2022 - JAMB Mathematics Past Questions and Answers - page 3
If a poultry farmer realized 200 eggs from his birds and sold 5 \(\frac{1}{2}\) crates of eggs, what percentages of eggs are left?
82.5%
15%
17.5%
85%
5 crates = 30 eggs * 5
= 150eggs
1/2 crate = 15 eggs
total sold = 165
remainder = 200 - 165 = 35 => 17.5% of the realized eggs
Given sec\(^2\)θ + tan\(^2\)θ = 3, find the angle θ
90º
30º
45º
60º
sec\(^2\)θ + tan\(^2\)θ = 3
sec\(^2\)θ = 1 + tan\(^2\)θ
: Hence,
1 + tan\(^2\)θ + tan\(^2\)θ = 3
2tan\(^2\)θ = 3 - 1
2tan\(^2\)θ = 2
divide through by 2
tan\(^2\)θ = 1
tanθ = √1
tanθ = 1
θ = tan\(^{-1}\) (1)
θ = 45º
Find the limit of y = \(\frac{x^3 + 6x - 7}{x-1}\) as x tends to 1
9
8
0
7
\(\frac{x^3 + 6x - 7}{x-1}\):
When numerator is differentiated => 3x\(^2\) + 6
When the denominator is differentiated => 1
Hence,
\(\frac{3x^2 + 6}{1}\)
Substitute x for 1
\(\frac{3 * 1^2 + 6}{1}\) = \(\frac{3 + 6}{1}\)
= \(\frac{9}{1}\)
= 9
Find the equation of a straight line parallel to the line 2x - y = 5 and having intercept of 5
2x + y = 5
2x + y = -5
2x - y = -5
2x - y = 5
If two lines are parallel then their slopes (gradients) will be equal.
Line 2x - y = 5
Equation of a straight line: y = mx + c
y = 2x - 5
line 2x - y = 5 has a gradient of 2
A parallel line with a gradient of 2 and intercept of 5
=> 2x - y = -5
=> y = 2x + 5
Calculate the median of 14, 17, 10, 13, 18 and 10.
12.5
13.5
13.2
14.5
14, 17, 10, 13, 18 and 10.
=> 10, 10, 13, 14, 17, 18
median = \(\frac{13+14}{2}\)
= \(\frac{27}{2}\) or 13.5
Find the equivalence of (10110.011)\(_2\) in base 10
26.325
24.372
42.443
22.375
Apply the expansion method on (10110.011)\(_2\)
(1 * 2\(^4\)) + (0 * 2\(^3\)) + (1 * 2\(^2\)) + (1 * 2\(^1\)) (0 * 2\(^0\)) + (0 * 2\(^{-1}\)) + (1 * 2\(^{-2}\)) + (1 * 2\(^{-3}\))
(1*16) + 0 (1*4) + (1*2) + 0 + 0 + (1*\(\frac{1}{4}\)) + (1*\(\frac{1}{8}\))
16 + 4 + 2 + (0.25 + 0.125)
22 + 0.375
(10110.011)\(_2\) = 22.375\(_{10}\)
Given that 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?
3000
1000
2000
4000
if 20 students = 10000
₦500 per student
₦1,000,000 ÷ 500
= 2,000 students
The coordinates of the midpoint of the line joining the points (-3,5) and (2,10) is given by?
( \(\frac{1}{2}\), \(\frac{15}{2}\) )
( \(\frac{1}{2}\), \(\frac{-15}{2}\) )
( \(\frac{-1}{2}\), \(\frac{-15}{2}\) )
( \(\frac{-1}{2}\), \(\frac{15}{2}\) )
Given that x\(_1\) = -3, x\(_2\) = 2, y\(_1\) = 5, y\(_2\) = 10
Coordinates of the midpoint of the line = (\(\frac{x_1 + x_2}{2}\) , \(\frac{y_1 + y_2}{2}\))
(\(\frac{-3 +2}{2}\) , \(\frac{5 + 10}{2}\))
= \(\frac{-1}{2}\)) , \(\frac{15}{2}\))
Evaluate \(^{n^2 + 1}\)C\(_{n+5}\) if n = 3
55
45
35
25
\(^{3^2 + 1}\)C\(_{3+5}\)
\(^{9 + 1}\)C\(_{3+5}\)
\(^{10}\)C\(_{8}\) = \(\frac{10!}{8! 2!}\)
\(\frac{10 * 9 * 8!}{8! 2!}\) = \(\frac{10 * 9}{2}\)
= 45
Given that S = \(3t^{2}\) + 5t - 10 is the displacement of a particle in metres, calculate its initial velocity.
10m/s
2m/s
5m/s
6m/s