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JAMB - Mathematics (2022)

1
Solve for k in the equation \(\frac{1}{8}^{k+2}\) = 1
Answer
(C)
-2
2
Evaluate \((101_{two})^3\)
Answer
(C)
\(1111101_{two}\)
3

The shaded portion in the venn diagram above represents?

Answer
(B)
E' n F n G'
4
If a fair coin is tossed twice, what is the probability of obtaining at least one head?
Answer
(B)
0.75
5
If the mean of 2, 5, (x+1), (x+2), 7 and 9 is 6. Find the median 
Answer
(C)
6.5
6
If sin θ = -  \(\frac{3}{5}\) and θ lies in the third quadrant, find cos θ
Answer
(D)
- \(\frac{4}{5}\)
7
Simplify \(\frac{1}{3-√2}\) in the form of p + q√2
Answer
(D)
\(\frac{3}{7}\) + \(\frac{√2}{7}\)
8
Find the length of a chord 3cm from the centre of a circle of radius 5cm
Answer
(A)
8cm
9

Mr Adu spends his annual salary on food(f), rent(r), car maintenance, gifts(g), savings(s) and some miscellaneous (m) as indicate in the table below:

F R C G S M
28% 15% 20% 14% 10% 13%

If the above information is represented on a pie chart. What angle represents his spending on food?

Answer
(B)
100.8
10
A rectangular pyramid has an area 24cm\(^2\) and height 7.5cm. Find its volume?
Answer
(D)
60.0cm\(^3\)
11
The 10th term of an AP is 32. If the first term is 3/2, what is the 4th term?
Answer
(A)
35/3
12

In the diagram above angle LNM and angle YNZ are represented by g and h respectively. Find ∠MNY

Answer
(A)
180º - gº - hº
13
In how many ways can the letter of ZOOLOGY be arranged?
Answer
(C)
840
14
Integrate (2x+1)\(^3\)
Answer
(B)
\(\frac{{2x+1}^4}{8}\) + C
15
If A = \(\begin{pmatrix} 2 & 1 \\ 2 & 3 \\ 1 & 2 \end{pmatrix}\) and B = \(\begin{pmatrix} 3 & 2 \\ 4 & 2 \end{pmatrix}\). Find AB
Answer
(D)
\(\begin{pmatrix} 10 & 6 \\ 18 & 10 \\ 11 & 6 \end{pmatrix}\)
16
Given that r = \( \sqrt \frac{3v}{\pi h} \), make v the subject of the formula
Answer
(C)
v =  \(\frac{πr^2h}{3}\)
17
Find the determinant of the matrix A = \(\begin{pmatrix} 2 & 3 \\ 1 & 3 \end{pmatrix}\)
Answer
(D)
3
18
Evaluate Log\(_2\) 8√2
Answer
(C)
3.5
19
The locus of points equidistant from a fixed point.
Answer
(A)
circle
20
What will be the result obtained when the numerator of \(\frac{96}{50}\) is decreased by 37.5% and its denominator decreased by 20%.
Answer
(A)
1.5
21
A poultry farmer realized 200 eggs from his birds and sold 5 \(\frac{1}{2}\) crates of eggs. What percentages of eggs are left?
Answer
(C)
17.5%
22
If sec\(^2\)θ + tan\(^2\)θ = 3, then the angle θ is equal to?
Answer
(C)
45º
23
find the limit of y = \(\frac{x^3 + 6x - 7}{x-1}\) as x tends to 1
Answer
(A)
9
24
Find the equation of a straight line parallel to the line 2x - y = 5 and having intercept of 5
Answer
(C)
2x - y = -5
25
Calculate the median of 14, 17, 10, 13, 18 and 10.
Answer
(B)
13.5
26
The equivalent of (10110.011)\(_2\) in base 10 is?
Answer
(D)
22.375
27
The cost C of running a school is directly proportional to the number of students N, if 20 students cost #10,000, How many students can #1,000,000 cover?
Answer
(C)
2000
28
The coordinates of the mid-point of the line joining the points (-3,5) and (2,10) is given by? 
Answer
(D)
( \(\frac{-1}{2}\), \(\frac{15}{2}\) )
29
Evaluate \(^{n^2 + 1}\)C\(_{n+5}\) if n = 3 
Answer
(B)
45
30
Given that S = \(3t^{2}\) + 5t - 10 is displacement of a particle in metres, calculate it initial velocity.
Answer
(C)
5m/s
31

 

In the diagram above, XY = 8cm and OX = 5cm. Find Oz

 

Answer
(D)
3cm
32
Let (*) be a binary operation on a natural number defined by a * b = a - b + (ab)\(^2\), then find 3 * 5
Answer
(A)
223
33

If y varies inversely as x and x = 3 when y =4. Find the value of x when y = 12

 

Answer
(B)
1
34
If 8, p, q and 26 is an A.P. Find the values of p and q
Answer
(D)
p = 14 and q = 20
35
Find x if the mean of 2x, 4x, 2x - 13 and 6x is 4.
Answer
(B)
2.0