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
Answer
(C)
{3,5,7,11,13,17,19}
9
If S = \(\sqrt{t^2 - 4t + 4}\), find t in terms of S
Answer
(B)
S + 2
10
If x - 4 is a factor of x2 - x - k, then k is
Answer
(B)
12
11
The remainder when 6p3 - p2 - 47p + 30 is divided by p - 3 is
Answer
(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 =\(\frac{8}{5}\)
Answer
(C)
10
13
If r varies inversely as the square root of s and t, how does s vary with r and t?
Answer
(B)
s varies inverely as r2 and t
14
Evaluate 3(x + 2) > 6(x + 3)
Answer
(C)
x < -4
15
Solve for x: |x - 2| < 3
Answer
(C)
-1 < x < 5
16
The nth term of the progression \(\frac{4}{2}\), \(\frac{7}{3}\), \(\frac{10}{4}\), \(\frac{13}{5}\) is ...
Answer
(B)
\(\frac{3n + 1}{n + 1}\)
17
If a binary operation * is defined by x * y = x + 2y, find 2 * (3 * 4)
Answer
(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 \(\frac{\delta y}{\delta x}\)
Answer
(D)
sin x + x cos x
21
If y = (2x + 2)\(^3\), find \(\frac{\delta y}{\delta x}\)
Answer
(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.
Answer
(D)
0.88cm2S-1
23
Find the mean of t + 2, 2t - 4, 3t + 2 and 2t.
Answer
(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.
Answer
(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
Answer
(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
Answer
(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?
Answer
(A)
7
28
In how many ways can a student select 2 subjects from 5 subjects?
Answer
(C)
\(\frac{5!}{2!3!}\)
29
In how many ways can 3 seats be occupied if 5 people are willing to sit?
Answer
(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?
Answer
(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.
Answer
(B)
\(\frac{1}{3}\)
32
The graph above is correctly represented by
Answer
(A)
y = x2 - x - 2
33
In the diagram given, find the value of x.
Answer
(B)
40o
34
The value x in the figure given is
Answer
(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?
Answer
(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.
Answer
(B)
11
37
If the angles of a quadrilateral are (3y + 10)°, (2y + 30)°, (y + 20)° and 4y°. Find the value of y.
Answer
(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?
Answer
(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.
Answer
(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.
Answer
(C)
8\(\pi\) cm\(^2\)
41
The locus of the points which is equidistant from the line PQ forms a
Answer
(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.
Answer
(D)
(6,5)
43
Find the equation of the perpendicular bisector of the line joining P(2, -3) to Q(-5, 1)
Answer
(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.
Answer
(C)
\(\sqrt{92}\) cm
45
If \(\tan \theta = \frac{3}{4}\), find the value of \(\sin \theta + \cos \theta\).
