Get more SPM Trial paper: http ... Perlis SPM Tria… · Get more SPM Trial paper:
75911764-SPM-2011-PAPER-1
-
Upload
theuniquecollection -
Category
Documents
-
view
222 -
download
0
Transcript of 75911764-SPM-2011-PAPER-1
-
7/28/2019 75911764-SPM-2011-PAPER-1
1/3
Retyped by Mr. Sim Kwang Yaw
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
2/3
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 ]
-
7/28/2019 75911764-SPM-2011-PAPER-1
3/3
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