JAMB - Mathematics (2023)

1
How many different 8 letter words are possible using the letters of the word SYLLABUS?
תְשׁוּבָה
(C)
\(\frac{8!}{2! 2!}\)
2
Evaluate: 16\(^{0.16}\) × 16\(^{0.04}\) × 2\(^{0.2}\)
תְשׁוּבָה
(A)
2
3
Let '*' and '^' be two binary operations such that a * b = a\(^2\)b and a ^ b = 2a + b. Find (-4 * 2) ^ (7 * -1).
תְשׁוּבָה
(D)
15
4
Evaluate \(\int_0^1 4x - 6\sqrt[3] {x^2}dx\)
תְשׁוּבָה
(B)
- \(\frac{8}{5}\)
5
The population of a village decreased from 1,230 to 1,040 due to breakout of an epidemic. What is the percentage decrease in the population?
תְשׁוּבָה
(D)
15.45%
6
The interior angle of a regular polygon is five times the size of its exterior angle. Identify the polygon.
תְשׁוּבָה
(A)
dodecagon
7
The area A of a circle is increasing at a constant rate of 1.5 cm\(^2s^{-1}\). Find, to 3 significant figures, the rate at which the radius r of the circle is increasing when the area of the circle is 2 cm\(^2\).
תְשׁוּבָה
(D)
0.299 cms\(^{-1}\)
8
Make x the subject of the formula: y = \(\frac {3x - 9c}{4x + 5d}\)
תְשׁוּבָה
(D)
x = \(\frac {-(9c + 5dy)}{4y - 3}\)
9
Solve for x: 3(x – 1) ≤ 2 (x – 3)
תְשׁוּבָה
(A)
x ≤ -3
10

The diagram above is a circle with centre C. P, Q and S are points on the circumference. PS and SR are tangents to the circle. ∠PSR = 36\(^o\). Find ∠PQR
תְשׁוּבָה
(A)
72\(^0\)
11
If a car runs at a constant speed and takes 4.5 hrs to run a distance of 225 km, what time will it take to run 150 km?
תְשׁוּבָה
(C)
3 hrs
12
Divide 1101001\(_{two}\) by 101\(_{two}\)
תְשׁוּבָה
(D)
10101\(_{two}\)
13
If \(\frac {3 - \sqrt 3}{2 + \sqrt 3} = a + b\sqrt 3\), what are the values a and b?
תְשׁוּבָה
(A)
a = 9, b = -5
14
Find the value of t, if the distance between the points P(–3, –14) and Q(t, –5) is 9 units.
תְשׁוּבָה
(C)
- 3
15
At simple interest, a man made a deposit of some money in the bank. The amount in his bank account after 10 years is three times the money deposited. If the interest rate stays the same, after how many years will the amount be five times the money deposited?
תְשׁוּבָה
(C)
20 years
16
Evaluate the following limit: \(lim_{x\to2} \frac {x^2 + 4x - 12}{x^2 - 2x}\)
תְשׁוּבָה
(A)
4
17
The ages of students in a small primary school were recorded in the table below.

Age 5 - 6 7 - 8 9 -10

Frequency 29 40 38

Estimate the mean
תְשׁוּבָה
(A)
7.7
18
A committee of 5 people is to be chosen from a group of 6 men and 4 women. How many committees are possible if there is to be a majority of women?
תְשׁוּבָה
(C)
66
19
If D = \(\begin{bmatrix}2& -1&3\\4&1&2\\1&-3&1\\\end{bmatrix}\)

Find |D|
תְשׁוּבָה
(C)
-23
20
A boat sails 8 km north from P to Q and then sails 6 km west from Q to R. Calculate the bearing of R from P. Give your answer to the nearest degree.
תְשׁוּבָה
(B)
323\(^o\)
21
A coin is thrown 3 times. What is the probability that atleast one head is obtained?
תְשׁוּבָה
(A)
\(\frac {7}{8}\)
22
Find the equation of straight line passing through (2, 3) and perpendicular to the line \(3x + 2y + 4 = 0\)
תְשׁוּבָה
(D)
3y = 2x + 5
23
Differentiate the function y = \(\sqrt[3]{x^2}(2x - x^2)\)
תְשׁוּבָה
(B)
\(\frac {dy}{dx} = \frac {10x^{2/3}}{3} - \frac {8x^{5/3}}{3}\)
24
Calculate the mean deviation of the first five prime numbers.
תְשׁוּבָה
(A)
2.72
25
Determine the area of the region bounded by y = \(2x^2\) + 10 and Y = \(4x + 16\).
תְשׁוּבָה
(D)
\(\frac {64}{3}\)
26
Find the value of y if \(402_y = 102_{ten}\)
תְשׁוּבָה
(C)
5
27
Find the value of y, if log (y + 8) + log (y - 8) = 2log 3 + 2log 5
תְשׁוּבָה
(C)
y = ±17
28
In a group of 500 people, 350 people can speak English, and 400 people can speak French. Find how many people can speak both languages.
תְשׁוּבָה
(C)
250
29
Factorize: \(16x^4 - y^4\)
תְשׁוּבָה
(A)
\((2x - y)(2x + y)(4x^2 + y^2)\)
30
If A = { 1, 2, 3, 4, 5, 6}, B = { 2, 4, 6, 8 }. Find (A – B) ⋃ (B – A).
תְשׁוּבָה
(A)
{1, 3, 5, 8}
31
A bag contains 8 red balls and some white balls. If the probability of drawing a white ball is half of the probability of drawing a red ball then find the probability of drawing a red ball and a white ball if the balls are drawn without replacement.
תְשׁוּבָה
(D)
\(\frac {8}{33}\)
32
The ages of students in a small primary school were recorded in the table below.

Age 5-6 7-8 9-10

Frequency 29 40 38

Estimate the median.
תְשׁוּבָה
(A)
7.725
33
Find the matrix A

A \(\begin {bmatrix} 0 & 1\\2 & -1 \end {bmatrix}\) = \(\begin {bmatrix} 2 & -1\\1 & 0 \end {bmatrix}\)

תְשׁוּבָה
(B)
\(\begin {bmatrix} 0 & 1\\^1/_2 & ^1/_2 \end {bmatrix}\)
34
How many students scored at least 25%
תְשׁוּבָה
(A)
16
35
If \(-2x^3 + 6x^2 + 17x\) - 21 is divided by \((x + 1)\), then the remainder is
תְשׁוּבָה
(C)
-30
36
Let a binary operation '*' be defined on a set A. The operation will be commutative if
תְשׁוּבָה
(A)
a*b = b*a
37
Solve the following quadratic inequality: \(x^2 - x\) - 4 ≤ 2
תְשׁוּבָה
(B)
\(-2 ≤ x ≤ 3\)
38
What is the general term of the sequence 3, 8, 13, 18, ...?
תְשׁוּבָה
(A)
5n - 2
39
The locus of a point equidistant from two intersecting lines is
תְשׁוּבָה
(D)
pair of bisectors of the angles between the two lines
40
Two numbers are respectively 35% and 80% more than a third number. The ratio of the two numbers is
תְשׁוּבָה
(B)
3 : 4
41
The angle of elevation and depression of the top and bottom of another building, measured from the top of a 24 m tall building, is 30° and 60°, respectively. Determine the second building's height.
תְשׁוּבָה
(D)
32 m
42
Calculate, correct to three significant figures, the length AB in the diagram above.
תְשׁוּבָה
(C)
36.2 cm
43
An article when sold for ₦230.00 makes a 15% profit. Find the profit or loss % if it was sold for ₦180.00
תְשׁוּבָה
(B)
10% loss
44
Calculate, correct to three significant figures, the length of the arc AB in the diagram above.
[Take \(\pi = ^{22}/_7\)]
תְשׁוּבָה
(B)
30.6 cm
45
A rectangular plot of land has sides with lengths of 38 m and 52 m corrected to the nearest m. Find the range of the possible values of the area of the rectangle
תְשׁוּבָה
(A)
1931.25 m\(^2\) ≤ A < 2021.25 m\(^2\)
46
A man sells different brands of an items. \(^1/_9\) of the items he has in his shop are from Brand A, \(^5/_8\) of the remainder are from Brand B and the rest are from Brand C. If the total number of Brand C items in the man's shop is 81, how many more Brand B items than Brand C does the shop has?
תְשׁוּבָה
(C)
54
47
Find the area, to the nearest cm\(^2\), of the triangle whose sides are in the ratio 2 : 3 : 4 and whose perimeter is 180 cm.
תְשׁוּבָה
(A)
1162 cm\(^2\)
48
Find the compound interest (CI) on ₦15,700 for 2 years at 8% per annum compounded annually.
תְשׁוּבָה
(D)
₦2,612.48
49
Find the volume of the cylinder above
[Take \(\pi= ^{22}/_7\)]
תְשׁוּבָה
(B)
14,784 cm\(^3\)
50
The third term of an A.P is 6 and the fifth term is 12. Find the sum of its first twelve terms
תְשׁוּבָה
(C)
198
51
Express 16.54 x 10\(^{-5}\) - 6.76 x 10\(^{-8}\) + 0.23 x 10\(^{-6}\) in standard form
תְשׁוּבָה
(A)
1.66 x 10\(^{-4}\)
52
The graph above depicts the performance ratings of two sports teams A and B in five different seasons

In the last five seasons, what was the difference in the average performance ratings between Team B and Team A?
תְשׁוּבָה
(A)
1.2
53
A student is using a graduated cylinder to measure the volume of water and reports a reading of 18 mL. The teacher reports the value as 18.4 mL. What is the student's percent error?
תְשׁוּבָה
(A)
2.17%
54
The difference between an exterior angle of (n - 1) sided regular polygon and an exterior angle of (n + 2) sided regular polygon is 6\(^o\), then the value of "n" is
תְשׁוּבָה
(B)
13
55
Two dice are tossed. What is the probability that the total score is a prime number.
תְשׁוּבָה
(A)
\(\frac{5}{12}\)
56
Find the volume of the composite solid above.
תְשׁוּבָה
(B)
2568 cm\(^3\)
57
Find the area and perimeter of a square whose length of diagonals is 20\(\sqrt2\) cm.
תְשׁוּבָה
(D)
400 cm\(^2\), 80 cm
58
Bello buys an old bicycle for ₦9,200.00 and spends ₦1,500.00 on its repairs. If he sells the bicycle for ₦13,400.00, his gain percent is
תְשׁוּבָה
(A)
25.23%
59
Evaluate \(\frac{5}{8} - \frac{3}{4} ÷ \frac{5}{12} \times \frac{1}{4}\)
תְשׁוּבָה
(C)
\(\frac{7}{40}\)
60
A rectangle has one side that is 6 cm shorter than the other. The area of the rectangle will increase by 68 cm\(^2\) if we add 2 cm to each side of the rectangle. Find the length of the shorter side.
תְשׁוּבָה
(C)
13 cm
61
The second term of a geometric series is \(^{-2}/_3\) and its sum to infinity is \(^3/_2\). Find its common ratio.
תְשׁוּבָה
(A)
\(^{-1}/_3\)
62
Find the value of the angle marked x in the diagram above

תְשׁוּבָה
(A)
60\(^0\)
63
The line \(3y + 6x\) = 48 passes through the points A(-2, k) and B(4, 8). Find the value of k.
תְשׁוּבָה
(B)
20
64
Tickets for the school play were priced at ₦520.00 each for adults and ₦250.00 each for kids. How many kids' tickets were sold if the total sales were ₦171,000.00 and there were 5 times as many adult tickets sold as children's tickets?
תְשׁוּבָה
(D)
60
65
Solve the logarithmic equation: \(log_2 (6 - x) = 3 - log_2 x\)

תְשׁוּבָה
(A)
\(x\) = 4 or 2
66
Calculate the area of the composite figure above.
תְשׁוּבָה
(B)
3969 m\(^2\)
67
Find the value of x in the diagram above
תְשׁוּבָה
(A)
10 units
68
Which inequality describes the graph above?
תְשׁוּבָה
(B)
\(5y + 4x ≤ 20\)
69
Find the volume of a cone which has a base radius of 5 cm and slant height of 13 cm.
תְשׁוּבָה
(D)
\(100\pi\) cm\(^3\)
70
Study the given histogram above and answer the question that follows.

What is the total number of students that scored at most 50 marks?
תְשׁוּבָה
(C)
360
71
The area of a trapezium is 200 cm\(^2\). Its parallel sides are in the ratio 2 : 3 and the perpendicular distance between them is 16 cm. Find the length of each of the parallel sides.
תְשׁוּבָה
(A)
10 cm and 15 cm
72
PQRS is a cyclic quadrilateral. Find \(x\) + \(y\)
תְשׁוּבָה
(D)
0
73
A student pilot was required to fly to an airport and then return as part of his flight training. The average speed to the airport was 120 km/h, and the average speed returning was 150 km/h. If the total flight time was 3 hours, calculate the distance between the two airports.
תְשׁוּבָה
(B)
200 km
74
The perimeter of an isosceles right-angled triangle is 2 meters. Find the length of its longer side.
תְשׁוּבָה
(D)
-2 + 2\(\sqrt2\) m
75
A ship sets sail from port A (86\(^o\)N, 56\(^o\)W) for port B (86\(^o\)N, 64\(^o\)W), which is close by. Find the distance the ship covered from port A to port B, correct to the nearest km.

[Take \(\pi\) = 3.142 and R = 6370 km]
תְשׁוּבָה
(A)
62 km

Age	5 - 6	7 - 8	9 -10
Frequency	29	40	38

Age	5-6	7-8	9-10
Frequency	29	40	38