Evaluate \(\frac{21}{9}\) to 3 significant figures
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(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
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(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?
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(A)
1
10
Make 'n' the subject of the formula if w = \(\frac{v(2 + cn)}{1 - cn}\)
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(A)
\(\frac{1}{c}(\frac{w - 2v}{v + w})\)
11
Find the remainder when 2x3 - 11x2 + 8x - 1 is divided by x + 3
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(D)
-178
12
Solve for x and y in the equations below
x2 - y2 = 4
x + y = 2
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(C)
x = 2, y = 0
13
If y varies directly as \(\sqrt{n}\) and y = 4 when n = 4, find y when n = 1\(\frac{7}{9}\)
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(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
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(A)
24
15
The value of y for which \(\frac{1}{5}y + \frac{1}{5} < \frac{1}{2}y + \frac{2}{5}\) is
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(C)
\(y > -\frac{2}{3}\)
16
Find the range of values of m which satisfy (m - 3)(m - 4) < 0
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(C)
3 < m < 4
17
The nth term of a sequence is n2 - 6n - 4. Find the sum of the 3rd and 4th terms.
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(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.
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(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)
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(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
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(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
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(C)
5
22
Given that I3 is a unit matrix of order 3, find |I3|
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(C)
1
23
The angles of a polygon are given by x, 2x, 3x, 4x and 5x respectively. Find the value of x.
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(D)
36o
24
Calculate the volume of a cuboid of length 0.76cm, breadth 2.6cm and height 0.82cm.
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(D)
1.62cm3
25
The gradient of the straight line joining the points P(5, -7) and Q(-2, -3) is
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(C)
\(-\frac{4}{7}\)
26
The distance between the point (4, 3) and the intersection of y = 2x + 4 and y = 7 - x is
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(B)
\(3\sqrt{2}\)
27
Find the equation of the line through the points (-2, 1) and (-\(\frac{1}{2}\), 4)
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(B)
y = 2x + 5
28
If angle \(\theta\) is 135o, evaluate cos\(\theta\)
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(C)
\(-\frac{\sqrt{2}}{2}\)
29
If y = x2 - \(\frac{1}{x}\), find \(\frac{\delta y}{\delta x}\)
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(D)
2x + \(\frac{1}{x^2}\)
30
Evaluate \(\int^2_1(x^2 - 4x)dx\)
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(D)
\(-\frac{11}{3}\)
31
Evaluate \(\int^{\frac{\pi}{4}}_0sec^2 \theta d \theta\)
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(A)
1
32
The mean of seven numbers is 96. If an eighth number is added, the mean becomes 112. Find the eighth number.
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(D)
224
33
Find the median of 2,3,7,3,4,5,8,9,9,4,5,3,4,2,4 and 5
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(D)
4
34
Find the range of 4,9,6,3,2,8,10 and 11
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(B)
9
35
Find the standard deviation of 2,3,8,10 and 12
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(A)
3.9
36
Evaluate n+1Cn-2 If n =15
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(D)
560
37
In how many ways can the letters of the word TOTALITY be arranged?
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(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?
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(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
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(D)
\(\frac{13}{15}\)
40
The shaded region above is represented by
the equation
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(C)
y ≤ -4x + 4
41
In diagram above, QR//TU, < PQR = 80° and < PSU = 95°. Calculate < SUT.
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(A)
15o
42
In the diagram above, PQR is a circle centre O. If < QPR is x°, find < QRP.
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(B)
(90 – x)°
43
Find the area of the trapezium above.
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(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?
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(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?
