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Question 1 of 49
1. Question
Convert 27_{10} to another number in base three.
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Question 2 of 49
2. Question
3 girls share a number of apples in the ratio 5:3:2. If the highest share is 40 apples, find the smallest share.
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Question 3 of 49
3. Question
Evaluate \( \frac{1.25 \: \times \: 0.025}{0.05} \)
correct to 1 decimal place.
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Question 4 of 49
4. Question
Calculate the time taken for ₦ 3000 to earn ₦ 600 if invested at 8% simple interest.
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Question 5 of 49
5. Question
Simplify \( \frac{3^{5n}}{9^{1\:\:n}} \scriptsize \: \times \: 27^{n\: +\:1}\)
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Question 6 of 49
6. Question
If log_{10}4 = 0.6021
Evaluate \( \scriptsize \log 4^{\frac{1}{3}} \)
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Question 7 of 49
7. Question
Simplify \(\frac{\sqrt{5}\left(\sqrt{147} \: – \: \sqrt{12} \right)}{\sqrt{15}}\)
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Question 8 of 49
8. Question
P, Q and R are subsets of the universal set U. The Venn diagram showing the relationship \( \scriptsize (P \cap Q) \cup R \: is \)
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Question 9 of 49
9. Question
If P = {x: x is odd, – 1 < x ≤ 20} and Q = {y: y is prime; 2< y < 25}, find P n Q
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Question 10 of 49
10. Question
If \( \scriptsize S = \sqrt{t^2 \: – \: 4t \: + \: 4} \)
find t in terms of S
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Question 11 of 49
11. Question
If x – 4 is a factor of \( \scriptsize x^2 \: \: x \: – \: k \)
then k is
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Question 12 of 49
12. Question
The remainder when 6p^{3} – p^{2} – 47p + 30 is divided by p – 3 is
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Question 13 of 49
13. Question
P varies jointly as m and u, and varies inversely as q. Given that p = 4, m = 3 and u = 2 and q = 1, find the value of p when m = 6, u = 4 and q = ^{8}/_{5}
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Question 14 of 49
14. Question
If r varies inversely as the square root of s and t, how does s vary with r and t?
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Question 15 of 49
15. Question
Evaluate 3(x + 2) > 6(x + 3)
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Question 16 of 49
16. Question
The graph shown is correctly represented by
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Question 17 of 49
17. Question
Solve for x : x – 2<3
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Question 18 of 49
18. Question
If the sum of the first two terms of a G.P. is 3 and the sum of the second and the third terms is 6. Find the sum of the first term and the common ratio.
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Question 19 of 49
19. Question
The nth term of the progression \( \normalsize\frac{4}{2} \scriptsize, \: \normalsize\frac{7}{3} \scriptsize, \: \normalsize\frac{10}{4} \scriptsize, \: \normalsize\frac{13}{5} \scriptsize, \: is \)
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Question 20 of 49
20. Question
If a binary operation * is defined by x * y = x + 2y, find 2*(3*4)
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Question 21 of 49
21. Question
If P = \( \scriptsize \begin{pmatrix} 5 & 3 \\ 2 & 1 \end{pmatrix} \)
and Q = \( \scriptsize \begin{pmatrix} 4 & 2 \\ 3 & 5 \end{pmatrix} \)
Find 2P + Q
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Question 22 of 49
22. Question
Find the inverse of \( \scriptsize \begin{pmatrix} 5 & 3 \\ 6 & 4 \end{pmatrix} \)
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Question 23 of 49
23. Question
In the diagram given, find the value of x.
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Question 24 of 49
24. Question
The value x in the figure given is
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Question 25 of 49
25. Question
If the angles of a quadrilateral are (3 y + 10)°, (2 y +30)°, (y + 20)° and 4y°, find the value of y.
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Question 26 of 49
26. Question
A square tile has side 30cm. How many of these tiles will cover a rectangular floor of length 7.2m and width 4.2m?
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Question 27 of 49
27. Question
Find the length of a chord which subtends an angle of 90° at the centre of a circle whose radius is 8 cm.
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Question 28 of 49
28. Question
A chord of a circle subtends an angle of 120° at the centre of a circle of diameter 4√3 cm. Calculate the area of the major sector.
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Question 29 of 49
29. Question
The locus of the points which is equidistant from the line PQ forms a
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Question 30 of 49
30. Question
If the midpoint of the line PQ is (2, 3) and the point P is (2, 1), find the coordinate of the point Q.
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Question 31 of 49
31. Question
Find the equation of the perpendicular bisector of the line joining P(2, 3) to Q(5, 1)
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Question 32 of 49
32. Question
In triangle PQR, q = 8 cm, r = 6 cm and cos P = \( \frac{1}{12} \)
Calculate the value of p.
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Question 33 of 49
33. Question
If tanθ = \( \frac{3}{4} \)^{ }
find the value of \( \scriptsize sin \theta \: + \: cos \theta \)
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Question 34 of 49
34. Question
If y = x sin x
Find \( \frac{dx}{dy} \)
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Question 35 of 49
35. Question
If y = (2x + 2)^{3}
Find \( \frac{dx}{dy} \)
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Question 36 of 49
36. Question
What is the probability that an integer x (1≤ x ≤ 25) chosen at random is divisible by both 2 and 3?
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Question 37 of 49
37. Question
The radius of a circle is increasing at the rate of 0.02 cms^{1}. Find the rate at which the area is increasing when the radius of the circle is 7 cm.
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Question 38 of 49
38. Question
Integrate \(\frac{1\:+\:x}{x^3} \scriptsize dx \)
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Question 39 of 49
39. Question
Evaluate \(\scriptsize \int_{0} ^{\frac{\pi}{2}} \sin x \mathrm d x \)
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Question 40 of 49
40. Question
The bar chart above shows the allotment of time (in minutes) per week for selected subjects in a certain school. What is the total time allocated to the six subjects per week?
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Question 41 of 49
41. Question
In how many ways can a student select 2 subjects from 5 subjects
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Question 42 of 49
42. Question
The pie chart above shows the statistical distribution of 80 students in five subjects in an examination. Calculate how many students offer Mathematics.
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Question 43 of 49
43. Question
Find the mean of t + 2, 2t – 4, 3t + 2 and 2t.
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Question 44 of 49
44. Question
The mean of seven numbers is 10. If six of the numbers are 2, 4, 8, 14, 16 and 18, find the mode.
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Question 45 of 49
45. Question
\( \scriptsize \begin{array}{cc}Age & 20 & 25 & 30 & 35 & 40 & 45 \\ \hline \text{No. of people} & 3 & 5 & 1 & 1 & 2 & 3 \end{array} \)
Calculate the median age of the frequency distribution in the table above
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Question 46 of 49
46. Question
If the variance of 3 + x, 6. 4, x, and 7 – x is 4 and the mean is 5. Find the standard deviation.
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Question 47 of 49
47. Question
\(\scriptsize \begin{array}{cc} Score & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ \hline Frequency & 1 & 0 & 7 & 5 & 2 & 3 & 1 & 1 \end{array} \)
The table above shows the scores of 20 students in further mathematics test. What is the range of the distribution?
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Question 48 of 49
48. Question
In how many ways can three seats be occupied if 5 people are willing to sit?
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Question 49 of 49
49. Question
A basket contains 9 apples, 8 bananas, and 7 oranges. A fruit is picked from the basket, find the probability that it is neither an apple nor orange.
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