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8/22/2019 Koleksi Soalan Spm Add Maths Form 4 p1
1/15
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KOLEKSI SOALAN SPM
KERTAS 1
NAMA
...........................................................................................
8/22/2019 Koleksi Soalan Spm Add Maths Form 4 p1
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Koleksi Soalan Peperiksaan Sebenar SPM (Matematik Tambahan Kertas 1)
TOPIC: FUNCTION
1.SPM 2007P1Q1
2.SPM 2007 P1 Q2
Given that f : x 3x , 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 h2.
4. SPM 2003 P1 Q1
5.SPM 2003 P1 Q2
Given that g : x 5x+1 and h : x x2 -2x+3. find
(a) g-1 (3)(b) hg (x) [4 marks]
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]
h : x ax+b, where a and b are
constants, and a >0
h2
: x 36x -35
Find the value of a and b [3marks]
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]
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Koleksi Soalan Peperiksaan Sebenar SPM (Matematik Tambahan Kertas 1)
6. SPM 2004 P1Q1
7.SPM 2004 P1 Q2
Given that the functions h : x 4x+m and h-1
: x 2kx +5
8, where m and k are constants, find the
value of m and of k. [3marks]
8.SPM 2004 P1 Q3
Given that function h: x6
, 0xx
and the composite function hg(x) =3x, find
(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
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]
State
(a) the range of the relation(b) the type of the relation [2 marks]
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Koleksi Soalan Peperiksaan Sebenar SPM (Matematik Tambahan Kertas 1)
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. [3 marks]
11.SPM 2004 P1 Q 3
Given that function h(x) = 0,6
xx
and the composite function hg9x) =3x, find
(a) g(x)(b) the value of x when gh(x) =5 [4 marks]
12.SPM 2008 P1 Q 1
Diagram below shows the graph of function f(x) = 2 1x , for the domain 0 5x
State
(a)
the value of t(b) the range of f(x) corresponding to the given domain. [3marks][ , 0 ( ) 9f x ]
13. SPM 2008 P1 Q2
Given that functions g:x 5x+2 and h:x x2
- 4x + 3, find
(a) g-1(6)(b) hg(x)[ 4/5, 25x2 -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 [3 marks][ 4, 3 ]
0 t 5
1
y
x
8/22/2019 Koleksi Soalan Spm Add Maths Form 4 p1
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Koleksi Soalan Peperiksaan Sebenar SPM (Matematik Tambahan Kertas 1)
TOPIC : QUADRATIC EQUATIONS
1.SPM 2003 P1 Q3
Solve the quadratic equation 2x(x-4) =(1-x)(x+2). Give your answer correct to four significant figures.
(ans: 2.591, -0.2573) [3 marks]
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 marks]
3.SPM 2004 P1Q4
From the quadratic which has the roots -3 and . Give your answer in the form ax2 +bx+c=0, where a, b
and c are constants. (ans:2x2
+5x-3=0) [2 marks]
4.SPM 2005 P1Q4
The straight line y = 5x-1 does not intersect the curve y=2x2 +x+p. Find the range of values of p.
[3 marks] (ans: p4+x. (ans:x1) [2 marks]
8.SPM 2004 P1Q5
Find the range of values of x for which x(x-4) 12 . [3 marks]
(ans: -2 6)x
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Koleksi Soalan Peperiksaan Sebenar SPM (Matematik Tambahan Kertas 1)
9.SPM 2007P1Q4
(a) Solve the following quadratic equation : 3x2
+5x -2 =0
(b) The quadratic equation hx2 +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 2x2 1+x. [3 marks]
11. SPM 2008 P1Q4
It is given that -1 is one of the roots of the quadratic equation x2-4x-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
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Koleksi Soalan Peperiksaan Sebenar SPM (Matematik Tambahan Kertas 1)
TOPIC : QUADRATIC FUNCTIONS
1.SPM 2003 P2 Q2
The function f(x) = x2 -4kx+5k2 +1 has a minimum value of r2 +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= r2
-1 [4marks]
[k =3,r = -1]
2.SPM 2004 P1Q6
3. SPM 2005 P1 Q6
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. [3marks]
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.
[3marks]
[ k = 1, x =1, (1, -2) ]
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Koleksi Soalan Peperiksaan Sebenar SPM (Matematik Tambahan Kertas 1)
[ -1, 2, x = 1 ]
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. [3marks]
[ x=3, f(x) = (x-3)2
-4 ]
5. .SPM 2007 P1 Q6
The quadratic function f(x) = x2 +2x-4 can be express in the formf(x) =(x+m)2- n, where m and n are
constants. Find the value of m and n. [3marks]
[ 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 [ 3marks][ ans p>0, -3, -4]
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Koleksi Soalan Peperiksaan Sebenar SPM (Matematik Tambahan Kertas 1)
TOPIC : CIRCULAR MEASURES
1.SPM 2003P1Q19
2.SPM 2004 P1 Q19
3. SPM 2005 P1Q18
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. [3 marks]
(ans:0.8153]
Given that length of the major arc AB is 45.51 cm,
find the length , in cm, of the radius.
(use 3.142 ) [3 marks]
(Ans:7.675]
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. [3 marks]
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Koleksi Soalan Peperiksaan Sebenar SPM (Matematik Tambahan Kertas 1)
4.SPM 2006 P1Q16
5. SPM 2007 P1 Q18
6. SPM 2008 P1 Q18
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 cm2, of the shaded region. [4 marks]
ans: 0.7 rad, 26.2
Diagram shows a sector BOC of a circle with centre O.
1.85BOC rad
It is given that AD =8 cm and BA=AO=OD=DC=5 cm.
Find
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
=900, find
(a) QOR, in radians
(b) the area, in cm2, of the coloured region. [4marks]
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Koleksi Soalan Peperiksaan Sebenar SPM (Matematik Tambahan Kertas 1)
TOPIC: INDICES AND LOGARITHMS
1. SPM 2003P1Q5Given that
2 4log log 3T V , express T in terms of V. [4marks]
( ans: T= 8 V )
2.SPM 2003P1Q6
Solve the equation 2 14 7x x [4 marks]
(ans:1.677)
3.SPM 2004 P1Q7
Solve the equation 4 8 632 4x x [3 marks]
(ans: 3)
4.SPM 2004 P1Q8
Given that 5 5log 2 , log 7 ,m and p express log 5 4.9 in terms of ma and p.
(ans:2p-m-1) [4 marks]
5.SPM 2005 P1Q7
Solve the equation4 32 2 1x x [3 marks]
(ans:x = -3)
6.SPM 2005 P1Q8
Solve the equation 3 3log 4 log (2 1) 1x x [3 marks]
(ans: 3/2)
7.SPM 2005 P1Q9
Given that27
log 2 , log 3 , exp log ( )4
m m m
mp and r ress in terms of p and r.
(ans:3r-2p+1) [4 marks]
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Koleksi Soalan Peperiksaan Sebenar SPM (Matematik Tambahan Kertas 1)
8.SPM 2006 P1Q6
Solve the equation 2 32
18
4
x
x
(ans:1) [3 marks]
9.SPM 2006 P1Q7
Given that 2 2 2log 2 3log log ,xy x y express y in terms of x. [3marks]
(ans:y = 4x)
10.SPM 2006 P1Q8
Solve the equation 2+ log 3 (x-1) =log 3 x (ans:9/8) [3marks]
11. SPM 2007P1 Q7
Given that log2 b = x and log2 c= y, express log48b
c
in terms of x and y. [4marks]
[ 3/2 + x/2y/2 ]
12.SPM 2007 P1Q8
Given that 9(3n-1) = 27n, find the value of n. [3marks]
[1/2]
13. SPM 2008 P1 Q7
Solve the equation: 162x-3
= 84x
[ 3marks]
(ans: -3 )
14. SPM 2008 P1 Q8
Given that log4 x = log2 3, find the value of x [3marks]
( ans: 9 )
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Koleksi Soalan Peperiksaan Sebenar SPM (Matematik Tambahan Kertas 1)
TOPIC: STATISTICS
1.SPM2007 P1 Q22
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 [3 marks]
(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. [3marks]
{ ans : 63, 5 }
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Koleksi Soalan Peperiksaan Sebenar SPM (Matematik Tambahan Kertas 1)
TOPIC: DIFFERENTIATION
1.SPM 2003 P1Q16
Given that y = x2 +5x, use differentiation to find the small change in y when x increases from 3 to 3.01.
[Ans:0.11] [3marks]
2.SPM 2004 P1Q20
Differentiate 3x2(2x-5)
4with respect to x [3marks]
[ 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 [3marks]
[Ans: 8/5]
4. SPM 2005 P1Q19
Given that h(x) =2
1
(3 5)x , evaluate h (1) [4marks]
[ 27/8]
5.SPM 2005 P1Q20
The volume of water, V cm3, in a container is given by
31 8 ,3
V h h where h cm is the height of the
water in the container. Water is poured into the container at the rate of 10 cm3s
-1. Find the rate of
change of the height of water, in cm s-1-, at the instant when its height is 2 cm. [3 marks]
[ 0.8333]
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. [3 marks]
[ (7,4)]
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Koleksi Soalan Peperiksaan Sebenar SPM (Matematik Tambahan Kertas 1)
7.SPM 2006 P1 Q18
It is given that y= 72
3u , where u=3x-5. Find
dy
dxin terms of x. [4marks]
[ 14(3x-5)6 ]
8. SPM 2007 P1 Q19
The curve y = f(x) is such that 3 5dy
kxdx
, where k is a constant. The gradient of the curve at x =2
is 9. Find the value of k [2 marks]
[ 2/3]
9.SPM 2007 P1 Q 20
The curve y = x2
-32x+64 has a minimum point at x = p, where p is a constant. Find the value of p.
[3marks]
[ Ans: 16]
10.SPM 2008 P1 Q19
Two variables, x and y , are related by the equation2
16y
x . Express, in terms of h, the approximate
change in y, when x changes from 4 to 4+h, where h is a small value. [3marks]
( ans :1
2h )
11. SPM 2008 P1 Q20
The normal to the curve y=x2 -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}