if P = {x:x is odd, \(-1 < x \leq 20\)} and Q is {y:y is prime, \(-2 < y \leq 25\), find P \(\cap\) Q
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(C)
{3,5,7,11,13,17,19}
9
If S = \(\sqrt{t^2 - 4t + 4}\), find t in terms of S
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(B)
S + 2
10
If x - 4 is a factor of x2 - x - k, then k is
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(B)
12
11
The remainder when 6p3 - p2 - 47p + 30 is divided by p - 3 is
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(B)
42
12
P varies jointly as m and u, and varies inversely as q. Given that p = 4, m = 3 and u = 2 and q = 1, find the value of p when m = 6, u = 4 and q =\(\frac{8}{5}\)
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(C)
10
13
If r varies inversely as the square root of s and t, how does s vary with r and t?
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(B)
s varies inverely as r2 and t
14
Evaluate 3(x + 2) > 6(x + 3)
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(C)
x < -4
15
Solve for x: |x - 2| < 3
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(C)
-1 < x < 5
16
The nth term of the progression \(\frac{4}{2}\), \(\frac{7}{3}\), \(\frac{10}{4}\), \(\frac{13}{5}\) is ...
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(B)
\(\frac{3n + 1}{n + 1}\)
17
If a binary operation * is defined by x * y = x + 2y, find 2 * (3 * 4)
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(A)
24
18
If P = \(\begin{pmatrix} 5 & 3 \\ 2 & 1 \end{pmatrix}\) and Q = \(\begin{pmatrix} 4 & 2 \\ 3 & 5 \end{pmatrix}\), find 2P + Q
If y = x sin x, find \(\frac{\delta y}{\delta x}\)
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(D)
sin x + x cos x
21
If y = (2x + 2)\(^3\), find \(\frac{\delta y}{\delta x}\)
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(D)
6(2x +2)2
22
The radius of a circle is increasing at the rate of 0.02cms-1. Find the rate at which the area is increasing when the radius of the circle is 7cm.
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(D)
0.88cm2S-1
23
Find the mean of t + 2, 2t - 4, 3t + 2 and 2t.
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(B)
2t
24
The mean of seven numbers is 10. If six of the numbers are 2, 4, 8, 14, 16 and 18, find the mode.
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(B)
8
25
Age
20
25
30
35
40
45
No of people
3
5
1
1
2
3
Calculate the median age of the frequency distribution in the table above
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(A)
25
26
If the variance of 3+x, 6, 4, x and 7-x is 4 and the mean is 5, find the standard deviation
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(B)
2
27
\(\begin{array}{c|c} Score & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ \hline Frequency & 1 & 0 & 7 & 5 & 2 & 3 & 1 & 1 \end{array}\)
The table above shows the scores of 20 students in further mathematics test. What is the range of the distribution?
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(A)
7
28
In how many ways can a student select 2 subjects from 5 subjects?
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(C)
\(\frac{5!}{2!3!}\)
29
In how many ways can 3 seats be occupied if 5 people are willing to sit?
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(A)
60
30
What is the probability that an integer x \((1 \leq x \leq 25)\) chosen at random is divisible by both 2 and 3?
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(C)
\(\frac{4}{25}\)
31
A basket contains 9 apples, 8 bananas and 7 oranges. A fruit is picked from the basket, find the probability that it is neither an apple nor an orange.
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(B)
\(\frac{1}{3}\)
32
The graph above is correctly represented by
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(A)
y = x2 - x - 2
33
In the diagram given, find the value of x.
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(B)
40o
34
The value x in the figure given is
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(D)
130o
35
The bar chart above shows the allotment of time(in minutes) per week for selected subjects in a certain school. What is the total time allocated to the six subjects per week?
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(B)
720mins
36
The pie chart above shows the statistical distribution of 80 students in five subjects in an examination. Calculate how many student offer Mathematics.
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(B)
11
37
If the angles of a quadrilateral are (3y + 10)°, (2y + 30)°, (y + 20)° and 4y°. Find the value of y.
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(C)
30°
38
A square tile has side 30 cm. How many of these tiles will cover a rectangular floor of length 7.2m and width 4.2m?
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(B)
336
39
Find the length of a chord which subtends an angle of 90° at the centre of a circle whose radius is 8 cm.
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(D)
\(8\sqrt{2}\) cm
40
A chord of a circle subtends an angle of 120° at the centre of a circle of diameter \(4\sqrt{3} cm\). Calculate the area of the major sector.
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(C)
8\(\pi\) cm\(^2\)
41
The locus of the points which is equidistant from the line PQ forms a
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(D)
pair of parallel lines to PQ
42
If the midpoint of the line PQ is (2,3) and the point P is (-2, 1), find the coordinate of the point Q.
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(D)
(6,5)
43
Find the equation of the perpendicular bisector of the line joining P(2, -3) to Q(-5, 1)
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(C)
8y - 14x - 13 = 0
44
In triangle PQR, q = 8 cm, r = 6 cm and cos P = \(\frac{1}{12}\). Calculate the value of p.
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(C)
\(\sqrt{92}\) cm
45
If \(\tan \theta = \frac{3}{4}\), find the value of \(\sin \theta + \cos \theta\).
