If x = 3 - \(\sqrt{3}\), find x2 + \(\frac{36}{x^2}\)
Answer
(C)
24
8
If x = (all prime factors of 44) and y = (all prime factors of 60), the elements of X ∪ Y and X ∩ Y respectively are
Answer
(D)
(2, 3, 5, 11) and (2)
9
If U = (1, 2, 3, 6, 7, 8, 9, 10) is the universal set. E = (10, 4, 6, 8, 10) and F = {x: 1x\(^{2}\) = 2\(^{6}, x is odd}. Find (E ∩ F)', where ' means the complement of a set.
Answer
(D)
\(\phi\)
10
Factorize \(9p^2 - q^2 + 6qr - 9r^2\)
Answer
(C)
(3p - q + 3r)(3p + q - 3r)
11
Solve the equation: \(y - 11\sqrt{y} + 24 = 0\)
Answer
(B)
64, 9
12
Make t the subject of formula S = ut + \(\frac{1}{2} at^2\)
Answer
(A)
\(\frac{1}{a}\) (-u + \(\sqrt{U^2 - 2as}\))
13
A man invested a sum of N280.00 partly at 5% and partly at 4%. if the total interest is N12.80 per annum, find the amount invested at 5%
Answer
(D)
160.00
14
If x + 1 is a factor of x3 + 3x2 + kx + 4, find the value of k
Answer
(A)
6
15
Resolve \(\frac{3}{x^2 + x - 2}\) into partial fractions
Answer
(A)
\(\frac{1}{x - 1} - \frac{1}{x + 2}\)
16
Find all values of x satisfying the inequality -11 \(\leq\) 4 - 3x \(\leq\) 28
Answer
(C)
-8 \(\leq\) x \(\leq\) 5
17
Find the sum to infinity to the following series 3 + 2 + \(\frac{4}{3}\) + \(\frac{8}{9}\) + \(\frac{16}{17}\) + .....
Answer
(D)
9
18
What is the n-th term of the sequence 2, 6, 12, 20...?
Answer
(C)
n2 + n
19
For an arithmetical sequence, the first term is 2 and the common difference is 3. Find the sum of the first 11 terms
Answer
(B)
187
20
If the binary operation \(\ast\) is defined by m \(\ast\) n = mn + m + n for any real number m and n, find the identity of the elements under this operation
Answer
(D)
e = 0
21
p = \(\begin{vmatrix} x & 3 & 0 \\ 2 & y & 3\\ 4 & 2 & 4 \end{vmatrix}\)
Q = \(\begin{vmatrix} x & 2 & z \\ 3 & y & 2\\ 0 & 3 & z \end{vmatrix}\) Where pT is the transpose P calculate /pT/ when x = 0, y = 1 and z = 2
Answer
(B)
24
22
p = \(\begin{vmatrix} x & 3 & 0 \\ 2 & y & 3\\ 4 & 2 & 4 \end{vmatrix}\)
Q = \(\begin{vmatrix} x & 2 & z \\ 3 & y & 2\\ 0 & 3 & z \end{vmatrix}\)
PQ is equivalent to
Answer
(A)
PPT
23
If the angles of quadrilateral are (p + 10)°, (2p - 30)°, (3p + 20)° and 4p°, find p.
Answer
(C)
36
24
Determine the distance on the earth's surface between two town P (lat 60°N, Long 20°E) and Q(Lat 60°N, Long 25°W) (Radius of the earth = 6400km)
Answer
(C)
800\(\pi\) km
25
If in the diagram, FG is parallel to KM, find the value of x
Answer
(B)
95o
26
X is a point due east of point Y on a coast: Z is another point on the coast but 6√3km due south of y.
If the distance XZ is 12Km. Calculate the bearing of Z from X
Answer
(B)
210o
27
The locus of a point which is equidistant from two given fixed points is the
Answer
(A)
perpendicular bisector of the straight line joining them
28
What is the perpendicular distance of a point (2, 3) from the line 2x - 4y + 3 = 0?
Answer
(A)
\(\frac{\sqrt{5}}{2}\)
29
find then equation line through (5, 7) parallel to the line 7x + 5y = 12
Answer
(B)
7x + 5y = 70
30
Given that \(\theta\) is an acute angle and sin \(\theta\) = \(\frac{m}{n}\), find cos \(\theta\)
Ice forms on a refrigerator ice-box at the rate of (4 - 06t)g per minute after t minutes. If initially there are 2g of ice in the box, find the mass of ice formed in 5 minutes
Answer
(C)
14.5
34
Obtain a maximum value of the function f(x) x\(^3\) - 12x + 11
Answer
(D)
27
35
a student blows a balloon and its volume increases at a rate of \(\pi\)(20 - t2)cm3S-1 after t seconds. If the initial volume is 0 cm3, find the volume of the balloon after 2 seconds
Answer
(B)
37.33\(\pi\)
36
Evaluate the integral \(\int^{\frac{\pi}{4}}_{\frac{\pi}{12}} 2 \cos 2x \mathrm {d} x\)
Answer
(C)
\(\frac{1}{2}\)
37
A store keeper checked his stock of five commodities and arrived at the following statics
\(\begin{array}{c|c} Comoditiy & Quantity\\ \hline F & 125\\ G & 113\\ H & 108\\ K & 216 \\ M & 68\end{array}\)
What angle will commodity H represent on a pie chart?
Answer
(D)
62o
38
\(\begin{array}{c|c} x & 2 & 4 & 6 & 8\\ \hline f & 4 & y & 6 & 5 \end{array}\)
If the mean of the above frequency distribution is 5.2, find y
Answer
(C)
5.0
39
\(\begin{array}{c|c} \text{No. of children} & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline \text{No. of families} & 7 & 11 & 6 & 7 & 7 & 5 & 3 \end{array}\)
Find the mode and median respectively of the distribution above
Answer
(B)
1, 2
40
If the scores of 3 students in a test are 5, 6 and 7, find the standard deviation of their scores
Answer
(C)
\(\sqrt{\frac{2}{3}}\)
41
Two perfect dice are thrown together, Determine the probability of obtaining a total score of 8
Answer
(B)
\(\frac{5}{36}\)
42
The probability of an event P is \(\frac{3}{4}\) while that of another event Q is \(\frac{1}{6}\). If the probability of both P and Q is \(\frac{1}{2}\). What is the probability of either P or Q.
Answer
(D)
\(\frac{11}{12}\)
43
Five people are to be arranged in a row for a group photograph. How many arrangements are there if a married couple in the group insist on sitting next to each other?
Answer
(A)
48
44
A student has 5 courses to take from Mathematics and physics. There are 4 courses in Mathematics and 3 in Physics which he can choose his courses so that he takes exactly two courses in Physics?
Answer
(B)
12
45
The sketch is the curve of y = ax2 + bx + c. Find a, b and c respectively
