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2 1. SPM 2007P1Q1 TOPIC: FUNCTION Diagram shows the linear function h (a) state the value of m (b) (b) by using the function notation, express h in terms of x [ 2marks] 2.SPM 2007 P1 Q2 Given that f : x x 3, find the values of a such that f(x) =5. [2marks] 3. SPM 2007 P1 Q3 The following information is about the function h and the composite function h 2. h : x ax+b, where a and b are constants, and a >0 h 2 : x 36x -35 Find the value of a and b 4. SPM 2003 P1 Q1 P= { 1, 2, 3 } Q = { 2, 4,6, 8,10 } Based on the above information, the relation between P and Q is defined by the set of ordered pairs {(1,2),(1,4),(2,6),(2,8) State (a) the image of 1 (b) the object of 2 [2marks] 5.SPM 2003 P1 Q2 Given that g : x 5x+1 and h : x x 2-2x+3. find (a) g -1 (3) (b) hg (x)

3 6. SPM 2004 P1Q1 Diagram shows the relation between set P and set Q. State (a) the range of the relation (b) (b) the type of the relation [2 marks] 7.SPM 2004 P1 Q2 Given that the functions h : x 4x+m and h -1 : x 2kx + 5, where m and k are constants, find the 8 value of m and of k. 8.SPM 2004 P1 Q3 Given that function h: x 6, x 0and the composite function hg(x) =3x, find x (a) g(x) (b) the value of x when gh(x) =5 [4marks] 9.SPM 2005 P1 Q1 Diagram below shows the relation between set P and set Q State (a) the range of the relation (b) the type of the relation [2 marks]

4 10. SPM 2004 P1 Q2 Given that the function h:x 4x+m and h -1 : x 2kx + 8 5, where m and k are constants, find the value of m and of k. 11.SPM 2004 P1 Q 3 6 Given that function h(x) =, x 0 and the composite function hg9x) =3x, find x (a) g(x) (b) the value of x when gh(x) =5 12.SPM 2008 P1 Q 1 Diagram below shows the graph of function f(x) = 2x 1, for the domain 0 x 5 y 1 0 t 5 x State (a) the value of t (b) the range of f(x) corresponding to the given domain. [ ½, 0 f( x) 9 ] 13. SPM 2008 P1 Q2 Given that functions g:x 5x+2 and h:x x 2-4x + 3, find (a) g -1 (6) (b) hg(x) [ 4/5, 25x 2-1] 14. SPM 2008 P1 Q3 Given the functions f(x) = x-1 and g(x) = kx+2, find (a) f(5) (b) the value of k such that gf(5) =14 [ 4, 3 ]

5 1.SPM 2003 P1 Q3 TOPIC : QUADRATIC EQUATIONS Solve the quadratic equation 2x(x-4) =(1-x)(x+2). Give your answer correct to four significant figures. (ans: 2.591, ) 2.SPM 2003 P1Q4 The quadratic equation x(x+1) = px-4 has two distinct roots. Find the range of values of p. (ans: 5, -3) 3.SPM 2004 P1Q4 From the quadratic which has the roots -3 and ½. Give your answer in the form ax 2 +bx+c=0, where a, b and c are constants. (ans:2x 2 +5x-3=0) [2 marks] 4.SPM 2005 P1Q4 The straight line y = 5x-1 does not intersect the curve y=2x 2 +x+p. Find the range of values of p. (ans: p<1) 5.SPM 2005 P1 Q5 Solve the quadratic equation x(2x-5) =2x-1. Give your answer correct to three decimal places. (ans: 8.153, 0.149) 6.SPM 2006 P1Q3 A quadratic equation x 2 +px+9 =2x has two equal roots. Find the possible values of p. (ans: 8, -4) 7. SPM2006 P1Q5 Find the range of the values of x for (2x-1)(x+4)>4+x. (ans:x<-4,x>1) [2 marks] 8.SPM 2004 P1Q5 Find the range of values of x for which x(x-4) 12. (ans: -2 x 6)

6 9.SPM 2007P1Q4 (a) Solve the following quadratic equation : 3x 2 +5x -2 =0 (b) The quadratic equation hx 2 +kx+3 =0, where h and k are constants, has two equal roots, express h in terms of k. [4marks] 10. SPM 2007 P1 Q5 Find the range of values of x for which 2x 2 1+x. 11. SPM 2008 P1Q4 It is given that -1 is one of the roots of the quadratic equation x 2-4x-p=0. Find the value of p. [ ans 5] [2marks] 7. SPM 2008 P1Q6 Find the range of values of x for (x-3) 2 < 5-x [ 3marks] [ ans 1<x<4]

7 1.SPM 2003 P2 Q2 TOPIC : QUADRATIC FUNCTIONS The function f(x) = x 2-4kx+5k 2 +1 has a minimum value of r 2 +2k, where k are constants. (a) By using the method of completing the square, show that r =k -1 [4marks] (b) Hence, or otherwise, find the values of k and r if the graph of the function is symmetrical about x= r 2-1 [4marks] [k =3,r = -1] 2.SPM 2004 P1Q6 Diagram shows the graph of the function y = - ( x- k ) 2 2, where k is a constant. Find (a) the value of k (b) the equation of the axis of symmetry (c) the coordinates of the maximum point. 3. SPM 2005 P1 Q6 [ k = 1, x =1, (1, -2) ] Diagram below shows the graph of a quadratic function f(x) = 3 (x+p) 2 +2, where p is a constant. The curve y=f(x) has the minimum point (1,q), where q is a constant. State (a) the value of p. (b) the value of q (c) the equation of the axis of symmetry. [ -1, 2, x = 1 ]

8 4. SPM 2006 P1 Q4 Diagram below shows the graph of a quadratic function y = f(x). The straight line y = -4 is a tangent to the curve y = f(x) (a) Write the equation of the axis of symmetry of the curve. (b) Express f(x) in the form of (x+b) 2 +c, where b and c are constants. [ x=3, f(x) = (x-3) 2-4 ] 5..SPM 2007 P1 Q6 The quadratic function f(x) = x 2 +2x-4 can be express in the form f(x) = (x+m) 2 - n, where m and n are constants. Find the value of m and n. [ ans : 1, 5] 6. SPM 2008 P1 Q5 The quadratic function f(x) = p(x+q) 2 +r, where p,q and r are constants, has a minimum value of -4. The equation of the axis of symmetry is x=3. State (a) the range of value of p (b) the value of q (c) the value of r [ ans p>0, -3, -4] [ 3marks]

9 TOPIC : CIRCULAR MEASURES 1.SPM 2003P1Q19 The length of the arc RS is 7.24 cm and the perimeter of the sector ROS is 25 cm. Find the value of, in rad. (ans:0.8153] 2.SPM 2004 P1 Q19 Given that length of the major arc AB is cm, find the length, in cm, of the radius. (use ) (Ans:7.675] 3. SPM 2005 P1Q18 The length of the minor arc AB is 16 cm and the angle of the major sector AOB is 290. Using =3.142, find (a) the value of, in radians, (b) the length, in cm, of the radius of the circle. (ans: 1.222, 13.09]

10 4.SPM 2006 P1Q16 Diagram shows sector OAB with centre O and sector AXY with centre A. Given that OB=10 cm,ay=4 cm, XAY=1.1 radians and the length of arc AB= 7 cm, calculate (a) the value of in radian. (b) The area, in cm 2, of the shaded region. (ans: 0.7 rad, 26.2] 5. SPM 2007 P1 Q18 Diagram shows a sector BOC of a circle with centre O. BOC 1.85rad It is given that AD =8 cm and BA=AO=OD=DC=5 cm. Find (a) the length, in cm, of the arc BC (b) the area, in cm 2, of the shaded region [4marks] 6. SPM 2008 P1 Q18 Diagram beside shows a circle with centre O and radius 10 cm. Given that P, Q and R are points such that OP=PQ and OPR =90 0, find (a) QOR, in radians (b) the area, in cm 2, of the coloured region. [4marks] Ues =3.142 ( /3, 30.7)

11 TOPIC: INDICES AND LOGARITHMS 1. SPM 2003P1Q5 Given that log 2T log 4V 3, express T in terms of V. ( ans: T= 8 V ) 2.SPM 2003P1Q6 Solve the equation 2x 1 x 4 7 (ans:1.677) 3.SPM 2004 P1Q7 4x Solve the equation 32 8x6 4 (ans: 3) 4.SPM 2004 P1Q8 Given that log52 m, and log57 p, express log in terms of ma and p. (ans:2p-m-1) 5.SPM 2005 P1Q7 Solve the equation x4 x (ans:x = -3) 6.SPM 2005 P1Q8 Solve the equation log34x log 3(2x 1) 1 (ans: 3/2) 7.SPM 2005 P1Q9 27m Given that log m 2 p, and log m 3 r, exp ress log m ( ) in terms of p and r. 4 (ans:3r-2p+1)

12 8.SPM 2006 P1Q6 Solve the equation 8 2x 3 1 x 2 4 (ans:1) 9.SPM 2006 P1Q7 Given that log 2 xy 2 3log 2 x log 2 y, express y in terms of x. (ans:y = 4x) 10.SPM 2006 P1Q8 Solve the equation 2+ log 3 (x-1) =log 3 x (ans:9/8) 11. SPM 2007P1 Q7 Given that log 2 b = x and log 2 c= y, express log 4 [ 3/2 + x/2 y/2 ] 12.SPM 2007 P1Q8 Given that 9(3 n-1 ) = 27 n, find the value of n. [1/2] 13. SPM 2008 P1 Q7 Solve the equation: 16 2x-3 = 8 4x (ans: -3 ) 14. SPM 2008 P1 Q8 Given that log 4 x = log 2 3, find the value of x ( ans: 9 ) 8b c in terms of x and y. [4marks] [ 3marks]

13 1.SPM2007 P1 Q22 TOPIC: STATISTICS A set of data consists of five numbers. The sum of the numbers is 60 and the sum of the squares of the numbers is 800. Find, for the five number (a) the mean (b) the standard deviation (ans : 12, 4) 2. SPM 2008 P1Q22 A set of seven numbers has a mean of 9. (a) Find x (b) when a number k is added to this set, the new mean is 8.5. find the value of k. { ans : 63, 5 }

14 1.SPM 2003 P1Q16 TOPIC: DIFFERENTIATION Given that y = x 2 +5x, use differentiation to find the small change in y when x increases from 3 to [Ans:0.11] 2.SPM 2004 P1Q20 Differentiate 3x 2 (2x-5) 4 with respect to x [ 6x(6x-5)(2x-5) 3 ] 3.SPM 2004 P1Q21 Two variables, x and y are related by the equation y = 3x+ 2 x. Given that y increases at a constant rate of 4 units per second, find the rate of change of x when x=2 [Ans: 8/5] 4. SPM 2005 P1Q19 1 Given that h(x) = 2 (3x 5), evaluate h (1) [4marks] [ 27/8] 5.SPM 2005 P1Q20 1 The volume of water, V cm 3 3, in a container is given by V h 8 h, where h cm is the height of the 3 water in the container. Water is poured into the container at the rate of 10 cm 3 s -1. Find the rate of change of the height of water, in cm s -1-, at the instant when its height is 2 cm. [ ] 6.SPM 2006 P1Q17 The point P lies on the curve y=(x-5) 2. It is given that gradient of the normal at P is -1/4. Find the coordinates of P. [ (7,4)]

15 7.SPM 2006 P1 Q18 It is given that y= [ 14(3x-5) 6 ] SPM 2007 P1 Q19 7 dy u, where u=3x-5. Find dx in terms of x. [4marks] dy The curve y = f(x) is such that 3kx 5, where k is a constant. The gradient of the curve at x =2 dx is 9. Find the value of k [2 marks] [ 2/3] 9.SPM 2007 P1 Q 20 The curve y = x 2-32x+64 has a minimum point at x = p, where p is a constant. Find the value of p. [ Ans: 16] 10.SPM 2008 P1 Q19 16 Two variables, x and y, are related by the equation y. Express, in terms of h, the approximate 2 x change in y, when x changes from 4 to 4+h, where h is a small value. ( ans : 1 2 h ) 11. SPM 2008 P1 Q20 The normal to the curve y=x 2-5x at point P is parallel to the straight line y = -x+12. find the equation of the normal to the curve at point P. [4marks] { ans : y = -x-3}

16 1.SPM 2003 P1Q7 TOPIC: PROGRESSIONS The first three terms of an arithmetic progression are k-3, k+3, 2k+2. Find a) the value of k b) the sum of the first 9 terms of the progression. [ans: 7, 252] 2.SPM 2003 P1Q8 In a geometric progression, the first term is 64 and the fourth term is 27. calculate (a) the common ration, (b) the sum to infinity of the geometric progression. [ans: ¾, 256] 3.SPM 2004 P1Q9 Given a geometric progression y,2, 4 y,p, express p in terms of y. [2 marks] [ans: p= 8/y 2 ] 4.SPM 2004 P1 Q 10 Given an arithmetic progression -7, -3, 1,, state three consecutive terms in this progression which sum up to 75. [ans: 29, 25, 21 ] 5. SPM 2004 P1 Q 11 The volume of water in a tank is 450 litres on the first day. Subsequently, 10 litres of water is added to the tank everyday. Calculate the volume, in litres. Of water in the tank at the end of the 7 th day. [ans : 510] 6.SPM 2004 P1Q12 [2 marks] Express the recurring decimal as a fraction in its simplest form. [ans : 32/33]

17 7.SPM 2005 P1 Q 10 The first three terms of a sequence are 2, x, 8. Find the positive value of x so that the sequence is (a) an arithmetic progression (b) a geometric progression. [ans:5,4] [2 marks] 8. SPM 2005 P1 Q 11 The first three terms of an arithmetic progression are 5, 9, 13. Find (a) the common difference of the progression, (b) the sum of the first 20 terms after the 3 rd term. [ans:4, 1100] 9.SPM 2005 P1 Q 12 The sum of the first n terms of the geometric progression 8, 24, 72, is Find (a) the common ration of the progression (b) the value of n [ans: 3, 7 ] 10.SPM 2006 P1 Q9 The 9 th term of an arithmetic progression is 4+5p and the sum of the four terms of the progression is 7p- 10, where p is a constant. Given that common difference of the progression is 5, find the value of p. [ans: 8] 11.SPM 2006 P1 Q 10 The third term of a geometric progression is 16. The sum of the third term and the fourth term is 8. Find (a) the first term and the common ratio of the progression. (b) The sum to infinity of the progression. [ans: 64, 42 2/3 ] 12.SPM 2007 P1 Q9 (a) determine whether the following sequence is an arithmetic progression or a geometric progression. (b) Give a reason for the answer in part (a) [2 marks] Answer :GP, the ratio of two consecutive terms of the sequence is a constant

18 13.SPM 2007 P1 Q10 Three consecutive terms of an arithmetic progression are 5-x, 8, 2x. Find the common difference of the progression. Answer : SPM 2007 P1 Q 11 The first three terms of a geometric progression are 27, 18,12. Find the sum to infinity of the geometric progression. Answer : SPM 2008 P1 Q9 It is given that the first four terms of a geometric progression are 3, -6, 12 and x. Find the value of x. [2marks] [ ans -24 ] 16. SPM 2008 P1 Q10 The first three terms of an arithmetic progression are 46, 43 and 40. the nth term of this progression is negative. Find the least value of n. [ans 17] 17. SPM 2008 P1 Q 11 In a geometric progression, the first term is 4 and the common ratio is r. Given that the sum to infinity of this progression is 16, find the value of r. [2marks] [ ans : ¾]

19 1. SPM 2003 Paper 1 Q10 TOPIC: LINEAR LAW x and y are related by the equation y = px 2 + qx, where p and q are constants. A straight line is obtained by plotting y/x against x as shown in the diagram below. Calculate the values of p and q [4marks] Solution: Step 1: Change non linear equation y p( x) q x :, Step 2: Find the gradient, p = y px qx to linear equation Step 3: Find the y intercept, substitute any one point which the line passes through, Exercises: (6,1) 1=-2(6) +q, q=13 1.SPM 2004 P1Q13 Diagram below shows a straight line graph against x. Given that y=6x-x 2, calculate the value of k and of h. {ans:h=3, k=4}

20 2. SPM 2005 P1 Q SPM 2006P1 Q11 The variables x and y are related by the equation y=kx 4, where k is a constant. (a) convert the equation y=kx 4 to linear form. (b) Diagram shows the straight line obtained by plotting log 10 y against log 10 x. Find the value of (i) log 10 k (ii) h {ans:1000,11} The first diagram shows the curve y = 3x The second graph shows the straight line graph obtained when y = -3 x 2 +5 is expresses in the linear form Y= 5X+c. Express X and Y in terms of a and/or y (ans:x=9/25 x 2, Y=-3/5 y) 4. SPM 2007 P1 Q12 The variables x and y are related by the equation y 2 =2x(10-x). A straight line graph is obtained by plotting against x y x 2 Find the value of p and of q

21 5.SPM 2008 P1 Q11 k The variables x and y are related by the equation y, where k is a constant. Diagram below shows 5 x the straight line graph obtained by plotting log 10 y against x. log 10 y 0 x (0, -2) k (a) Express the equation y in its linear form used to obtained the straight line graph shown in 5 x the diagram above. (b) Find the value of k [ 4marks] [ ans log y = -x log 5 + log k, 0.01 ]

22 1.SPM 2003 P1Q18 TOPIC: INTERGRATION Diagram shows the curve y=3x 2 and the straight line x=k. If the area of the shaded region is 64 unit 2, find the value of k. [ans: 4] 2.SPM 2004 P1Q22 Given that k (2x 3) dx 6, where k>-1, find the value of k. 1 [ANS: 5] 3.SPM 2005 P1Q 21 Given that 6 6 f ( x ) dx 7 and (2 f ( x ) kx ) dx 10, find the value of k. 2 2 [ 4 marks] 4.SPM 2005 P1Q 21 Given that 6 6 f ( x ) dx 7 and (2 f ( x ) kx ) dx 10, find the value of k. 2 2 [ ANS: ¼] [ 4 marks] 5.SPM 2008 P1 Q Given that (6x 1) dx px x c, where p and c are constants, find (a) the value of p, 2 (b) the value of c if (6x 1) dx 13 where x =1. {ans : 2, 10}

23 6. SPM 2006 P1Q 20 Given that the area of the shaded region is 5 unit 2, find the value of 2 2 f ( x ) dx b a [2 marks] [ -10] 7.SPM 2006 P1 Q21 Given that 5 1 g ( x ) dx 8, find (a) the value of 1 5 g ( x ) dx 5 (b) the value of k if [ kx g ( x )] dx 10 [ -8, 3/2] 8.SPM 2007 P1Q21 1 Given that 7 2 h( x ) dx 3, find (a) (b) h( x ) dx [5 h( x )] dx [ -3, 22]

24 1. SPM 2003 P1 Q12 TOPIC: VECTORS Diagram shows two vectors, OP andqo. Express x (a) OP in the form y (b) OQ in the form xi yj [2marks] 2.SPM2003 P1Q13 p = 2a +3 b q = 4 a b r = ha + (h-k) b, where h and k are (ans constants : -13) ( 5, -8i+4j) 3 Use the information given to find the values of h and k when r = 3p -2q 3. SPM 2003 P1 Q 14 Diagram shows a parallelogram ABCD with BED as a straight line. Given that AB 6 p, AD 4q and DE =2EB, express in terms of p and q (ans: -6p+4q, 2p+ 8q/3} (a) BD ( b) EC [4marks] 4 SPM 2004 P1 Q16 Given that O(0,0) A(-3,4) and B(2,16), find in terms of unit vectors, i and j, (a) AB (b) the unit vector in the direction of AB [4marks] (ans :, )

25 5 SPM 2004 P1 Q17 Given that A(-2,6), B(4,2) and C(m,p), find the value of m and of p such that AB 2BC 10i 12 j (ans : m=6, p=-2 ) 6 SPM 2005 P1Q15 [4marks] Diagram shows vector OA drawn on a Cartesian plane. x (a) Express OA in the form y (b) Find the unit vector in the direction of OA [2marks] (ans :, ) SPM 2005 P1 Q 16 Diagram shows a parallelogram, OPQR, drawn on a Cartesian plane. It is given that OP 6i 4j and PQ 4i 5j Find PR (ans : -10i+j) 8. SPM 2006 P1 Q 13 Diagram shows two vectors, OA and AB Express x (a) OA in the form y (b) AB in the form xi yj [2marks] 4 (ans :, 3-4i-8j )

26 9. SPM 2006 P1 Q 14 The point P,Q, and R are collinear. It is given that PQ 4a 2b and QR 3 a (1 k ) b, where k is a constant. Find (a) the value of k, (b) the ration of PQ : QR (ans : -5/2, 4:3 ] [4marks] 10.SPM 2007 P1 Q16 The following information refers to the vectors a and b 2 1 a, b, find 8 4 (a) the vector 2a b, (b) the unit vector in the direction of 2a b (a) (b) SPM 2007 P1 Q x 4 4 y 12.SPM 2008 P1 Q15 The vectors a and b are non zero and non parallel. It is given that (h+3) a = (k-5) b, where h and k are constants. Find the value of (a) h Diagram shows a rectangle OABC and the point D lies on the straight line OB. It is given that OD=3DB. Express OD, in terms of x and y (b) k [2marks] [ans ; -3, 5

27 13. SPM 2008 P1 Q16 Diagram below shows a triangle PQR Q 6 b T P 4 a R The point T lies on QR such that QT: TR =3:1 Express in terms of a and b : (a) QR (b) PT [4marks] [ans: 4a-6b, 3a+3b/2 ]

28 1.SPM 2007 P1 Q 17 TOPIC: TRIGONOMETRIC FUNCTIONS.Solve the equation cot x + 2 cos x =0 for 0 x 360 [ 90, 210, 270,330] 2.SPM 2003 P1 Q20 Given that tan = t, o 90, express, in terms of t : (a) cot (b) sin ( 90 - ) [ 3marks] [ans : 1/t, 1/ 2 t 1 ] 3. SPM 2003 P1Q21 Solve the equation 6 sec 2 A -13 tan A =0, [ans : 33.69, , 56.31, ] 4. SPM 2003P2Q8(a) Prove that tan + cot = 2 cosec 2 5. SPM 2004 P1 Q18 Solve the equation cos 2 x sin 2 x = sin x for [ans : 30,150,270] 6.SPM 2005 P1 Q17 Solve the equation 3 cos 2x = 8 sin x -5 for 0 x 360 [ ans : 41.81, ]

29 7. SPM 2006 P1Q 15 Solve the equation 15 sin 2 x = sin x +4sin 30 for 0 x 360 [ ans : 23 35, , , ] 8. SPM 2008 P1 Q17 Given that sin p, where p is a constant and Find in terms of p (a) cosec (b) sin 2 [ 3 marks] 2 (ans; 1/p, -2p 1 p ) 9. SPM 2008 P1 Q4 2 tan x Prove that tan 2x 2 2 sec x [2 marks]

30 1. SPM 2007 P1 Q23 TOPIC: PERMUTATION AND COMBINATION A coach wants to choose 5 players consisting of 2 boys and 3 girls to form a badminton team. These 5 players are chosen from a group of 4 boys and 5 girls. Find (a) the number of ways the team can be formed, (b) the number of ways the team members can be arranged in a row for a group photograph. If the three girls sit next to each other. [ 60, 36] 2.SPM 2003 P1 Q22 A B C D E Diagram above 5 letters and 3 digits. A code is to be formed using those letters and digits. The code must consists of 3 letters followed by 2 digits. How many codes can be formed if no letter or digit is repeated in each code. [360] 3. SPM 2003 P1 Q23 A badminton team consists of 7 students. The team will be chosen from a group of 8 boys and 5 girls. Find the number of teams that can be formed such that each team consists of (a) 4 boys (b) not more than 2 girls. [4marks] (answers : 700, 708) 4.SPM 2004 P1 Q 23 Diagram below shows 5 cards of different letters. H E B A T (a) Find the number of possible arrangements, in a row, of all the cards. [120] (b) Find the number of these arrangement in which the letter E and A are side by Side. [48] 5. SPM 2004 P1 Q 24 A box contains 6 white marbles and k black marbles. If a marble is picked randomly from the box, the probability of getting a black marble is 3/5. Find the value of k [9].

31 6. SPM 2005 P1 Q 22 A debating team consists of 5 students. These 5 students are chosen from 4 monitors, 2 assistant monitors and 6 prefects. Calculate the number of different ways the team can be formed if (a) there is no restriction (b) the team contains only 1 monitor and exactly 3 prefects. [4marks] [ 792, 160] 7.SPM 2005 P1 Q 24 Table shows the number of coloured cards in a box. Two cards are drawn at random from the box. Find the probability that both cards are of the same colour Colour Number of cards Black 5 Blue 4 Yellow 3 8. SPM 2006 P1 Q 22 [ 19/66] U N I F O R M Diagram shows seven letter cards.a four letter code is to be formed using four of these cards. Find (a) the number of different four-letter codes that can be formed. (b) the number of different four-letter codes which end with a consonant. [ 840, 480 ] 9.SPM 2006 P1 Q 23 [4marks] The probability that Hamid qualifies for the final of a track event is 2/5 while the probability that Mohan qualifies is 1/3. Find the probability that (a) both of them qualify for the final (b) only one of them qualifies for the final [ 2/15, 7/15 ]

32 10. SPM 2008 P1 Q23 Diagram below shows six numbered cards A four-digit number is to be formed by using four of these cards. How any (a) different numbers can be formed? (b) different odd numbers can be formed? { ans : 360, 240} 11 SPM 2008 P1 Q24 The probability of sarah being chosen as a school prefect is 3 while the probability of Aini being chosen 5 is 7. Find the probability that 12 (a) neither of them is chosen as a school prefect (b) only one of them is chosen as a school prefect. { 1/6, 29/60}

33 1.SPM 2003 P1 Q 24 TOPIC: PROBABILITY DISTRIBUTION Diagram below shows a standard normal distribution graph. F(z) 0 k z If P(0< z < k)=0.3128, find P(z > k) [2 marks] [0.1872] 2.SPM 2003 P1 Q 25 In an examination, 70% of the students passed. If a sample of 8 students is randomly selected, find the probability that 6 students from the sample passed the examination. [0.2965] 3.SPM 2004 P1 Q25 X is a random variable of a normal distribution with a mean of 5.2 and a variance of Find (a) the Z score if X =6.7, (b) P(5.2 X 6.7) [ 1.25, ] 4. SPM 2005 P1 Q 25 the mass of students in a school has a normal distribution with a mean of 54kg and a standard deviation of 12 kg. find (a) the mass of the students which gives a standard score of 0.5 (b) the percentage of student a with mass greater than 48 kg [ 60, ] [4marks]

34 5.SPM 2006P1 Q25 [ 1.03, 82.09] 6. SPM 2007 P1 Q24 The probability that each shot fired by Ramli hits a target is 1/3 (a) If Ramli fires 10 shots, find the probability that exactly 2 shots hit the target. (b) If Ramli fires n shots, the probability that all the n shots hit the target is 1/243. Find the value of n. [ , 5] 7. SPM 2007 P1Q25 X is a continuous random variable of a normal distribution with a mean of 52 and a standard deviation of 10. Find Diagram shows a standard normal distribution graph. The probability represented by the area of the shaded region is (a) Find the value of k (b) X is a continuous random variable which is normally distributed with a mean of 79 and a standard deviation of 3. Find the value of X when the z-score is k [4marks] (a) the z-score when X= 67.2 (b) the value of k when P(z<k) = [ 1.52, 1.2] 8. SPM 2008 P1 Q25 The masses of a group of students in a school have a normal distribution with a mean of 40 kg and a standard deviation of 5 kg. Calculate the probability that a student chosen at random from this group has a mass of (a) more than 45 kg (b) between 35 kg and 47.8 kg {ans : , } [ 4 marks]