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