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Question 1 of 47
1. Question
Convert 72_{6} to a number in base three
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Question 2 of 47
2. Question
Simplify \( \frac{2\frac{2}{3} \: \times \: 1 \frac{1}{2}}{4 \frac{4}{5}} \)
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Question 3 of 47
3. Question
A man earns ₦3,500 per month out of which he spends 15% on his children’s education If he spends an additional ₦1,950 on food, how much does he have left?
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Question 4 of 47
4. Question
If \( \scriptsize 27^{x\:+\:2} \: \div\: 9^{x\:+\:1} = 3^{2x} \)
find x
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Question 5 of 47
5. Question
If \( \scriptsize \log_3x^2 = \: 8 \)
What is x
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Question 6 of 47
6. Question
Simplify \( \scriptsize \left(\sqrt{6} \: +\: 2 \right)^2 \: \: \left(\sqrt{6} \: \: 2 \right)^2 \)
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Question 7 of 47
7. Question
If P is a set of all prime factors of 30 and Q is a set of all factors of 10 less than 10, find P ∩ Q.
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Question 8 of 47
8. Question
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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Question 9 of 47
9. Question
Make n the subject of the formula if w = \( \frac {v(2 \: + \: cn)}{1 \: – \: cn} \)
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Question 10 of 47
10. Question
Find the remainder when 2x^{3} – 11x^{2} + 8x – 1 is divided by x + 3
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Question 11 of 47
11. Question
Solve for x and y in the equations below
x^{2} – y^{2} = 4
x + y = 2CorrectIncorrect 
Question 12 of 47
12. Question
If y varies directly as \( \scriptsize \sqrt{n}\) and y = 4 when n = 4.
Find y when n = \( \scriptsize 1 \frac{7}{9} \)
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Question 13 of 47
13. Question
U is inversely proportional to the cube of V and U = 81 when V = 2.
Find U when V = 3.
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Question 14 of 47
14. Question
The value of y for which \( \normalsize \frac{1}{5} \scriptsize y \: + \: \normalsize\frac{1}{5} \: < \: \frac{1}{2}\scriptsize y \: +\: \normalsize \frac{2}{5} \)
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Question 15 of 47
15. Question
Find the range of values of m which satisfy (m – 3)(m – 4) < 0
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Question 16 of 47
16. Question
The shaded region above is represented by the equation
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Question 17 of 47
17. Question
The nth term of a sequence is n^{2 }– 6n – 4. Find the sum of the 3rd and 4th terms.
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Question 18 of 47
18. Question
The sum to infinity of a geometric progression is – ^{1}/_{10 } and the first term is – ^{1}/_{8}
Find the common ratio of the progression.
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Question 19 of 47
19. Question
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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Question 20 of 47
20. Question
The binary operation on the set of real numbers is defined by m*n = ^{mn}/_{2} for all m, n ∈ R.
If the identity element is 2, find the inverse of 5
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Question 21 of 47
21. Question
If \( \scriptsize \begin{vmatrix} 5 & 3 \\ x & 2 \end{vmatrix} \)
Find the value of x
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Question 22 of 47
22. Question
Given that I_{3} is a unit matrix of order 3, find I_{3}⎸
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Question 23 of 47
23. Question
In the diagram above. QR//TU, ∠PQR = 80°and ∠PSU = 95°. Calculate ∠SUT.
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Question 24 of 47
24. Question
The angles of a polygon are given by x, 2x, 3x and 5x respectively. Find the value of x.
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Question 25 of 47
25. Question
In the diagram above, PQR is a circle centre O. If ∠QPR is x°, find ∠QRP.
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Question 26 of 47
26. Question
Find the area of the trapezium above.
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Question 27 of 47
27. Question
A circular arc subtends angle 150° at the centre of a circle of radius 12 cm. Calculate the area of the sector of the arc.
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Question 28 of 47
28. Question
Calculate the volume of a cuboid of length 0.76 cm, breadth 2.6 cm and height 0.82 cm.
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Question 29 of 47
29. Question
The locus of a point equidistant from the intersection of lines 3x – 7y + 7 = 0 and 4x – 6y +1 = 0 is a
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Question 30 of 47
30. Question
The gradient of the straight line joining the points P(5, 7) and Q(2, 3) is
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Question 31 of 47
31. Question
The distance between the points (4, 3) and the intersection of y =2x + 4 and y = 7 – x is
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Question 32 of 47
32. Question
Find the equation of the line through the points (2, 1) and \( \left( \frac{1}{2}\scriptsize, \: 4\right) \)
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Question 33 of 47
33. Question
If angle θ is 135°, evaluate cos θ.
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Question 34 of 47
34. Question
A man stands on a tree 150 cm high and sees a boat at an angle of depression of 74°. Find the distance of the boat from the base of the tree.
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Question 35 of 47
35. Question
If y = \( \scriptsize x^2 \: \: \normalsize \frac{1}{x}\)
Find \( \frac{dy}{dx} \)
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Question 36 of 47
36. Question
Find \( \frac{dy}{dx} \)
If y = cos x
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Question 37 of 47
37. Question
Evaluate \( \scriptsize \int^2_1(x^2\: \: 4x)dx \)
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Question 38 of 47
38. Question
Evaluate \(\scriptsize \int^{\frac{\pi}{4}}_0 sec^2 \theta d \theta \)
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Question 39 of 47
39. Question
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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Question 40 of 47
40. Question
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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Question 41 of 47
41. Question
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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Question 42 of 47
42. Question
Find the range of 4, 9, 6, 3, 2, 8, 10 and 11.
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Question 43 of 47
43. Question
Find the standard deviation of 2, 3, 8, 10 and 12.
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Question 44 of 47
44. Question
Evaluate ^{n+1}C_{n2}
If n =15
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Question 45 of 47
45. Question
In how many ways can the letters of the word TOTALITY be arranged?
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Question 46 of 47
46. Question
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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Question 47 of 47
47. Question
The probabilities that a man and his wife live for 80 years are ^{2}/_{3} and ^{3}/_{5} respectively.
Find the probability that at least one of them will live up to 80 years.CorrectIncorrect