MID-YEAR EXAMINATION QUESTION
PAPER1 ANSWER 1 Diagram 1 shows the relation between set M and set N
PAPER1 ANSWER 1 Diagram 1 shows the relation between set M and set N
set M set N
1------------>3
2------------->4
3------------>5
1------------>3
2------------->4
3------------>5
Diagram
1
State
State
(a) the
codomain of the relation.
{3,4,5}
(b) the type of the relation. [2 marks]
one to one
{3,4,5}
(b) the type of the relation. [2 marks]
one to one
2 Given f(x) = 2x –
5, find the value of q if f(q) = q.
5 [2 marks]
5 [2 marks]
3. A function is defined by
f: x → 2x – 5.
Find (a) the object of image 7,
(b) the object which maps onto itself.
[3 marks]
6, 5
f: x → 2x – 5.
Find (a) the object of image 7,
(b) the object which maps onto itself.
[3 marks]
6, 5
4 Given
the functions f : x → x –
1 and g : x →3/x , find
(a) the
composite function gf,
gf(x)= 3/(x-1)
gf(x)= 3/(x-1)
(b) the
value of x if gf(x) = 9. [3 marks]
x = 4/3
x = 4/3
5 Given
the functions f : x → 2 – x
and g : x → 4x2 + 1,
find the value of x if gf = –fg. [4 marks]
x= 9/8
find the value of x if gf = –fg. [4 marks]
x= 9/8
6 Given the
function f : x → 5x +
3, find the value of x if
f (x)= -7
x = -2 [3 marks]
f (x)= -7
x = -2 [3 marks]
7 It
is given that x = 1 is one of the
roots of the quadratic equation 2x2 – 3x +
1 = 0. Find the value of another root. x= 1/2 [2 marks]
8 Form
a quadratic equation which has the roots of x = 3p and x =
p in the form of ax2 + bx + c
= 0, where a, b, and c are constants. Then, find the
values of p if f(x) = ax2 + bx
+ c = 27 at the y-axis. [3 marks]
9 It is given that the straight line y = c – 4x does not intersect the curve xy = 16. Find the range of c. [3 marks]
c <16
9 It is given that the straight line y = c – 4x does not intersect the curve xy = 16. Find the range of c. [3 marks]
c <16
10 Calculate the value of k for which the
line y = 5(x + 2) is a tangent to the curve y = x2
– 3x + k [3 marks]
11 The curve y2 = p(x2
– 1) meets the straight line y = 3 only at one point. Find the
negative value of p.
p = -36
12 The quadratic equation 4x + c = 16 – (2 – x)2 has two equal roots. Find the value of c. c = 13
13 The curve y = 2x2 + 2tx + 3t – 4 touches the x-axis at the values of t = a and t = b, where a < b. Find the values of a and b. [3 marks]
p = -36
12 The quadratic equation 4x + c = 16 – (2 – x)2 has two equal roots. Find the value of c. c = 13
13 The curve y = 2x2 + 2tx + 3t – 4 touches the x-axis at the values of t = a and t = b, where a < b. Find the values of a and b. [3 marks]
14 Find the range of values of k for which
the line y = kx + 2 does not intersect the curve x2
+ y2 = 2. [4 marks]
15 Find
the range of values of k for which the line y + 4(kx
+ 1) = 0 meets the curve y = 2x2 + 7k. [4 marks]
16 Solve the following simultaneous equations:
x = y + 1
(x – y) y = 1 [2 marks]
x= 2, y=1
17 Solve the simultaneous equations y = 4x – 1 and (x + 1)(y + 2) = 0. [3 marks]
x= -1, y= 5
x= -1/4, y= -2
x= 2, y=1
17 Solve the simultaneous equations y = 4x – 1 and (x + 1)(y + 2) = 0. [3 marks]
x= -1, y= 5
x= -1/4, y= -2
18 Solve
the following simultaneous equations:
y =
2x and y2 = 4x
– 1
[3 marks]
x= 1/2, y= 1
x= 1/2, y= 1
19 Solve the
simultaneous equations x – y = –1 and x2
+ y2 = 25.
[4 marks]
x= -4, y= -3
x= 3, y= 4
x= -4, y= -3
x= 3, y= 4
20 Solve
the following simultaneous equations:
x + 1 = 2y x2
+ xy – 26 =
0
[4 marks]
x= -13/3, y= -5/3
x= 4, y= 5/2
x= -13/3, y= -5/3
x= 4, y= 5/2
21 Solve
the following simultaneous equations:
2
log10 x =
log10 (x + y)
x
– y =
0 [4 marks]
x=0, y=0
x=0, y=0
x=2, y=2
22Solve the equation 8x . 21 – x = 321 +
2x. [3 marks]
x= - 1/2
x= - 1/2
23 Given
that log3 x + 1 = 2 log9 (x +
y), prove that
8x2 – 2xy – y2 = 0. [4 marks]
8x2 – 2xy – y2 = 0. [4 marks]
24 Solve
the equation log2 (5x + 2) + log2 (x
– 1) = 2 + log2
(1 – 4x).
x= 2/5 x= -1/3 [4 marks]
(1 – 4x).
x= 2/5 x= -1/3 [4 marks]
25 Given
that y = kxm – 3 where k and m
are constants. Find the values of k
and m if y = 24 when x = 3 and y = 240 when
x = 9.
x = 9.
[4 marks]
