Find the values of p and q such that (x - 1)and (x - 3) are factors of px3 + qx2 + 11x - 6
Απάντηση
(B)
1, -6
13
If a = 1, b = 3, solve for x in the equation \(\frac{a}{a - x}\) = \(\frac{b}{x - b}\)
Απάντηση
(C)
\(\frac{3}{2}\)
14
Solve for r in the following equation \(\frac{1}{r - 1}\) + \(\frac{2}{r + 1}\) = \(\frac{3}{r}\)
Απάντηση
(A)
3
15
Find P if \(\frac{x - 3}{(1 - x)(x + 2)}\) = \(\frac{p}{1 - x}\) + \(\frac{Q}{x + 2}\)
Απάντηση
(A)
\(\frac{-2}{3}\)
16
Find the range of values of x for which \(\frac{1}{x}\) > 2 is true
Απάντηση
(C)
0 < x < \(\frac{1}{2}\)
17
If the 6th term of an arithmetic progression is 11 and the first term is 1, find the common difference.
Απάντηση
(D)
2
18
Find the value of log10 r + log10 r2 + log10 r4 + log10 r8 + log10 r16 + log10 r32 = 63
Απάντηση
(C)
10
19
Find the nth term of the sequence 3, 6, 10, 15, 21.....
Απάντηση
(C)
\(\frac{(n + 1)(n + 2)}{2}\)
20
A binary operation \(\oplus\) is defines on the set of all positive integers by a \(\oplus\) b = ab for all positive integers a, b. Which of the following properties does NOT hold?
Απάντηση
(D)
inverse
21
\(\begin{array}{c|c} \oplus mod 10 & 2 & 4 & 6 & 8 \\ \hline 2 & 4 & 8 & 2 & 6 \\4 & 8 & 6 & 4 & 2\\ 4 & 8 & 6 & 4 & 2\\ 6 & 2 & 4 & 6 & 8\\ 8 & 6 & 2 & 8 & 4\end{array}\)
The multiplication table above has modulo 10 on the set S = (2, 4, 6, 8). Find the inverse of 2
Απάντηση
(A)
2
22
Solve for x and y \(\begin{pmatrix} 1 & 1 \\ 3 & y \end{pmatrix}\)\(\begin{pmatrix} x \\ 1 \end{pmatrix}\) = \(\begin{pmatrix} 4 \\ 1\end{pmatrix}\)
Απάντηση
(B)
x = 3, y = -8
23
The determination of the matrix \(\begin{pmatrix} 1 & 3 & 3 \\ 4 & 5 & 6\\ 2 & 0 & 1 \end{pmatrix}\) is
Απάντηση
(C)
-1
24
\(\begin{array}{c|c} \text{Age in years} & 10 & 11 & 12 \\ \hline \text{Number of pupils} & 6 & 27 & 7\end{array}\)
The table above shows the number of pupils in each age group in a class. What is the probability that a pupil chosen at random is at least 11 years old?
Απάντηση
(B)
\(\frac{17}{20}\)
25
If three angles of a quadrilateral are (3y - x - z)o, 3xo, (2z - 2y - x)o find the fourth angle in terms of x, y and z
Απάντηση
(A)
(360 - x- y - z)o
26
An open rectangular box is made of wood 2cm thick. If the internal dimensions of the box are 50cm long, 36cm wide and 20cm deep, the box volume of wood in the box is
Απάντηση
(A)
11 520cm3
27
Calculate the perimeter, in cm, of a sector of a circle of radius 8cm and angle 45o
Απάντηση
(C)
16 + 2\(\pi\)
28
What is the locus of a point P which moves on one side of a straight line XY, so that the angle XPY is always equal to 90o?
Απάντηση
(D)
a semi circle
29
If M(4, q) is the mid-point of the line joining L(p, -2) and N(q, p). Find the values of p and q
Απάντηση
(D)
p = 6, q = 2
30
The angle of depression of a boat from the top of a cliff 10m high is 30. How far is the boat from the foot of the cliff?
Απάντηση
(C)
10√3m
31
What is the value of sin(-690)?
Απάντηση
(D)
\(\frac{1}{2}\)
32
If y = 3t3 + 2t2 - 7t + 3, find \(\frac{dy}{dt}\) at t = -1
Απάντηση
(C)
-2
33
Find the point (x, y) on the Euclidean plane where the curve y = 2x2 - 2x + 3 has 2 as gradient
Απάντηση
(A)
(1, 3)
34
Evaluate \(\int^{1}_{-1}(2x + 1)^2 \mathrm d x\)
Απάντηση
(D)
4\(\frac{2}{3}\)
35
\(\begin{array}{c|c} x & 1 & 2 & 3 & 4 & 5 \\ \hline f & y + 2 & y - 1 & 2y - 3 & y + 4 & 3y - 4\end{array}\)
This table shows the frequency distribution of a data if the mean is \(\frac{43}{14}\), find y
Απάντηση
(B)
2
36
Find the mean deviation of the set of numbers 4, 5, 9
Απάντηση
(B)
2
37
Class interval
1 - 5
6 - 10
11 - 15
16 - 20
21 - 25
Frequency
6
15
20
7
2
Estimate the median of the frequency distribution above
Απάντηση
(C)
12
38
\(\begin{array}{c|c} x & 1 & 2 & 3 & 4 & 5 \\ \hline f & 2 & 1 & 2 & 1 & 2\end{array}\)
Find the variance of the frequency distribution above
Απάντηση
(B)
\(\frac{9}{4}\)
39
In a survey, it was observed that 20 students read newspapers and 35 read novels. If 40 of the students read either newspapers or novels, what is the probability of the students who read both newspapers and novels?
Απάντηση
(C)
\(\frac{3}{8}\)
40
The equation of the graph is
Απάντηση
(C)
y = x3 - 27
41
Find the inequality which represents the shaded portion in the diagram
Απάντηση
(A)
2x - y - 2 \(\geq\) 0
42
In the diagram, PQRS is a parallelogram. Find the value of < SQR
Απάντηση
(D)
100o
43
In the diagram, O is the centre of the circle. If SOQ is a diameter and < PRS is 38o, what is the value of < PSQ
Απάντηση
(D)
52o
44
In the diagram, PTS is a tangent to the circle TQR at T. Calculate < RTS
