Mathematics (Core), 2021, JAMB Exam, Exam, Paper 1 | Objectives

Paper Info

Year :

2021

Title :

Mathematics (Core)

Exam :

JAMB Exam

Paper 1 | Objectives

11 - 20 of 40 Questions

#	Question	Ans
11.	At what rate would a sum of N100.00 deposited for 5 years raise an interest of N7.50? A. \(\frac{1}{2}\)% B. 2\(\frac{1}{2}\)% C. 1.5% D. 25% Show Content Detailed Solution Interest I = \(\frac{PRT}{100}\) ∴ R = \(\frac{100 \times 1}{100 \times 5}\) = \(\frac{100 \times 7.50}{500 \times 5}\) = \(\frac{750}{500}\) = \(\frac{3}{2}\) = 1.5% There is an explanation video available below.	C
12.	Three children shared a basket of mangoes in such a way that the first child took \(\frac{1}{4}\) of the mangoes and the second \(\frac{3}{4}\) of the remainder. What fraction of the mangoes did the third child take? A. \(\frac{3}{16}\) B. \(\frac{7}{16}\) C. \(\frac{9}{16}\) D. \(\frac{13}{16}\) Show Content Detailed Solution You can use any whole numbers (eg. 1. 2. 3) to represent all the mangoes in the basket. If the first child takes \(\frac{1}{4}\) it will remain 1 - \(\frac{1}{4}\) = \(\frac{3}{4}\) Next, the second child takes \(\frac{3}{4}\) of the remainder which is \(\frac{3}{4}\) i.e. find \(\frac{3}{4}\) of \(\frac{3}{4}\) = \(\frac{3}{4}\) x \(\frac{3}{4}\) = \(\frac{9}{16}\) the fraction remaining now = \(\frac{3}{4}\) - \(\frac{9}{16}\) = \(\frac{12 - 9}{16}\) = \(\frac{3}{16}\) There is an explanation video available A
13.	Simplify and express in standard form \(\frac{0.00275 \times 0.00640}{0.025 \times 0.08}\) A. 8.8 x 10^-1 B. 8.8 x 10^-2 C. 8.8 x 10^-3 D. 8.8 x 10³ Show Content Detailed Solution \(\frac{0.00275 \times 0.0064}{0.025 \times 0.08}\) Removing the decimals = \(\frac{275 \times 64}{2500 \times 800}\) = \(\frac{88}{10^4}\) 88 x 10-4 = 88 x 10-1 x 10-4 = 8.8 x 10-3 There is an explanation video available below.	C
14.	Simplify \(\sqrt{27}\) + \(\frac{3}{\sqrt{3}}\) A. 4\(\sqrt{3}\) B. \(\frac{4}{\sqrt{3}}\) C. 3\(\sqrt{3}\) D. \(\frac{\sqrt{3}}{4}\) Show Content Detailed Solution \(\sqrt{27}\) + \(\frac{3}{\sqrt{3}}\) = \(\sqrt{9 \times 3}\) + \(\frac{3 \times {\sqrt{3}}}{{\sqrt{3}} \times {\sqrt{3}}}\) = 3\(\sqrt{3}\) + \(\sqrt{3}\) = 4\(\sqrt{3}\) There is an explanation video available below.	A
15.	Three brothers in a business deal share the profit at the end of a contract. The first received \(\frac{1}{3}\) of the profit and the second \(\frac{2}{3}\) 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 Show Content Detailed Solution use "T" to represent the total profit. The first receives \(\frac{1}{3}\) T remaining, 1 - \(\frac{1}{3}\) = \(\frac{2}{3}\)T The seconds receives the remaining, which is \(\frac{2}{3}\) also \(\frac{2}{3}\) x \(\frac{2}{3}\) x \(\frac{4}{9}\) The third receives the left over, which is \(\frac{2}{3}\)T - \(\frac{4}{9}\)T = (\(\frac{6 - 4}{9}\))T = \(\frac{2}{9}\)T The third receives \(\frac{2}{9}\)T which is equivalent to N12000 If \(\frac{2}{9}\)T = N12, 000 T = \(\frac{12 000}{\frac{2}{9}}\)	B
16.	P(-6, 1) and Q(6, 6) are the two ends of the diameter of a given circle. Calculate the radius. A. 6.5 units B. 13.0 units C. 3.5 units D. 7.0 units Show Content Detailed Solution PQ\(^2\) = (x2 - x1)\(^2\) + (y2 - y1)\(^2\) = 12\(^2\) + 5\(^2\) = 144 + 25 = 169 PQ = √169 = 13 But PQ = diameter = 2r, r = PQ/2 = 6.5 units There is an explanation video available below.	A
17.	The angle of a sector of a circle, radius 10.5cm, is 48°, Calculate the perimeter of the sector A. 8.8cm B. 25.4cm C. 25.6cm D. 29.8cm Show Content Detailed Solution Length of Arc AB = \(\frac{\theta}{360}\) 2\(\pi\)r = \(\frac{48}{360}\) x 2\(\frac{22}{7}\) x \(\frac{21}{2}\) = \(\frac{4 \times 22 \times \times 3}{30}\) \(\frac{88}{10}\) = 8.8cm Perimeter = 8.8 + 2r = 8.8 + 2(10.5) = 8.8 + 21 = 29.8cm There is an explanation video available below.	D
18.	Find the length of a side of a rhombus whose diagonals are 6cm and 8cm A. 8cm B. 5cm C. 4cm D. 3cm Show Content Detailed Solution The diagonal of a rhombus is a line segment that joins any two non-adjacent vertices. A rhombus has two diagonals that bisect each other at right angles. i.e this splits 6cm into 3cm each AND 8cm to 4cm Using Hyp\(^2\) = adj\(^2\) + opp\(^2\) Hyp\(^2\) = 3\(^2\) + 4\(^2\) Hyp\(^2\) = 25 Hyp = 5 ∴ Length (L) is 5cm because a rhombus is a quadrilateral with 4 equal lengths There is an explanation video available below.	B
19.	Each of the interior angles of a regular polygon is 140°. How many sides has the polygon? A. 9 B. 8 C. 7 D. 5 Show Content Detailed Solution Each interior angle = \(\frac{(n - 2)180}{n}\) 140 = \(\frac{(n - 2)180}{n}\) Cross multiply: 140n = 180n - 360 40n = 360 n = 9 sides ( A Nonagon) There is an explanation video available below.	A
20.	A cylinder pipe, made of metal is 3cm thick.If the internal radius of the pipe is 10cm.Find the volume of metal used in making 3m of the pipe. A. 153\(\pi\)cm³ B. 207\(\pi\)cm³ C. 15 300\(\pi\)cm³ D. 20 700\(\pi\)cm³ Show Content Detailed Solution Volume of a cylinder = πr\(^2\)h First convert 3m to cm by multiplying by 100 Volume of External cylinder = \(π \times 13^2 \times 300\) Volume of Internal cylinder = \(π \times 10^2 \times 300\) Hence; Volume of External cylinder - Volume of Internal cylinder Total volume (v) = \(π (169 - 100) \times 300\) V = \(π \times 69 \times 300\) V = 20700πcm\(^3\) There is an explanation video available below.	D

11.	At what rate would a sum of N100.00 deposited for 5 years raise an interest of N7.50? A. \(\frac{1}{2}\)% B. 2\(\frac{1}{2}\)% C. 1.5% D. 25% Show Content Detailed Solution Interest I = \(\frac{PRT}{100}\) ∴ R = \(\frac{100 \times 1}{100 \times 5}\) = \(\frac{100 \times 7.50}{500 \times 5}\) = \(\frac{750}{500}\) = \(\frac{3}{2}\) = 1.5% There is an explanation video available below.	C
12.	Three children shared a basket of mangoes in such a way that the first child took \(\frac{1}{4}\) of the mangoes and the second \(\frac{3}{4}\) of the remainder. What fraction of the mangoes did the third child take? A. \(\frac{3}{16}\) B. \(\frac{7}{16}\) C. \(\frac{9}{16}\) D. \(\frac{13}{16}\) Show Content Detailed Solution You can use any whole numbers (eg. 1. 2. 3) to represent all the mangoes in the basket. If the first child takes \(\frac{1}{4}\) it will remain 1 - \(\frac{1}{4}\) = \(\frac{3}{4}\) Next, the second child takes \(\frac{3}{4}\) of the remainder which is \(\frac{3}{4}\) i.e. find \(\frac{3}{4}\) of \(\frac{3}{4}\) = \(\frac{3}{4}\) x \(\frac{3}{4}\) = \(\frac{9}{16}\) the fraction remaining now = \(\frac{3}{4}\) - \(\frac{9}{16}\) = \(\frac{12 - 9}{16}\) = \(\frac{3}{16}\) There is an explanation video available A
13.	Simplify and express in standard form \(\frac{0.00275 \times 0.00640}{0.025 \times 0.08}\) A. 8.8 x 10^-1 B. 8.8 x 10^-2 C. 8.8 x 10^-3 D. 8.8 x 10³ Show Content Detailed Solution \(\frac{0.00275 \times 0.0064}{0.025 \times 0.08}\) Removing the decimals = \(\frac{275 \times 64}{2500 \times 800}\) = \(\frac{88}{10^4}\) 88 x 10-4 = 88 x 10-1 x 10-4 = 8.8 x 10-3 There is an explanation video available below.	C
14.	Simplify \(\sqrt{27}\) + \(\frac{3}{\sqrt{3}}\) A. 4\(\sqrt{3}\) B. \(\frac{4}{\sqrt{3}}\) C. 3\(\sqrt{3}\) D. \(\frac{\sqrt{3}}{4}\) Show Content Detailed Solution \(\sqrt{27}\) + \(\frac{3}{\sqrt{3}}\) = \(\sqrt{9 \times 3}\) + \(\frac{3 \times {\sqrt{3}}}{{\sqrt{3}} \times {\sqrt{3}}}\) = 3\(\sqrt{3}\) + \(\sqrt{3}\) = 4\(\sqrt{3}\) There is an explanation video available below.	A
15.	Three brothers in a business deal share the profit at the end of a contract. The first received \(\frac{1}{3}\) of the profit and the second \(\frac{2}{3}\) 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 Show Content Detailed Solution use "T" to represent the total profit. The first receives \(\frac{1}{3}\) T remaining, 1 - \(\frac{1}{3}\) = \(\frac{2}{3}\)T The seconds receives the remaining, which is \(\frac{2}{3}\) also \(\frac{2}{3}\) x \(\frac{2}{3}\) x \(\frac{4}{9}\) The third receives the left over, which is \(\frac{2}{3}\)T - \(\frac{4}{9}\)T = (\(\frac{6 - 4}{9}\))T = \(\frac{2}{9}\)T The third receives \(\frac{2}{9}\)T which is equivalent to N12000 If \(\frac{2}{9}\)T = N12, 000 T = \(\frac{12 000}{\frac{2}{9}}\)	B

16.	P(-6, 1) and Q(6, 6) are the two ends of the diameter of a given circle. Calculate the radius. A. 6.5 units B. 13.0 units C. 3.5 units D. 7.0 units Show Content Detailed Solution PQ\(^2\) = (x2 - x1)\(^2\) + (y2 - y1)\(^2\) = 12\(^2\) + 5\(^2\) = 144 + 25 = 169 PQ = √169 = 13 But PQ = diameter = 2r, r = PQ/2 = 6.5 units There is an explanation video available below.	A
17.	The angle of a sector of a circle, radius 10.5cm, is 48°, Calculate the perimeter of the sector A. 8.8cm B. 25.4cm C. 25.6cm D. 29.8cm Show Content Detailed Solution Length of Arc AB = \(\frac{\theta}{360}\) 2\(\pi\)r = \(\frac{48}{360}\) x 2\(\frac{22}{7}\) x \(\frac{21}{2}\) = \(\frac{4 \times 22 \times \times 3}{30}\) \(\frac{88}{10}\) = 8.8cm Perimeter = 8.8 + 2r = 8.8 + 2(10.5) = 8.8 + 21 = 29.8cm There is an explanation video available below.	D
18.	Find the length of a side of a rhombus whose diagonals are 6cm and 8cm A. 8cm B. 5cm C. 4cm D. 3cm Show Content Detailed Solution The diagonal of a rhombus is a line segment that joins any two non-adjacent vertices. A rhombus has two diagonals that bisect each other at right angles. i.e this splits 6cm into 3cm each AND 8cm to 4cm Using Hyp\(^2\) = adj\(^2\) + opp\(^2\) Hyp\(^2\) = 3\(^2\) + 4\(^2\) Hyp\(^2\) = 25 Hyp = 5 ∴ Length (L) is 5cm because a rhombus is a quadrilateral with 4 equal lengths There is an explanation video available below.	B
19.	Each of the interior angles of a regular polygon is 140°. How many sides has the polygon? A. 9 B. 8 C. 7 D. 5 Show Content Detailed Solution Each interior angle = \(\frac{(n - 2)180}{n}\) 140 = \(\frac{(n - 2)180}{n}\) Cross multiply: 140n = 180n - 360 40n = 360 n = 9 sides ( A Nonagon) There is an explanation video available below.	A
20.	A cylinder pipe, made of metal is 3cm thick.If the internal radius of the pipe is 10cm.Find the volume of metal used in making 3m of the pipe. A. 153\(\pi\)cm³ B. 207\(\pi\)cm³ C. 15 300\(\pi\)cm³ D. 20 700\(\pi\)cm³ Show Content Detailed Solution Volume of a cylinder = πr\(^2\)h First convert 3m to cm by multiplying by 100 Volume of External cylinder = \(π \times 13^2 \times 300\) Volume of Internal cylinder = \(π \times 10^2 \times 300\) Hence; Volume of External cylinder - Volume of Internal cylinder Total volume (v) = \(π (169 - 100) \times 300\) V = \(π \times 69 \times 300\) V = 20700πcm\(^3\) There is an explanation video available below.	D