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