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SPM 2011 PAPER 1

1 It is given that the relation between set X{0, 1, 4, 9, 16} and set Y = {0, 1, 2, 3, 4, 5,

6} is square of.(a) Find the image of 9.(b) Express the relation in the form of

ordered pairs.

2 It is given that the functions g(x) = 4x 7and h(x) = 2x. Find the value of gh(2).

[9]

3 The inverse function h-1 is defined by

h- 1 : x 2

3 x, x 3. Find

(a) h(x),(b) the value of x such that h(x) = 5.

[(a) 3 2xx

(b) 14

]

4 The quadratic equation mx2 + (1 + 2m)x +

m 1 = 0 has two equal roots. Find thevalue of m.

[1

8]

5 Diagram shows the graph of the quadratic

function f(x) = (x + 3)2

+ 2k 6, where k isa constant.

(a) State the equation of the axis ofsymmetry of the curve.

(b) Given that the minimum value of thefunction is 4, find the value of k.

[(a) x = 3 (b) 5]

6 Find the range of values of x for 3x2 5x

16 x(2x + 1).

[2 x 8]

7 Solve the equation 23x = 8 + 23x 1

[4

3]

8 Given that log2 x = h and log2 y = k,

express log2

3

xy

in terms of h and k.

[3h k]

9 It is given that x, 5, 8, , 41, is anarithmetic progression.

(a) State the value of x.(b) Write the three consecutive terms after

41.

[(a) 2 (b) 44, 47, 50]

10 The second term of an arithmetic

progression is 3 and the sixth term is 13.Find the first term and the common

difference of the progression.

[a = 7, d = 4]

11 It is given that x2, x4, x6, x8, is ageometric progression such that 0 < x < 1.

The sum to infinity of the progression is1

3.

Find

(a) the common ratio of the progression interms of x.

(b) the value of x.[(a) x

2(b)

1

2]

12 The variables x and y are related by the

equation 3y = (p 1)x +12

x, where p is a

constant. The diagram shows the straight

line QR obtained by plotting xy against x2.

7/28/2019 75911764-SPM-2011-PAPER-1

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Retyped by Mr. Sim Kwang Yaw

(a) Express the equation 3y = (p 1)x +12

xin its linear form, which is used to

obtain the straight line graph in the

diagram.

(b)Given that the gradient of QR is 2,find the value of p and of t.

[(a) xy =21 4

3

px

(b) p = 5, t =

2

3]

13 A straight line2 6

x y = 1 cuts the x-axis at

P and the y-axis at Q. Find

(a) the gradient of the straight line,(b) the equation of the perpendicular

bisector of the straight line.

[(a) 3 (b) 3y = x + 8]

14 Solve the equation sin 2 = cos for 0o 360

o[30o, 90o, 150o, 270o]

15 It is given that tan A =3

4and tan B =

7

24,

where A is an acute angle and B is an reflex

angle. Find(a) cot A(b) sin (A + B)

[(a)

4

3 (b)

4

5 ]

16 The diagram shows a parallelogram ODEFdrawn on a Cartesian plane.

It is given that 3 2OD i j

and

5 3DE i j

. FindDF

.

[ 8i j

]

17 It is given that vector8

2r

and vector

7

hs

, where h is a constant.

(a) Express vector r s in terms of h.(b) Given that r s

= 13 units, find the

possible values of h.

[(a)8

5

h

(b) 4, 20]

18 The diagram shows a sector POQ of a circlewith centre O.

It is given that OR = 8 cm and OP = 10 cm.

[Use = 3.142] Find(a) the value of in radian,(b) the perimeter, in cm, of the shaded

region.

[(a) 0.6435 rad (b) 14.44 cm]

19 Given that y = 25 1x

x and dy

dx= g(x), find

the value of

3

0

2 ( )g x dx .

[3]

20 It is given that y = 10 12

x. Find the small

change in x, in terms of p, when the valueof y changes from 4 to 4 + p.

[3

p]

21 Find

4

( 1)

a

x dx in terms of a

[

2

122

aa ]

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Retyped by Mr. Sim Kwang Yaw

22 A group of 6 students has a total mass of

240 kg. The sum of the squares of theirmass is 9654 kg2. Find(a) the mean mass of the 6 students,(b) the standard deviation.

[(a) 40 kg (b) 3 kg]

23 The diagram shows seven letter cards.

A five-letter code is formed using five of

these cards.

Find(a) the number of different five-letters

codes that can be formed,

(b) the number of different five-letter codeswhich begin with a vowel and end with

a consonant.[(a) 2 520 (b) 600]

24 A sample space of an experiment is given

by S = {1, 2, 3, , 20}. Events M and N

are defined as follows:M : {3, 6, 9, 12, 15, 18}

N : {1, 3, 5, 15}Find(a) P(M)(b) P(M and N)

[(a)3

10(b)

1

10]

25 Diagram 25 shows the graph of a binomialdistribution of X.

Find

(a) P(X 1)(b) the value of m.

[(a)19

27(b)

8

27]

K H I D M A T