Revision Form 4 Additional Mathematics

(1) The diagram shows the relation between set X and set Y.

(x) (g(x)) (x)

( 2) ( 4 )

( 2) (x)

( 3) (1)

( 6) ( 4)

(Set Y) (Set X)

(a) State the value of x

(b) State the domain, codomain, objects, image and range of the relation

(c) State the types of the relation.

(d) State the function by using function notation

(e) Represent the relation by using set of ordered pair.

(2)

Given the function g : x . Find the values of x if g(x) = 4.

(3)

Given the functions f(x) = 4x m and , where k and m are constants. Find the values of k and m.

(4) Given the function and , find

(a) f 2(x)

(b)

(c)

(5) Given the function h(x) = 4x + 5 and the composite function hg(x) = 8x + 7. Find g(x) (x0(-3, k) f(x)= 2(x+ h)2 2)

(6) Diagram shows a graph of a quadratic function f(x) = 2(x+ h)2 2 where k is a constant.

Find

(a) the value of k

(b) the value of h

(c) the equation of axis of symmetry. (22) (22) (22)

(7) (3y(k, 3)0x)The diagram shows the graph of a quadratic function y = (x 4)2 1.

Find

(a)the value of k,

(b)the equation of the axis of symmetry,

(c)the coordinate of the maximum point.

(8) Find the values of p if the quadratic function f(x) = 2x2 + 2px (p + 1) has a minimum value of 5.

(9)

Find the range of values of x for

(10)

Find the range of values of x for x(4 2x) 3(x 2).

(11)

One of the roots of the quadratic equation is 4. Find the value of k.

(12)

Given the quadratic equation has no real roots. Find the range of the values of p.

(13) Solve the following simultaneous equations 2x y = 1 and 9x 2 2y2 + 9 = 0

(14) Solve the following simultaneous equations 2x + y = 1 and 2x 2 + y 2 + xy = 5. Give the answers correct to three decimal places.

(15) Solve the equation .

(16) Solve the equation .

(17) Solve log9 (3x + 6) = 1 + log3 2

(18)

The volume of water, V cm3, in a container is given by , where h cm is the height of the water in the container. Water is poured into the container at the rate of 10 cm3 s -1. Find the rate of change of water, in cm s-1, at the instant when its height is 2 cm.

(19) In Diagram 2, BCD is a straight line.

Find

(a) ACD,

(b) the length of BC,

(c) the area of triangle ABD.

(20) Diagram below is a bar chart indicating the weekly cost of the items P,Q,R ,S and T for the year 1990. Table below shows the prices indices for the items.

Weekly Cost For the items

Items

Weekly Cost

P

RM 15

Q

RM 30

R

RM 24

S

RM 33

T

RM 12

Items

Price in 1990

Price in 1995

Price index in 1995 based on 1990

P

x

RM 0.70

175

Q

RM2.00

RM2.50

125

R

RM4.00

RM5.50

y

S

RM6.00

RM9.00

150

T

RM2.50

Z

120

(a) Find the value of

(i) x (ii) y (iii) z

(b) Calculate the composite index for the items in the year 1995 based on the year 1990.

(c) The total monthly cost of the items in the year 1990 is RM456. Calculate the corresponding total monthly cost for the year 1995.

(d) The cost of the items increases by 20% from the year 1995 to the year 2000. Find the composite index for the year 2000 based on the year 1990.

Answer:RM0.40, 137.5,RM3.00, 140.9 RM642.5

(21)

(xyOA (-4, 9)BC)In Diagram 5, ABC = 900 and the equation of the straight line BC is 2y + x + 6 = 0.

(a) Find

(i) the equation of the straight line AB

(ii) the coordinates of B [5 marks]

(b) The straight line AB is extended to a point D such that AB : BD = 2 : 3. Find the coordinates of D. [2 marks]

(c) A point P moves such that its distance from point A is always 5 units. Find the equation of the locus of P. [3 marks]

x

x

6

24

)

4

(

2

-