Koleksi Soalan Spm Add Maths Form 4 p1

8/22/2019 Koleksi Soalan Spm Add Maths Form 4 p1

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KOLEKSI SOALAN SPM

KERTAS 1

NAMA

...........................................................................................


2/15

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]


3/15


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]


4/15


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


5/15


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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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


7/15


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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[ -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]


9/15


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]


10/15


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]


11/15


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]


12/15


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 )


13/15


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 }


14/15


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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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}

Koleksi Soalan Spm Add Maths Form 4 p1

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