Make q the subject of the formula in the equation \(\frac{mn}{a^2} - \frac{pq}{b^2} = 1\)
Sagot
(A)
\(q = \frac{b^2(mn - a^2)}{a^2 p}\)
2
The angle of elevation of the top of a tree from a point on the ground 60m away from the foot of the tree is 78°. Find the height of the tree correct to the nearest whole number.
Sagot
(C)
282m
3
A binary operation \(\otimes\) is defined by \(m \otimes n = mn + m - n\) on the set of real numbers, for all m, n \(\in\) R. Find the value of 3 \(\otimes\) (2 \(\otimes\) 4).
Sagot
(C)
15
4
Age in years
7
8
9
10
11
No of pupils
4
13
30
44
9
The table above shows the number of pupils in a class with respect to their ages. If a pie chart is constructed to represent the age, the angle corresponding to 8 years old is
Sagot
(C)
46.8°
5
In a class of 50 students, 40 students offered Physics and 30 offered Biology. How many offered both Physics and Biology?
If P varies inversely as the square root of q, where p = 3 and q = 16, find the value of q when p = 4.
Sagot
(C)
9
32
Tade bought 200 mangoes at 4 for ₦2.50. 30 out of the mangoes got spoilt and the remaining were sold at 2 for ₦2.40. Find the percentage profit or loss.
Sagot
(C)
63.2% profit
33
The simple interest on ₦8550 for 3 years at x% per annum is ₦4890. Calculate the value of x to the nearest whole number.
Sagot
(A)
19%
34
Simplify 81\(^{\frac{-3}{4}}\) x 25\(^{\frac{1}{2}}\) x 243\(^{\frac{2}{5}}\)
Sagot
(D)
\(\frac{5}{3}\)
35
Find the value of \(\frac{(0.5436)^3}{0.017 \times 0.219}\) to 3 significant figures.
Sagot
(B)
43.1
36
If S = (4t + 3)(t - 2), find ds/dt when t = 5 secs.
Sagot
(B)
35 units per sec
37
The angles of a polygon are given by 2x, 5x, x and 4x respectively. The value of x is
Sagot
(B)
30°
38
The weight of a day-old chick was measured to be 0.21g. If the actual weight of the chick is 0.18g, what was the percentage error in the measurement?
Sagot
(D)
16.7%
39
Evaluate \((\frac{6}{0.32} \div \frac{2}{0.084})^{-1}\) correct to 1 decimal place.
Sagot
(A)
1.3
40
If 2\(^{x + y}\) = 16 and 4\(^{x - y} = \frac{1}{32}\), find the values of x and y.
Sagot
(B)
x = \(\frac{3}{4}\), y = \(\frac{13}{4}\)
41
Simplify \(\frac{0.0839 \times 6.381}{5.44}\) to 2 significant figures.
Sagot
(D)
0.098
42
Find the value of x and y in the simultaneous equation: 3x + y = 21; xy = 30
Sagot
(C)
x = 2 or 5, y = 15 or 6
43
Points X and Y are 20km North and 9km East of point O, respectively. What is the bearing of Y from X? Correct to the nearest degree.
Sagot
(D)
156°
44
If \(P = (\frac{Q(R - T)}{15})^{\frac{1}{3}}\), make T the subject of the formula.
Sagot
(B)
\(T = R - \frac{15P^3}{Q}\)
45
In the diagram above, O is the centre of the circle ABC, < ABO = 26° and < BOC = 130°. Calculate < AOC.
Sagot
(D)
102°
46
Each of the interior angles of a regular polygon is 140°. Calculate the sum of all the interior angles of the polygon.
Sagot
(B)
1260°
47
A man bought a car newly for ₦1,250,000. He had a crash with the car and later sold it at the rate of ₦1,085,000. What is the percentage gain or loss of the man?
Sagot
(C)
13.2% loss
48
If the volume of a frustrum is given as \(V = \frac{\pi h}{3} (R^2 + Rr + r^2)\), find \(\frac{\mathrm d V}{\mathrm d R}\).
Sagot
(A)
\(\frac{\pi h}{3} (2R + r)\)
49
Express \((0.0439 \div 3.62)\) as a fraction.
Sagot
(C)
\(\frac{12}{1000}\)
50
If \(25^{1 - x} \times 5^{x + 2} \div (\frac{1}{125})^{x} = 625^{-1}\), find the value of x.
Sagot
(A)
x = -4
51
A bricklayer charges ₦1,500 per day for himself and ₦500 per day for his assistant. If a two bedroom flat was built for ₦95,000 and the bricklayer worked 10 days more than his assistant, how much did the assistant receive?
Sagot
(A)
N20,000
52
Find the equation of the locus of a point A(x, y) which is equidistant from B(0, 2) and C(2, 1)
Sagot
(C)
4x - 2y = 1
53
A factory worker earns ₦50,000 per month out of which he spends 15% on his children's education, ₦13,600 on Food, 3% on electricity and uses the rest for his personal purpose. How much does he have left?
Sagot
(C)
N27,400
54
A binary operation Δ is defined by a Δ b = a + 3b + 2.
Find (3 Δ 2) Δ 5
Sagot
(C)
28
55
If M varies directly as N and inversely as the root of P. Given that M = 3, N = 5 and P = 25. Find the value of P when M = 2 and N = 6.
Sagot
(D)
81
56
This table below gives the scores of a group of students in a Further Mathematics Test.
Score
1
2
3
4
5
6
7
Frequency
4
6
8
4
10
6
2
Find the mode of the distribution.
Sagot
(C)
5
57
This table below gives the scores of a group of students in a Further Mathematics Test.
