If \(1011_2\) + \(X_7\) = \(25_{10}\), solve for X.
პასუხი
(A)
207
2
Evaluate [\(\frac{1}{0.03}\) \(\div\) \(\frac{1}{0.024}\)]-1 correct to 2 decimal places
პასუხი
(B)
1.25
3
If \(b^3\) = \(a^{-2}\) and \(c^{\frac{1}{3}}\) = \(a^\frac{1}{2}\)b, express c in terms of a
პასუხი
(A)
a-\(\frac{1}{2}\)
4
Given that log4(Y - 1) + log4(\(\frac{1}{2}\)x) = 1 and log2(y + 1) + log2x = 2, solve for x and y respectively
პასუხი
(C)
-2, -3
5
Find the value of k if \(\frac{k}{\sqrt{3} + \sqrt{2}}\) = k\(\sqrt{3 - 2}\)
პასუხი
(D)
\(\sqrt 2\)
6
A market woman sells oil in cylindrical tins 10cm deep and 6cm in diameter at N15.00 each. If she bought a full cylindrical jug 18cm deep and 10cm in diameter for N50.00, how much did she make by selling all the oil?
პასუხი
(D)
N25.00
7
A man is paid r naira per hour for normal work and double rate for overtime. if he does a 35-hour week which includes q hours of overtime, what is his weekly earning in naira?
პასუხი
(D)
r(35 + 2q)
8
When the expression pm\(^2\) + qm + 1 is divided by (m - 1), it has a remainder is 2, and when divided by (m + 1), the remainder is 4. Find p and q respectively
პასუხი
(A)
2, -1
9
Factorize r2 - r(2p + q) + 2pq
პასუხი
(C)
(r - q)(r - 2p)
10
Solve for the equation \(\sqrt{x}\) - \(\sqrt{(x - 2)}\) - 1 = 0
პასუხი
(D)
\(\frac{9}{4}\)
11
Make \(\frac{a}{x}\) the subject of formula \(\frac{x + a}{x - a}\) = m
Express in partial fractions \(\frac{11x + 2}{6x^2 - x - 1}\)
პასუხი
(D)
\(\frac{1}{3x + 1}\) + \(\frac{3}{2x - 1}\)
14
If x is a positive real number, find the range of values for which \(\frac{1}{3x}\) + \(\frac{1}{2}\) > \(\frac{1}{4x}\)
პასუხი
(D)
0 < x < \(\frac{1}{6}\)
15
If p + 1, 2P - 10, 1 - 4p2are three consecutive terms of an arithmetic progression, find the possible values of p
პასუხი
(C)
-\(\frac{4}{11}\), 2
16
The sum of the first three terms of a geometric progression is half its sum to infinity. Find the positive common ratio of the progression.
პასუხი
(B)
\(\frac{1}{\sqrt[3]{2}}\)
17
The identity element with respect to the multiplication shown in the diagram below is \(\begin{array}{c|c} \otimes & p & p & r & s \\ \hline p & r & p & r & p
\\ q & p & q & r & s\\ r & r & r & r & r\\ s & q & s & r & q\end{array}\)
პასუხი
(B)
q
18
The binary operation \(\ast\) is defined by x \(\ast\) y = xy - y - x for all real values x and y. If x \(\ast\) 3 = 2\(\ast\) x, find x
პასუხი
(C)
1
19
The determinant of matrix \(\begin{pmatrix} x & 1 & 0 \\ 1-x & 2 & 3 \\ 1 & 1+x & 4\end{pmatrix}\) in terms of x is
პასუხი
(B)
-3x2 + 9x - 1
20
Let I = \(\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}\) p = \(\begin{pmatrix} 2 & 3 \\ 4 & 5 \end{pmatrix}\) Q = \(\begin{pmatrix} u & 4+u \\ -2v & v \end{pmatrix}\) be 2 x 2 matrices such that PQ = I. Find (u, v)
პასუხი
(A)
(-\(\frac{5}{2}\) - 1)
21
a cylindrical drum of diameter 56 cm contains 123.2 litres of oil when full. Find the height of the drum in centimeters
პასუხი
(D)
50.00
22
The locus of all points at a distance 8cm from a point N passes through points T and S. If S is equidistant from T and N, find the area of triangle STN.
პასუხი
(B)
16\(\sqrt{3cm^2}\)
23
If the distance between the points (x, 3) and (-x, 2) is 5. Find x
პასუხი
(C)
\(\sqrt{6}\)
24
The midpoint of the segment of the line y = 4x + 3 which lies between the x-ax 1 is and the y-ax 1 is
პასუხი
(D)
(-\(\frac{3}{8}\), \(\frac{3}{2}\))
25
solve the equation cos x + sin x = \(\frac{1}{cos x - sinx}\) for values of such that 0 \(\leq\) x < 2\(\pi\)
პასუხი
(D)
0, \(\pi\)
26
From the top of a vertical mast 150m high., two huts on the same ground level are observed. One due east and the other due west of the mast. Their angles of depression are 60o and 45o respectively. Find the distance between the huts
პასუხი
(B)
50(3 + \(\sqrt{3}\))m
27
If y = 243(4x + 5)-2, find \(\frac{dy}{dx}\) when x = 1
პასუხი
(A)
\(\frac{-8}{3}\)
28
Differentiate \(\frac{x}{cosx}\) with respect to x
პასუხი
(D)
x sec x tan x + secx
29
Evaluate ∫\(^{\pi}_{2}\)(sec2 x - tan2x)dx
პასუხი
(B)
\(\pi\) - 2
30
find the equation of the curve which passes through by 6x - 5
პასუხი
(D)
3x2 - 5x + 3
31
If m and n are the mean and median respectively of the set of numbers 2, 3, 9, 7, 6, 7, 8, 5, find m + 2n to the nearest whole number
Estimate the mode of the above frequency distribution
პასუხი
(C)
12.9
33
Find the variance of the numbers k, k+1, k+2,
პასუხი
(A)
\(\frac{2}{3}\)
34
Find the positive value of x if the standard deviation of the numbers 1, x + 1, 2x + 1 is 6
პასუხი
(C)
3
35
A bag contains 16 red balls and 20 blue balls only. How many white balls must be added to the bag so that the probability of randomly picking a red ball is equal to \(\frac{2}{5}\)
პასუხი
(A)
4
36
In a recent zonal championship games involving 10 teams, teams X and Y were given probabilities \(\frac{2}{5}\) and \(\frac{1}{3}\) respectively of winning the gold in the football event. What is the probability that either team will win the gold?
პასუხი
(C)
\(\frac{11}{15}\)
37
If x, y can take values from the set (1, 2, 3, 4), find the probability that the product of x and y is not greater than 6
პასუხი
(A)
\(\frac{5}{8}\)
38
For what value of x does 6 sin (2x - 25)o attain its maximum value in the range 0o \(\leq\) x \(\leq\) 180o
პასუხი
(C)
57\(\frac{1}{2}\)
39
In the venn diagram, the shaded region is?
პასუხი
(C)
(P \(\cap\) Q1) \(\cap\) R
40
The shaded area represents
პასუხი
(A)
x \(\leq\) 0, y \(\leq\) 0, 2y + 3x \(\leq\) 6
41
In the diagram, PR is a diameter of the circle PQRS. PST and QRT are straight lines. Find QRS
პასუხი
(B)
25o
42
In diagram, PQ || ST and < PQR = 120º, < RST = 130º, find the angle marked x
პასუხი
(C)
70
43
In the figure, PQST is a parallelogram and TSR is a straight line. If the area of \(\bigtriangleup\)QRS is 20cm2, find the area of the trapezium PQRT.
პასუხი
(C)
70cm2
44
TQ is tangent to circle XYTR, < YXT = 32o, RTQ = 40o. find < YTR
პასუხი
(A)
108o
45
In the diagram, QTR is a straight line and < PQT = 30o. find the sin of < PTR
