Evaluate \(\frac{21}{9}\) to 3 significant figures
Answer
(D)
2.33
4
A man earns N3,500 per month out of which he spends 15% on his children's education. If he spends additional N1,950 on food, how much does he have left?
If P is a set of all prime factors of 30 and Q is a set of all factors of 18 less than 10, find P \(\cap\) Q
Answer
(B)
{2,3}
9
In a class of 46 students, 22 play football and 26 play volleyball. If 3 students play both games, how many play neither?
Answer
(A)
1
10
Make 'n' the subject of the formula if w = \(\frac{v(2 + cn)}{1 - cn}\)
Answer
(A)
\(\frac{1}{c}(\frac{w - 2v}{v + w})\)
11
Find the remainder when 2x3 - 11x2 + 8x - 1 is divided by x + 3
Answer
(D)
-178
12
Solve for x and y in the equations below
x2 - y2 = 4
x + y = 2
Answer
(C)
x = 2, y = 0
13
If y varies directly as \(\sqrt{n}\) and y = 4 when n = 4, find y when n = 1\(\frac{7}{9}\)
Answer
(C)
\(\frac{8}{3}\)
14
U is inversely proportional to the cube of V and U = 81 when V = 2. Find U when V = 3
Answer
(A)
24
15
The value of y for which \(\frac{1}{5}y + \frac{1}{5} < \frac{1}{2}y + \frac{2}{5}\) is
Answer
(C)
\(y > -\frac{2}{3}\)
16
Find the range of values of m which satisfy (m - 3)(m - 4) < 0
Answer
(C)
3 < m < 4
17
The nth term of a sequence is n2 - 6n - 4. Find the sum of the 3rd and 4th terms.
Answer
(D)
-25
18
The sum to infinity of a geometric progression is \(-\frac{1}{10}\) and the first term is \(-\frac{1}{8}\). Find the common ratio of the progression.
Answer
(B)
\(-\frac{1}{4}\)
19
The binary operation * is defined on the set of integers such that p * q = pq + p - q. Find 2 * (3 * 4)
Answer
(B)
13
20
The binary operation on the set of real numbers is defined by m*n = \(\frac{mn}{2}\) for all m, n \(\in\) R. If the identity element is 2, find the inverse of -5
Answer
(A)
\(-\frac{4}{5}\)
21
If \(\begin{vmatrix} 5 & 3 \\ x & 2 \end{vmatrix}\) = \(\begin{vmatrix} 3 & 5 \\ 4 & 5 \end{vmatrix}\), find the value of x
Answer
(C)
5
22
Given that I3 is a unit matrix of order 3, find |I3|
Answer
(C)
1
23
The angles of a polygon are given by x, 2x, 3x, 4x and 5x respectively. Find the value of x.
Answer
(D)
36o
24
Calculate the volume of a cuboid of length 0.76cm, breadth 2.6cm and height 0.82cm.
Answer
(D)
1.62cm3
25
The gradient of the straight line joining the points P(5, -7) and Q(-2, -3) is
Answer
(C)
\(-\frac{4}{7}\)
26
The distance between the point (4, 3) and the intersection of y = 2x + 4 and y = 7 - x is
Answer
(B)
\(3\sqrt{2}\)
27
Find the equation of the line through the points (-2, 1) and (-\(\frac{1}{2}\), 4)
Answer
(B)
y = 2x + 5
28
If angle \(\theta\) is 135o, evaluate cos\(\theta\)
Answer
(C)
\(-\frac{\sqrt{2}}{2}\)
29
If y = x2 - \(\frac{1}{x}\), find \(\frac{\delta y}{\delta x}\)
Answer
(D)
2x + \(\frac{1}{x^2}\)
30
Evaluate \(\int^2_1(x^2 - 4x)dx\)
Answer
(D)
\(-\frac{11}{3}\)
31
Evaluate \(\int^{\frac{\pi}{4}}_0sec^2 \theta d \theta\)
Answer
(A)
1
32
The mean of seven numbers is 96. If an eighth number is added, the mean becomes 112. Find the eighth number.
Answer
(D)
224
33
Find the median of 2,3,7,3,4,5,8,9,9,4,5,3,4,2,4 and 5
Answer
(D)
4
34
Find the range of 4,9,6,3,2,8,10 and 11
Answer
(B)
9
35
Find the standard deviation of 2,3,8,10 and 12
Answer
(A)
3.9
36
Evaluate n+1Cn-2 If n =15
Answer
(D)
560
37
In how many ways can the letters of the word TOTALITY be arranged?
Answer
(A)
6720
38
The probability that a student passes a physics test is \(\frac{2}{3}\). If he takes three physics tests, what is the probability that he passes two of the tests?
Answer
(C)
\(\frac{4}{27}\)
39
The probabilities that a man and his wife live for 80 years are \(\frac{2}{3}\) and \(\frac{3}{5}\) respectively. Find the probability that at least one of them will live up to 80 years
Answer
(D)
\(\frac{13}{15}\)
40
The shaded region above is represented by
the equation
Answer
(C)
y ≤ -4x + 4
41
In diagram above, QR//TU, < PQR = 80° and < PSU = 95°. Calculate < SUT.
Answer
(A)
15o
42
In the diagram above, PQR is a circle centre O. If < QPR is x°, find < QRP.
Answer
(B)
(90 – x)°
43
Find the area of the trapezium above.
Answer
(C)
60 cm2
44
The grades of 36 students in a class test are as shown in the pie chart above. How many students have excellent?
Answer
(D)
7
45
The bar chart above shows the distribution of marks in a class test. If the pass mark is 5, what percentage of students failed the test?
