 0 Answer: x 1. Given that f ( x) dx 6, calculate f ( x) dx. 5 5 [ marks] 1 Answer:... It is given that the sum of 5 numbers is α. The mean of the sum of the square is 00 and the variance is β. Express α in terms of β. [ marks] 1 7/1 008 Hak Cipta SBP [Lihat sebelah
15 7/1 Answer:... A pack of present containing three pens are chosen from blue pens and 5 black pens. Find the probability of getting at least one black pen in the pack of present. [ marks] Answer: P O L I T E Diagram 6 Diagram 6 shows six cards of different letters. (a) Find the number of possible arrangements beginning with P. (b) Find the number of these arrangements in which the vowels are separated. [ marks ] Answer: ( a ) ( b ) 7/1 008 Hak Cipta SBP [ Lihat sebelah 15
16 5. X is a random variable which is normally distributed with mean µ and standard deviation of 6. Find (a) the value of µ, if the z-value is 1.5 when x, (b) P( X < 7 ). [ marks ] 5 Answer: ( a) ( b )... END OF QUESTION PAPER 16 7/1 008 Hak Cipta SBP [Lihat sebelah
17 7/1 7/1 008 Hak Cipta SBP [ Lihat sebelah 17
SEKOLAH MENENGAH ZON A KUCHING LEMBAGA PEPERIKSAAN PEPERIKSAAN PERCUBAAN SPM 2008
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