SPM MODEL PAPER..
(For answers, user must
first download
and unzip this file)
PAPER 1
Time: Two hours
This paper consists of 25 questions.
Answer all the questions. Write your answers clearly in the spaces provided in
the paper. Show your working. It may help you to get marks. The marks allocated
for each question and sub-part of a question are shown in brackets. You may use
non-programmable scientific calculator.
1. Given a set
of ordered pairs [(a,3), (b,5), (c,4), (d,5), (e,7)], state
(a)
The objects of 5
(b)
The type of the relation
Answer
2. Given that
f:x → 2x ,
x ≠k, find
3x – 1
(a)
The value of k
(b)
The value of x which maps onto itself. Answer
3. The
functions f and g are defined by f: x →2x2–x and g:x →5x
+ 4. Find
(a)
g -1f
(b)
The value of x if g -1 f = g -1 Answer
4.
The range of values of x which 2x2 +2x + 3 > 6x + x2 Answer
5. If one of the roots of the quadratic equation
x2–kx + 32 = 0 is two times the
other,
find the values of k. Answer
f(x) = (x + p)2–7, where p is a constant. The curve y = f(x) has a
minimum point at (5,q). State
(a)
The value of p
(b) The
value of q
(c)
The equation of the axis of symmetry
Answer
7. the equation 2x. 6x+2=
5184 Answer
8. Given that log5 4 = p and log4 6 = 2q, express
log 5 24 in term of p and q. Answer
9. Given x + 9, x + 3 and x are the
three consecutive terms in a geometric progression
(a) Find the value of x
(b)
If x + 9 is the third term, find the first term Answer
10. Given a geometric progression k, 4, 16, n
...... , express n in terms of k. Answer
k
11. A
multilevel company starts with 4 branches. Each branch will produce 2 more for
each level.
Find the number of branches in the 10th
level. Answer
12. Express the recurring decimal
0.131313...... as a fraction in its simplest form Answer
13.
The variables x & y are related by the equation y
= axn , where a & n are constants. A straight line is obtained bt plotting log10y
against log10x, as shown in the Diagram. Calculate the value of a
& n. Answer
14.
The Diagram
shows a straight line AB in a Cartesan plane. Find the equation of the
perpendicular bisector of AB. Answer
15. Given
the points O (0,0), A(2,5) and B(3,1), find the following in terms of vectors i
and j
(a) Find AB
(b) Find Unit Vector in the
direction of AB. Answer
16. Given c
= 3i + 2j and d = 2i
- j. If mc + nd
= 7i + 7j, Find the values of m and n Answer
17. Points C(2,4), D(6,1) and Q(x,y) lie on the circumference of a circle of diameter CD. Find
the equation of the moving point
Q. Answer
18. Solve
the equation 2 sin θ – cot θ =
cosec θ for 0° = x = 360° Answer
19. Differentiate x3 with respect to x. Answer
1 + x
20.
The Diagram shows a circle with centre O. Given that
the length of the major arc is 125.68 cm,
find the length of the radius of the circle
(Use P = 3.142)
Answer
21. Given y = 2x3 + 4, use differentiation to
find the small change in y when x decreases from
1 to
0.98.
Answer
3
22.
Find the value for ò (3 – 4x)
dx Answer
1
23.
|
V |
I |
S |
U |
A |
L |
The diagram shows six cubes of
different letters. Find
(a) The number of
possible arrangements, in a row, of all the cards.
(b) The number of arrangements where the vowels must at the three starts. Answer
24. A fair dice is rolled
(a) Find the
probability of getting an odd number
(b) If the same dice is rolled 5 times,
find the probability of getting an even number in exactly 3 times. Answer
25. The mass of a packet of paper is normally distributed with a mean of 120 g and a standard deviation of 4 g.
Find the probability that a packet of paper chosen at random from a sample will have mass
(a) More than 120 g
(b) Between 115 g and
130 g
Answer