SMS MUZAFFAR SYAH, MELAKA

Size: px

Start display at page:

Download "SMS MUZAFFAR SYAH, MELAKA"

Sandra Wright
5 years ago
Views:

1 SULIT 7/ ADDITIONAL MATHEMATICS PAPER AUGUST 008 HOURS NAMA : KELAS : NO K.P : A. GILIRAN : - JABATAN PELAJARAN NEGERI SABAH SIJIL PELAJARAN MALAYSIA TAHUN 008 EXCEL ADDITIONAL MATHEMATICS PAPER (KERTAS ) TWO HOURS (DUA JAM) JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU. Tuliskan angka giliran dan nombor kad pengenalan anda pada ruang yang disediakan.. Calon dikehendaki membaca arahan di halaman. This question paper consists of printed pages.

2 (Kertas soalan ini terdiri daripada halaman bercetak.) 7/ [Turn over (Lihat sebelah) INFORMATION FOR CANDIDATES. This question paper consists of 5 questions.. Answer all questions.. Give only one answer for each question.. Write your answers clearly in the space 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 are shown in brackets. 9. A list of formulae is provided on pages to A booklet of four-figure mathematical tables is provided.. You may use a non-programmable scientific calculator.. This question paper must be handed in at the end of the examination.

3 The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used. ALGEBRA. x b b ac a 8. log a logc b b log a c. a a a m n m n 9. T a ( n ) d n. a a a. ( a ) m n m n a m n mn 5. log mn log m log n a a a m 6. log log m log n a a a n 7. log m nlog m a a n n 0. Sn [ a ( n ) d].. Tn S n ar n n n a( r ) a( r ), r r r a. S, r r CALCULUS dy dv du. y uv, u v dx dx dx. Area under a curve = b a y dx or du dv v u u dy. y, dx dx v dx v = b x dy a. dy dy du dx du dx 5. Volume generated = b y dx a or

4 = b x dy a STATISTICS.... x x N x fx f ( x x) x x N N f ( x x) fx x f f I n n P r C r W I i W i i n! n r! n! n r! r! 0. P A B P A PB P A B N F 5. m L c fm Q 6. I 00 Q o. n r n P X r C p q r, p q. Mean, μ = np. npq. Z X r GEOMETRY. Distance. Area of triangle = = x x y y. Midpoint x x y y x, y,. A point dividing a segment of a line ( ) ( ) x y x y x y x y x y x y r x y rˆ xi yj x y

5 nx mx ny my m n m n x, y, 5 TRIGONOMETRY. Arc length, s r. Area of sector,.. 5. A sin A cos A sec A tan A cosec A cot A 6. sin A sin A cos A 7. cos cos sin r A A A cos A sin A 8. sin ( A B) sin A cos B cos Asin B 9. cos ( A B) cos Acos B sin A sin B 0. tan A tan B tan ( A B) tan A tan B tan A. tan A tan A.. a b c sin A sin B sin C a b c bc cos A. Area of triangle sin ab C

6 6 For Examiner s Use Answer all questions.. In Diagram, set P is the domain and set Q is the codomain of a relation. 9 6 Set P Diagram Set Q (a) State the type of relation between set P and set Q. (b) Using function notation, state the relation between set P and set Q. [ marks] Answer :. Given that f : x 7x. Find the value of p if f () 5 p. (a) (b).. [ marks]

7 7 Answer : p =. Given that g : x ax, and g( x) b x. Find the values of a and b. [ marks] For Examiner s Use Answer : a =.. b =... (a) Solve the following quadratic equation: x x 0 (b) Given the quadratic equation x px 9 0 has two equal roots. Find the values of p. [ marks] Answer : (a). (b). 5

8 8 5. Find the range of the values of x for ( x ) (x )( x ). [ marks] Answer : For Examiner s Use 6. The quadratic function f x x x ( ) 6 5 can be expressed in the form ( x p) q, where p and q are constants. Find the values of p and q. [ marks] 6 Answer : p =.. q =.. 7. Given that log p a and log q a, find the value of p q log a a. [ marks] 7 Answer :..

9 9 y 8. Solve the equation. [ marks ] y y 6 Answer :.. 9. An arithmetic progression has 5 as the second term and difference. List the first five terms of the progression. as the common [ marks] For Examiner s Use 9 Answer :. 0. The first three terms of an arithmetic progression are p, p, p. Find (a) the value of p, (b) the sum of the first 8 terms of the progression. [ marks] 0 Answer : (a). (b).

10 0. The first term and the fourth term of a geometric progression are 6 and respectively. Calculate the sum to infinity of the geometric progression. [ marks] Answer :.... For Examiner s Use. The variables x and y are related by the equation A straight line graph is obtained by plotting y (, p) x y x y 5x x. against x, as shown in Diagram. Diagram Find the values of p and q. (q, ) x [ marks] Answer : p =... q = x y. Given a straight line y mx is parallel to. Find the value of m. 5 [ marks]

11 Answer : m =.. Given that the points K(, ), L(,5h ) and M ( h, ) lie on a straight line, find the possible values of h. [ marks] Answer : h = In Diagram, PQRS is a parallelogram and the point H lies on the straight line PT. Given that PS b and PQ 0a. T is a midpoint of QR and PH HT. Express PH, in terms of a and b. [ marks] S R For Examiner s Use b H T P 0a Diagram Q 5 Answer : PH =

12 6. Given STUV is a parallelogram, TV i j and UV i j. Find (a) TU, (b) the unit vector in the direction of ST in terms of i and j. [ marks] Answer : (a). (b)..... For Examiner s Use 7. Solve the equation cos 8sin 5 for 0 o o 60. [ marks ] 7 Answer :.. dy p 8. The curve y f ( x) is such that, where p is a constant. dx x The gradient of the curve at x is. Find the value of p. [ marks] 8

13 Answer :.. 9. Diagram shows a circle with centre O and radius cm. Given that the area of the minor sector AOB is 9 cm, calculate the length, in cm, of the major arc AB. [Use =.] [ marks] cm A O B Diagram Answer :.. 0. The curve y x 8x has a maximum point at x = p, where p is a constant. Find the value of p. [ marks] For Examiner s Use Answer :. 0. Given that (a) the value of g( x) dx 6 (b) the value of p if g ( x ) dx,, find [ px g( x)] dx 8. [ marks]

14 Answer : (a)... (b).... A set of data consists of five numbers. The sum of the numbers is 75 and the sum of the squares of the numbers is 685. Find, for the five numbers (a) the mean, (b) the standard deviation. [ marks] Answer : (a)... (b)... For Examiner s Use. A badminton team that consists of 8 students is to be chosen from a group of 7 male students and 6 female students. Calculate the number of different teams that can be formed if each team must consist of (a) exactly male students, (b) not more than female students. [ marks] Answer : (a). (b).. In a shooting competition, the probability that Lim will strike the target is If Lim fires 6 shots, calculate the probability that (a) all the shots hit the target, (b) at least one of the shots hits the target. [ marks]

15 5 Answer : (a). (b). 5. X is a random variable of a normal distribution with a mean of 75 and a standard deviation of. (a) Find the Z-score if X is 70. (b) P(7 X 79). [ marks] Answer : (a). (b). END OF QUESTION PAPER

16 6 PERATURAN PEMARKAHAN EXCEL PAPER NO. SOLUTION AND MARK SCHEME SUB MARK TOTAL MARK. (a) many to one (b) f : x x or f ( x) x. P =.. B : 7() + = 5p + a =, b [both] B : b or, b a a x B : g ( x) b x or g( x) a a (a) x, (both) B : (x )( x ) 0 or (b) p = 6 B : p ()(9) 0 5 < x < or > x > ()( ) () B : B : (x + ) (x ) < 0 6 p =, q = (both) B : ( x ) + B : ( x x + 5 ) 7 or 7 or.5 B : + 8 y = B: log a p + log a q log a a B : y ( y ) y or y = y y B : or equivalent ( y) y

17 9 8, 5,, 9, 6 7 B: a = 8 0 (a) p = 8 B : ( p )( p ) ( p ) or equivalent (b) 8 B : S 8 = 8 [ () + 7 ( 7) ] or equivalent B : 6 ( ) or equivalent B : r = q =, p = ( both) B : = 5 q or p = ( ) + 5 B : 5 B : y = x + 5 x m 5 = B : gradient = m, gradient = 5 (both) h = 5 8, h = (both) B : 5h + h 8 = 0 5 B : h h h h 8 OR (5h ) h h ( 5 a + b ) B : PH (0 a 6 b ) B : PT 0a 6b or equivalent

18 6 (a) 5 or i + 5 j 8 B : or i + j ( i j ) (b) ( i + j ) or or equivalent B : Or 8 Or 7.8, 8.9 B : sin =, sin = ( both) B : ( sin ) ( sin +) = 0 B : ( sin ) = 8 sin 5 8 p = p B : ( ) 9 s = 0.6 cm B : s = (5.59) rad B : major AOB = ( 8 9 ) rad or 5.59 rad B : 9 = ( ) 0 p = B : x = 0 or p + 8 = 0 dy B : [ ( x ) ( ) + ] or x 8 dx (a) 6 (b) p = 6 p() B : ( ) 6 8 or equivalent px B : (a) mean = (b) B: (5) or equivalent

19 (a) 0 B : 7 C x 6 C 5 9 (b) B : 7 C 7 x 6 C + 7 C 6 x 6 C (a) B : 6 C 6 ( 0.75) 6 (0.5) 0 or equivalent (b) B : P( x = 0) 5 (a) Z = B : or equivalent (b) B : P(x ) P( x.) or equivalent

3472/1 Name :.. Matematik Tambahan

3472/1 Name :.. Matematik Tambahan 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