OTI 1 F4 2014
ADDITIONAL MATHEMATICS FORM 4
1
A relation from set P = {6, 7, 8, 9} to set Q = {0, 1, 2, 3, 4} is defined by ‘subtract by 5 from’. State [2 marks] (a) the object of 4, (b) the range of the relation.
2
The arrow diagram below shows the relation between Set A and Set B. [2 marks] Set A
Set B
16 12 9 4 1
3 2 1 1 State (a) the range of the relation, (b) the type of the relation.
3
The function f is defined by f : x → 2 – mx and f
−1
(8) = 2, find the value of m. [3 marks]
2014 All Rights Reserved SM IMTIAZ YT DUNGUN
1
4
5
6
2
If f : x → 3 x + 4 , gf : x → 3 − x and fh : x → 6 x + 7 , find (a) the function g, (b) the function h.
[4 marks]
Given the function f : x → 7 − 2 x. Find (a) the range of f corresponds to the domain 1 ≤ x ≤ 3 , (b) the value of x which map to itself.
[4 marks]
Given f : x → − 4 x + 3 , find (a) the image of –3, (b) the object which has the image of 5.
[4 marks]
OTI 1 F4 2014
ADDITIONAL MATHEMATICS FORM 4
The diagram below shows the mapping for the function f
7
−1
and g.
● ● ● f −1 g 2 6 4
`
b x Given that f (x) = ax + b and g (x) = a , calculate the value of a and b.
8
2 Given that f : x → 3 − 2 x and g ( x) = x − 1 find (a) f g(x) (b) g f(– 1)
2014 All Rights Reserved SM IMTIAZ YT DUNGUN
[3 marks]
[4 marks]
3
9
One of the roots of quadratic equation 2x2 + kx – 3 = 0 is 3, find the value of k.
[3 marks]
10 Given that the roots of the quadratic equation x2 – hx + 8 = 0 are p and 2p, find the values of h. [4 marks]
11
4
Given that the quadratic equation x2 + (m – 3)x = 2m – 6 has two equal roots, find the values of m. [4 marks]
OTI 1 F4 2014
ADDITIONAL MATHEMATICS FORM 4
12 Given that one of the roots of the quadratic equation 2x2 + 18x = 2 – k is twice the other root, find value of k. [4 marks]
13 Solve the equation 2(3x – 1)2 = 18.
the
[3 marks]
14 Solve the equation (x + 1)(x – 4) = 7. Give your answer correct to 3 significant figures. [3 marks]
15 Find the range of values of m such that the equation 2x2 = x - m has two different roots.[3 marks]
2014 All Rights Reserved SM IMTIAZ YT DUNGUN
5
16 Find the range of values of x for which (2x - 1)(x + 4) > x + 4
[3 marks]
17 Find the range of values of x for which x(x + 2) ≤ 8.
[3 marks]
18 Find the range of values of x for which 3x 2 ≥ 2 – 5x
[3 marks]
2 6
OTI 1 F4 2014
ADDITIONAL MATHEMATICS FORM 4
(4, k)
x y 0
19 In Diagram 1, (4, k) is a turning point of the curve y = a(x + h)2 + 18.
[3 marks]
Diagram 1 Determine the value of a, h and k.
20 Diagram 2 shows the graph of quadratic function f(x) = (x + p)2 + 3.
O ● f(x) x
(2, q)
k ●
2014 All Rights Reserved SM IMTIAZ YT DUNGUN
7
Diagram 2 Find (a) the values of k , p and q. (b)
21
equation of axis of symmetry
[4 marks]
Diagram3 shows the graph of a quadratic function y = f (x). The straight line y = – 6 is a tangent to the curve y = f (x). y = f (x) y = 6 x y O 1 5
Diagram 3 (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.
[3 marks]
22 Diagram 4 shows the graph of the function y = – (x – k)2 –1, where k is a constant.
8
OTI 1 F4 2014
ADDITIONAL MATHEMATICS FORM 4
3 (2, 3) x y O
Diagram 4 Find (a) The value of k, (b)
The equation of the axis of symmetry,
(c)
The coordinates of the maximum point.
2014 All Rights Reserved SM IMTIAZ YT DUNGUN
[4 marks]
9
23 Solve the simultaneous equations :
[5 marks]
3x – y = x2 – xy + y2 = 7
24 Solve the simultaneous equations : 2x – y = 3 5x – 2y2 x2 = 0 Give your answer correct to 2 decimal places.
10
[5 marks]
OTI 1 F4 2014
x 5y + 25 Solve the simultaneous equations 2y = x – 2 and y x = 5. Give your answers correct to two decimal places.
2014 All Rights Reserved SM IMTIAZ YT DUNGUN
ADDITIONAL MATHEMATICS FORM 4
[5 marks]
11