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