If \(1011_2\) + \(X_7\) = \(25_{10}\), solve for X.
Răspuns
(A)
207
2
Evaluate [\(\frac{1}{0.03}\) \(\div\) \(\frac{1}{0.024}\)]-1 correct to 2 decimal places
Răspuns
(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
Răspuns
(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
Răspuns
(C)
-2, -3
5
Find the value of k if \(\frac{k}{\sqrt{3} + \sqrt{2}}\) = k\(\sqrt{3 - 2}\)
Răspuns
(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?
Răspuns
(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?
Răspuns
(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
Răspuns
(A)
2, -1
9
Factorize r2 - r(2p + q) + 2pq
Răspuns
(C)
(r - q)(r - 2p)
10
Solve for the equation \(\sqrt{x}\) - \(\sqrt{(x - 2)}\) - 1 = 0
Răspuns
(D)
\(\frac{9}{4}\)
11
Make \(\frac{a}{x}\) the subject of formula \(\frac{x + a}{x - a}\) = m
Express in partial fractions \(\frac{11x + 2}{6x^2 - x - 1}\)
Răspuns
(D)
\(\frac{1}{3x + 1}\) + \(\frac{3}{2x - 1}\)
14
If x is a positive real number, find the range of values for which \(\frac{1}{3x}\) + \(\frac{1}{2}\) > \(\frac{1}{4x}\)
Răspuns
(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
Răspuns
(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.
Răspuns
(B)
\(\frac{1}{\sqrt[3]{2}}\)
17
The identity element with respect to the multiplication shown in the diagram below is \(\begin{array}{c|c} \otimes & p & p & r & s \\ \hline p & r & p & r & p
\\ q & p & q & r & s\\ r & r & r & r & r\\ s & q & s & r & q\end{array}\)
Răspuns
(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
Răspuns
(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
Răspuns
(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)
Răspuns
(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
Răspuns
(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.
Răspuns
(B)
16\(\sqrt{3cm^2}\)
23
If the distance between the points (x, 3) and (-x, 2) is 5. Find x
Răspuns
(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
Răspuns
(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\(\pi\)
Răspuns
(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
Răspuns
(B)
50(3 + \(\sqrt{3}\))m
27
If y = 243(4x + 5)-2, find \(\frac{dy}{dx}\) when x = 1
Răspuns
(A)
\(\frac{-8}{3}\)
28
Differentiate \(\frac{x}{cosx}\) with respect to x
Răspuns
(D)
x sec x tan x + secx
29
Evaluate ∫\(^{\pi}_{2}\)(sec2 x - tan2x)dx
Răspuns
(B)
\(\pi\) - 2
30
find the equation of the curve which passes through by 6x - 5
Răspuns
(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
Răspuns
(C)
12.9
33
Find the variance of the numbers k, k+1, k+2,
Răspuns
(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
Răspuns
(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 \(\frac{2}{5}\)
Răspuns
(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?
Răspuns
(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
Răspuns
(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
Răspuns
(C)
57\(\frac{1}{2}\)
39
In the venn diagram, the shaded region is?
Răspuns
(C)
(P \(\cap\) Q1) \(\cap\) R
40
The shaded area represents
Răspuns
(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
Răspuns
(B)
25o
42
In diagram, PQ || ST and < PQR = 120º, < RST = 130º, find the angle marked x
Răspuns
(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.
Răspuns
(C)
70cm2
44
TQ is tangent to circle XYTR, < YXT = 32o, RTQ = 40o. find < YTR
Răspuns
(A)
108o
45
In the diagram, QTR is a straight line and < PQT = 30o. find the sin of < PTR
