Mathematics 2021 Past Questions | JAMB
Study the following Mathematics past questions and answers for JAMB, WAEC NECO and Post-JAMB. Get prepared with official past questions and answers for upcoming examinations.
- Solve the following equation: \(\frac{2}{(2r – 1)}\) – \(\frac{5}{3}\) = \(\frac{1}{(r + 2)}\)
- A. ( 1,\(\frac{5}{2}\) )
- B. ( 1,-\(\frac{5}{2}\) )
- C. ( \(\frac{5}{2}\), 1 )
- D. (2,1)
Correct Option: Answer is B
Solution:
\(\frac{2}{(2r – 1)}\) – \(\frac{5}{3}\) = \(\frac{1}{(r + 2)}\)
\(\frac{2}{(2r – 1)}\) – \(\frac{1}{(r + 2)}\) = \(\frac{5}{3}\)
The L.C.M.: (2r – 1) (r + 2)
=> \(\frac{2(r + 2) – 1(2r – 1)}{(2r – 1) (r + 2)}\) = \(\frac{5}{3}\)
=> \(\frac{2r + 4 – 2r + 1}{ (2r – 1) (r + 2)}\) = \(\frac{5}{3}\)
cross multiply the solution
3 = (2r – 1) (r + 2) or 2r\(^2\) + 3r – 2
collect like terms
=> 2r\(^2\) + 3r – 2 – 3 = 0
=> 2r\(^2\) + 3r – 5 = 0
Factorize to get x = 1 or – \(\frac{5}{2}\)
2. In how many ways can 2 students be selected from a group of 5 students in a debating competition?
- A. 25 ways
- B. 10 ways
- C. 15 ways
- D. 20 ways
Correct Option: Answer is B
Solution:
Using combination method
In 5C2 ways =
\(In\hspace{1mm} ^{5}C_{2}\hspace{1mm}ways\hspace{1mm}=\frac{5!}{(5-2)!2!}\\=\frac{5!}{3!2!}\\=\frac{5\times4\times3!}{3!\times2\times1}\\=10\hspace{1mm}ways\)
3. What is the rate of change of the volume V of a hemisphere with respect to its radius r when r = 2?
- A. 8π
- B. 16π
- C. 2π
- D. 4π
Correct Option: Answer is A
Solution:
V = πr3
dV/dr= 2 πr2
dV/dr (r=2)2π(2)2 =8π
4. determine the maximum value of y=3x2+ 5x – 3
- A. 6
- B. 0
- C. 2
- D. 4
Correct Option: Answer is ?
Solution:
The equation in this form ax2 + bx + c, you can find the maximum by using the equation:
max = c – (b2 / 4a)
y=3x2 + 5x – 3
max = -3 (52 / 4 x 3)
= -3 x 25/12 = -25/4 =
5. A trapezium has two parallel sides of length 5cm and 9cm. If the area is 91cm2, find the distance between the parallel sides
- A. 13 cm
- B. 4 cm
- C. 6 cm
- D. 7 cm
Correct Option: Answer is A
Solution:
Solution:
Area of Trapezium = 1/2(sum of parallel sides) * h
91 = 1/2 (5 + 9)h
cross multiply
91 = 7h
h = 91/7
h = 13cm
6. find the value of p if the line which passes through (-1, -p) and (-2p,2) is parallel to the line 2y+8x-17=0?
- A. −2/7
- B. 2/7
- C. −6/7
- D. 6/7
Correct Option: Answer is D
Solution:
Line: 2y+8x-17=0
recall y = mx + c
2y = -8x + 17
(-1, -p) and (-2p, 2) exist.
(x1, y1)= (–1, –p)
(x2, y2)= (–2p, 2)
Gradient, m= (y2 – y1)/(x2 – x1)= (2 – (–p))/(–2p – (–1))
= (2 + p)/(–2p + 1)
The above result of the gradient of a line is parallel to the gradient of the line, 2y + 8x – 17= 0.
In that line, like y= mx + c, 2y= –8x + 17, y= –4x + 17/2
The condition for parallelism is such that:
(2 + p)/(–2p + 1)= –4
(2 + p)= –4(–2p + 1)
2 + p= +8p – 4
Collect like terms,
p – 8p= –4 – 2
–7p= –6
p= 6/7
7. The ratio of the length of two similar rectangular blocks is 2 : 3. If the volume of the larger block is 351cm3, then the volume of the other block is?
- A. 234.00 cm3
- B. 526.50 cm3
- C. 166.00 cm3
- D. 687cm3
Correct Option: Answer is A
Solution:
Let x represent total vol. 2 : 3 = 2 + 3 = 5
= 3/5x = 351
X = 351 x 5/3= 585
Volume of smaller block = 2/5 x 585
=234cm3
8. Find the derivatives of the function y = 2x2(2x – 1) at the point x = -1?
- A. 18
- B. 16
- C. -4
- D. -6
Correct Option: Answer is B
Solution:
y = 2x2(2x – 1)
y = 4x3 – 2x2
dy/dx = 2x2-4x
at x = -1
dy/dx = 2(-1)2-4(-1)
= 12 + 4 =16
9. Correct 241.34(3 x 10-3)2to 4 significant figures
- A. 0.0014
- B. 0.001448
- C. 0.0022
- D. 0.002172
Correct Option: Answer is D
Solution:
241.34(3 x 10-3)2 to 4 s.f
241.34(9 x 10-6)10=> 241.34 x 9 (10-6)
= 2172.06 x 10-6
= 0.00217206
= 0.002172
10. Find the mean deviation of 1, 2, 3 and 4
- A. 1.0
- B. 1.5
- C. 2.0
- D. 2.5
Correct Option: Answer is A
11. At what rate would a sum of N100.00 deposited for 5 years raise an interest of N7.50?
- A. %
- B. 2%
- C. 1.5%
- D. 25%
Correct Option: Answer is C
I = PRT/100
7.50 = 100 x R x 5 / 100
=> 7.5 = 100 x 5R / 100
=> R = 750/500 = 1.5%
12. Three children shared a basket of mangoes in such a way that the first child took 1/4 of the mangoes and the second 3/4 of the remainder. What fraction of the mangoes did the third child take?
- A. 3/16
- B. 7/16
- C. 9/16
- D. 13/16
Correct Option: Answer is A
- A. 8.8 x 10-1
- B. 8.8 x 10-2
- C. 8.8 x 10-3
- D. 8.8 x 103
Correct Option: Answer is C
\(\frac{0.00275 \times 0.0064}{0.025 \times 0.08}\) = \(\frac{275 \times 64}{25 \times 8}\)
=>
14. Simplify \(\sqrt{27}\) + \(\frac{3}{\sqrt{3}}\)
- A. 4\(\sqrt{3}\)
- B. \(\frac{4}{\sqrt{3}}\)
- C. 3\(\sqrt{3}\)
- D. \(\frac{\sqrt{3}}{4}\)
Correct Option: Answer is A
15. Three brothers in a business deal share the profit at the end of a contact. The first received 1/3 of the profit and the second 2/3 of the remainder. If the third received the remaining N12000.00 how much profit did they share?
- A. N60 000.00
- B. N54 000.00
- C. N48 000.00
- D. N42 000.00