1
MAHANAIM INTERNATIONAL HIGH SCHOOL
INTERNATIONAL GENERAL CERTIFICATE OF SECONDARY EDUCATION
NAME: __________________________________
PURE MATHEMATICS 1
MIDTERM EXAMS
(70Marks)
ADM NO___________________
(AS & A LEVEL)
TERM 1
9709
OCT 2020
1h 45 min
READ THESE INSTRUCTIONS FIRST
Candidates answer on the Question Paper.
No Additional Materials are required.
Write your name in the spaces at the top of this page.
Write in dark blue or black pen.
Do not use staples, paper clips, glue or correction fluid.
DO NOT WRITE IN ANY BARCODES.
Answer all questions.
Any rough working should be done in this booklet.
At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part question.
For official use only
MHIS/PM 1/9709/OCT/2020 @BN
2
1. Express 2x2 – 12x + 7 in the form a(x + b)2 + c where a, b and c are constants
(3 marks)
2. Find the set of values of k for which the line y = 2x – k meets the curve
y =x2 + kx -2 at two distinct points.
3. (i) Express 4x2 -12x in the form (2x + a)2 + b
MHIS/PM 1/9709/OCT/2020 @BN
(5 marks)
(2 marks)
3
(ii) Hence or otherwise, find the set of values of x which satisfying 4x2 – 12x > 7.
(2 marks)
4. Solve the inequality x2 – x -2 > 0
( 3 marks)
5. The equation x2 + px +q where p and q are constants, has roots -3 and 5.
(i)
Find the values of p and q
(ii)
Using these values of p and q, find the value of constant r for which the
equation
x2 +px + q + r = 0 has equal roots.
MHIS/PM 1/9709/OCT/2020 @BN
(2 marks)
(3 marks)
4
6. Find the set of values of m which the line y =mx +4 intersects the curve y =3x2 –
4x +7 at two distinct points.
7. Find the real roots of the equation 18/x4 + 1/x2 = 4
MHIS/PM 1/9709/OCT/2020 @BN
(5 marks)
(4 marks)
5
8. Find the coordinates of the points of intersection of the line y + 2x =11 and the
curve xy =12
(4 marks)
9. The functions f, g and h are defined by:
f(x) = 2x,
Find
(a) fg(x)
(b) gf(x)
(c) gh(x)
(d) fgh(x)
MHIS/PM 1/9709/OCT/2020 @BN
g(x) = x2 and
h(x) = 1/x.
(8 marks)
6
10. Find the inverse of the following functions
(4 marks)
(a) f(x) = 2x + 7
(b) g(x) =
9
𝑥+2
11. Show that x2 + 4x + 7 = (x + 2)2 + a, where a is to be determined.
i)
(3 marks)
Sketch the graph of y = x2 + 4x + 7, giving the equation of its axis of
symmetry and the co-ordinates of its vertex.
MHIS/PM 1/9709/OCT/2020 @BN
(4 marks)
7
The function f is defined by f(x) = x2 + 4x + 7 with domain the set of all real
numbers.
ii)
12.
Find the range of f(x).
(2 marks)
The point C lies on the perpendicular bisector of the line joining the points
A(4, 6) and B(10, 2). C also lies on the line parallel to AB through (3, 11).
(i)
Find the equation of the perpendicular bisector of AB.
(4 marks)
(ii)
Calculate the coordinates of C.
(3 marks)
MHIS/PM 1/9709/OCT/2020 @BN
8
13. (a) Find the equation of the circle with the centre (-4, 3) and radius 6. ( 3 marks)
b) Find the centre and the radius of the circle x2 + y2 +10x - 8y - 40 =0
(4 marks)
(c) Find the equation of a straight line with gradient -2 that passes through the point (4, 1)
(3 marks)
MHIS/PM 1/9709/OCT/2020 @BN