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