# 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 ^{5}C_{2} 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 = πr^{3}

dV/dr= 2 πr^{2}

dV/dr (r=2)2π(2)^{2 }=8π

**4. **determine the maximum value of y=3x^{2}+ 5x – 3

**A.**6**B.**0**C.**2**D.**4

**Correct Option: Answer is ?**

Solution:

The equation in this form *ax*^{2} + *bx* + *c*, you can find the maximum by using the equation:

max = *c* – (*b*^{2} / 4*a*)

y=3x^{2} + 5x – 3

max = -3 (5^{2} / 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 351cm^{3}, then the volume of the other block is?

**A.**234.00 cm^{3}**B.**526.50 cm^{3}**C.**166.00 cm^{3}**D.**687cm^{3}

**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

=234cm^{3}

**8. **Find the derivatives of the function y = 2x^{2}(2x – 1) at the point x = -1?

**A.**18**B.**16**C.**-4**D.**-6

**Correct Option: Answer is B**

Solution:

y = 2x^{2}(2x – 1)

y = 4x^{3} – 2x^{2}

dy/dx = 2x^{2}-4x

at x = -1

dy/dx = 2(-1)^{2}-4(-1)

= 12 + 4 =16

**9. **Correct 241.34(3 x 10-^{3})^{2}to 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**

**13.**Simplify and express in standard form \(\frac{0.00275 \times 0.0064}{0.025 \times 0.08}\)

**A.**8.8 x 10^{-1}**B.**8.8 x 10^{-2}**C.**8.8 x 10^{-3}**D.**8.8 x 10^{3}

**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