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JAMB - Mathematics (2019)

1
Make q the subject of the formula in the equation \(\frac{mn}{a^2} - \frac{pq}{b^2} = 1\)
Answer
(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.
Answer
(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).
Answer
(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

Answer
(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?
Answer
(B)
20
6
Rationalize \(\frac{\sqrt{2} + \sqrt{3}}{\sqrt{2} - \sqrt{3}}\)
Answer
(A)
\(-5 - 2\sqrt{6}\)
7

Find the length of the chord |AB| in the diagram shown above.

Answer
(D)
3.4 cm
8
Given \(\sin 58° = \cos p°\), find p.
Answer
(C)
32°
9
\(\frac{\frac{2}{3} \div \frac{4}{5}}{\frac{1}{4} + \frac{3}{5} - \frac{1}{3}}\)
Answer
(D)
\(\frac{50}{31}\)
10
If \(6x^3 + 2x^2 - 5x + 1\) divides \(x^2 - x - 1\), find the remainder.
Answer
(A)
9x + 9
11
If a fair coin is tossed 3 times, what is the probability of getting at least two heads?
Answer
(D)
\(\frac{1}{2}\)
12
In how many ways can the word MATHEMATICIAN be arranged?
Answer
(D)
129729600 ways
13
Given matrix M = \(\begin{vmatrix} -2 & 0 & 4 \\ 0 & -1 & 6 \\ 5 & 6 & 3 \end{vmatrix}\), find \(M^{T} + 2M\)
Answer
(B)
\(\begin{vmatrix} -6 & 0 & 13\\ 0 & -3 & 18 \\ 14 & 18 & 9 \end{vmatrix}\)
14
Score (x) 0 1 2 3 4 5 6
Freq (f) 5 7 3 7 11 6 7

Find the mean of the data.

 

Answer
(A)
3.26
15
Score (x) 0 1 2 3 4 5 6
Freq (f) 5 7 3 7 11 6 7

Find the variance

 

Answer
(D)
3.72
16
The locus of a point which moves so that it is equidistant from two intersecting straight lines is the
Answer
(C)
angle bisector of the two lines
17

From the cyclic quadrilateral MNOP above, find the value of x.

Answer
(D)
39°
18
If \(4\sin^2 x - 3 = 0\), find the value of x, when 0° \(\leq\) x \(\leq\) 90°
Answer
(C)
60°
19

In the figure above, |CD| is the base of the triangle CDE. Find the area of the figure to the nearest whole number.

Answer
(D)
34 cm\(^2\)
20

The marks scored by 30 students in a Mathematics test are recorded in the table below:

Scores (Mark) 0 1 2 3 4 5
No of students 4 3 7 8 6 2

What is the total number of marks scored by the children?

 

Answer
(D)
75
21
If given two points A(3, 12) and B(5, 22) on a x-y plane. Find the equation of the straight line with intercept at 2.
Answer
(A)
y = 5x + 2
22
If P(2, m) is the midpoint of the line joining Q(m, n) and R(n, -4), find the values of m and n.
Answer
(A)
m = 0, n = 4
23
If \(\begin{vmatrix} 2 & -4 \\ x & 9 \end{vmatrix} = 58\), find the value of x.
Answer
(A)
10
24
If \(y = 6x^3 + 2x^{-2} - x^{-3}\), find \(\frac{\mathrm d y}{\mathrm d x}\).
Answer
(C)
\(\frac{\mathrm d y}{\mathrm d x} = 18x^2 - 4x^{-3} + 3x^{-4}\)
25
\(\frac{d}{dx} [\log (4x^3 - 2x)]\) is equal to
Answer
(D)
\(\frac{12x^2 - 2}{4x^3 - 2x}\)
26
If \(f(x) = 3x^3 + 4x^2 + x - 8\), what is the value of f(-2)?
Answer
(C)
-18
27
Solve for x in \(\frac{4x - 6}{3} \leq \frac{3 + 2x}{2}\)
Answer
(B)
\(x \leq \frac{21}{2}\)
28
Solve the inequality: -7 \(\leq\) 9 - 8x < 16 - x
Answer
(D)
-1 < x \(\leq\) 2
29
The nth term of a sequence is given by 2\(^{2n - 1}\). Find the sum of the first four terms.
Answer
(D)
170
30
Integrate \(\int_{-1} ^{2} (2x^2 + x) \mathrm {d} x\)
Answer
(C)
\(7\frac{1}{2}\)
31
If P varies inversely as the square root of q, where p = 3 and q = 16, find the value of q when p = 4.
Answer
(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.
Answer
(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.
Answer
(A)
19%
34
Simplify 81\(^{\frac{-3}{4}}\) x 25\(^{\frac{1}{2}}\) x 243\(^{\frac{2}{5}}\)
Answer
(D)
\(\frac{5}{3}\)
35
Find the value of \(\frac{(0.5436)^3}{0.017 \times 0.219}\) to 3 significant figures.
Answer
(B)
43.1
36
If S = (4t + 3)(t - 2), find ds/dt when t = 5 secs.
Answer
(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
Answer
(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?
Answer
(D)
16.7%
39
Evaluate \((\frac{6}{0.32} \div \frac{2}{0.084})^{-1}\) correct to 1 decimal place.
Answer
(A)
1.3
40
If 2\(^{x + y}\) = 16 and 4\(^{x - y} = \frac{1}{32}\), find the values of x and y.
Answer
(B)
x = \(\frac{3}{4}\), y = \(\frac{13}{4}\)
41
Simplify \(\frac{0.0839 \times 6.381}{5.44}\) to 2 significant figures.
Answer
(D)
0.098
42
Find the value of x and y in the simultaneous equation: 3x + y = 21; xy = 30
Answer
(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.
Answer
(D)
156°
44
If \(P = (\frac{Q(R - T)}{15})^{\frac{1}{3}}\), make T the subject of the formula.
Answer
(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.

Answer
(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.
Answer
(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?
Answer
(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 \(\frac{\mathrm d V}{\mathrm d R}\).
Answer
(A)
\(\frac{\pi h}{3} (2R + r)\)
49
Express \((0.0439 \div 3.62)\) as a fraction.
Answer
(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.
Answer
(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?
Answer
(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)
Answer
(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?
Answer
(C)
N27,400
54
A binary operation Δ is defined by a Δ b = a + 3b + 2.
Find (3 Δ 2) Δ 5
Answer
(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.
Answer
(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.

Answer
(C)
5
57

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

Calculate the mean deviation for the distribution

Answer
(C)
1.51
58
Integrate \(\int (4x^{-3} - 7x^2 + 5x - 6) \mathrm d x\).
Answer
(A)
\(-2x^{-2} - \frac{7}{3}x^3 + \frac{5}{2} x^2 - 6x\)
59
Find the probability that a number selected at random from 21 to 34 is a multiple of 3
Answer
(C)
\(\frac{5}{14}\)
60
If the 3rd and 7th terms of a G.P are 9 and 1/9 respectively. Find the common ratio.
Answer
(A)
\(\frac{1}{3}\)
61
If the universal set μ = {x : 1 ≤ x ≤ 20} and
A = {y : multiple of 3}
B = |z : odd numbers}
Find A ∩ B
Answer
(C)
{3, 9, 15}
62
In a committee of 5, which must be selected from 4 males and 3 females. In how many ways can the members be chosen if it were to include 2 females?
Answer
(D)
12 ways
63
Find the value of k in the equation: \(\sqrt{28} + \sqrt{112} - \sqrt{k} = \sqrt{175}\)
Answer
(B)
7
64
Evaluate \(\frac{2\log_{3} 9 \times \log_{3} 81^{-2}}{\log_{5} 625}\)
Answer
(C)
-8
65
Find the value of x for \(\frac{2 + 2x}{3} - 2 \geq \frac{4x - 6}{5}\)
Answer
(C)
x \(\leq\) -1
66
Determine the values for which \(x^2 - 7x + 10 \leq 0\)
Answer
(D)
2 \(\leq\) x \(\leq\) 5
67
Find the polynomial if given q(x) = x\(^2\) - x - 5, d(x) = 3x - 1 and r(x) = 7.
Answer
(A)
3x\(^3\) - 4x\(^2\) - 14x + 12
68
If 2x\(^2\) + x - 3 divides x - 2, find the remainder.
Answer
(A)
7
69
If \(\begin{vmatrix} 2 & -5 & 3 \\ x & 1 & 4 \\ 0 & 3 & 2 \end{vmatrix} = 132\), find the value of x.
Answer
(B)
8
70
Given the matrix \(A = \begin{vmatrix} 3 & -2 \\ 1 & 6 \end{vmatrix}\). Find the inverse of matrix A.
Answer
(D)
\(\begin{vmatrix} \frac{3}{10} & \frac{1}{10} \\ \frac{-1}{20} & \frac{3}{20}\end{vmatrix}\)
71
If y = 8x\(^3\) - 3x\(^2\) + 7x - 1, find \(\frac{\mathrm d^2 y}{\mathrm d x^2}\).
Answer
(A)
48x - 6
72
Differentiate \(\frac{2x}{\sin x}\) with respect to x.
Answer
(D)
\(2\csc x(1 - x\cot x)\)
73
Find the distance between the points C(2, 2) and D(5, 6).
Answer
(D)
5 units
74
Find the equation of a line perpendicular to the line 4y = 7x + 3 which passes through (-3, 1)
Answer
(A)
7y + 4x + 5 = 0
75
Marks 1 2 3 4 5
Frequency 2y - 2 y - 1 3y - 4 3 - y 6 - 2y

The table above is the distribution of data with mean equals to 3. Find the value of y.

Answer
(B)
2