Find the values of p and q such that (x - 1)and (x - 3) are factors of px3 + qx2 + 11x - 6
отговор
(B)
1, -6
13
If a = 1, b = 3, solve for x in the equation \(\frac{a}{a - x}\) = \(\frac{b}{x - b}\)
отговор
(C)
\(\frac{3}{2}\)
14
Solve for r in the following equation \(\frac{1}{r - 1}\) + \(\frac{2}{r + 1}\) = \(\frac{3}{r}\)
отговор
(A)
3
15
Find P if \(\frac{x - 3}{(1 - x)(x + 2)}\) = \(\frac{p}{1 - x}\) + \(\frac{Q}{x + 2}\)
отговор
(A)
\(\frac{-2}{3}\)
16
Find the range of values of x for which \(\frac{1}{x}\) > 2 is true
отговор
(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.
отговор
(D)
2
18
Find the value of log10 r + log10 r2 + log10 r4 + log10 r8 + log10 r16 + log10 r32 = 63
отговор
(C)
10
19
Find the nth term of the sequence 3, 6, 10, 15, 21.....
отговор
(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?
отговор
(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
отговор
(A)
2
22
Solve for x and y \(\begin{pmatrix} 1 & 1 \\ 3 & y \end{pmatrix}\)\(\begin{pmatrix} x \\ 1 \end{pmatrix}\) = \(\begin{pmatrix} 4 \\ 1\end{pmatrix}\)
отговор
(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
отговор
(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?
отговор
(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
отговор
(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
отговор
(A)
11 520cm3
27
Calculate the perimeter, in cm, of a sector of a circle of radius 8cm and angle 45o
отговор
(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?
отговор
(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
отговор
(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?
отговор
(C)
10√3m
31
What is the value of sin(-690)?
отговор
(D)
\(\frac{1}{2}\)
32
If y = 3t3 + 2t2 - 7t + 3, find \(\frac{dy}{dt}\) at t = -1
отговор
(C)
-2
33
Find the point (x, y) on the Euclidean plane where the curve y = 2x2 - 2x + 3 has 2 as gradient
отговор
(A)
(1, 3)
34
Evaluate \(\int^{1}_{-1}(2x + 1)^2 \mathrm d x\)
отговор
(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
отговор
(B)
2
36
Find the mean deviation of the set of numbers 4, 5, 9
отговор
(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
отговор
(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
отговор
(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?
отговор
(C)
\(\frac{3}{8}\)
40
The equation of the graph is
отговор
(C)
y = x3 - 27
41
Find the inequality which represents the shaded portion in the diagram
отговор
(A)
2x - y - 2 \(\geq\) 0
42
In the diagram, PQRS is a parallelogram. Find the value of < SQR
отговор
(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
отговор
(D)
52o
44
In the diagram, PTS is a tangent to the circle TQR at T. Calculate < RTS
