2021 - JAMB Mathematics Past Questions and Answers - page 2
At what rate would a sum of N100.00 deposited for 5 years raise an interest of N7.50?
\(\frac{1}{2}\)%
2\(\frac{1}{2}\)%
1.5%
25%
Interest, I = \(\frac{PRT}{100}\)
Hence, R = \(\frac{100 \times 1}{100 \times 5}\)
= \(\frac{100 \times 7.50}{500 \times 5}\)
= \(\frac{750}{500}\)
= \(\frac{3}{2}\)
= 1.5%
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?
\(\frac{3}{16}\)
\(\frac{7}{16}\)
\(\frac{9}{16}\)
\(\frac{13}{16}\)
When the first child takes \(\frac{1}{4}\) it will remain 1 - \(\frac{1}{4}\) = \(\frac{3}{4}\)
Next, when the second child takes \(\frac{3}{4}\) of the remainder
=> \(\frac{3}{4}\) i.e. find \(\frac{3}{4}\) of \(\frac{3}{4}\)
= \(\frac{3}{4}\) x \(\frac{3}{4}\)
= \(\frac{9}{16}\)
Fraction remaining = \(\frac{3}{4}\) - \(\frac{9}{16}\)
= \(\frac{12 - 9}{16}\)
= \(\frac{3}{16}\)
Simplify and express in standard form \(\frac{0.00275 \times 0.00640}{0.025 \times 0.08}\)
8.8 x 10\(^{-1}\)
8.8 x 10\(^{-2}\)
8.8 x 10\(^{-3}\)
8.8 x 10\(^{3}\)
\(\frac{0.00275 \times 0.0064}{0.025 \times 0.08}\)
= \(\frac{275 \times 64}{2500 \times 800}\)
= \(\frac{88}{10^4}\)
88 x 10-4 = 88 x 10-1 x 10-4
= 8.8 x 10\(^{-3}\)
Simplify \(\sqrt{27}\) + \(\frac{3}{\sqrt{3}}\)
4\(\sqrt{3}\)
\(\frac{4}{\sqrt{3}}\)
3\(\sqrt{3}\)
\(\frac{\sqrt{3}}{4}\)
\(\sqrt{27}\) + \(\frac{3}{\sqrt{3}}\)
= \(\sqrt{9 \times 3}\) + \(\frac{3 \times {\sqrt{3}}}{{\sqrt{3}} \times {\sqrt{3}}}\)
= 3\(\sqrt{3}\) + \(\sqrt{3}\) = 4\(\sqrt{3}\)
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?
N60 000.00
N54 000.00
N48 000.00
N42 000.00
Let T = total profit.
The first brother receives \(\frac{1}{3}\) T
balance, 1 - \(\frac{1}{3}\)
= \(\frac{2}{3}\)T
The seconds brother receives the remnant: \(\frac{2}{3}\)
\(\frac{2}{3}\) x \(\frac{2}{3}\) x \(\frac{4}{9}\)
The third brother receives the left over: \(\frac{2}{3}\)T - \(\frac{4}{9}\)T = (\(\frac{6 - 4}{9}\))T
= \(\frac{2}{9}\)T
The third brother receives \(\frac{2}{9}\)T => N12000
If \(\frac{2}{9}\)T = N12, 000
T = \(\frac{12 000}{\frac{2}{9}}\) = N54, 000
P(-6, 1) and Q(6, 6) are the two ends of the diameter of a given circle. Calculate the radius.
6.5 units
13.0 units
3.5 units
7.0 units
PQ\(^2\) = (x2 - x1)\(^2\) + (y2 - y1)\(^2\)
= 12\(^2\) + 5\(^2\)
= 144 + 25
= 169
PQ = √169 = 13
PQ = Diameter = 2 * Radius, r
r = PQ/2 = 6.5
The angle of a sector of a circle, radius 10.5cm, is 48°, Calculate the perimeter of the sector
8.8cm
25.4cm
25.6cm
29.8cm
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 of sector = 8.8 + 2r
= 8.8 + 2(10.5)
= 8.8 + 21
= 29.8cm
Find the length of a side of a rhombus whose diagonals are 6cm and 8cm
8cm
5cm
4cm
3cm
For a rhombus,
- The diagonals bisect each other at right angles.
- The diagonals divide into four congruent right-angled triangles.
Hence, 6cm splits into 3cm each and 8cm to 4cm each
Hypotenuse(hyp) = Adjacent(adj) + Opposite(opp)
hyp\(^2\) = adj\(^2\) + opp\(^2\)
hyp\(^2\) = 3\(^2\) + 4\(^2\)
hyp\(^2\) = 25
hyp = 5
Length (L) = 5cm since a rhombus is a quadrilateral with 4 equal lengths
Each of the interior angles of a regular polygon is 140°. How many sides has the polygon?
9
8
7
5
Interior angles of a regular polygon = \(\frac{(n - 2)180}{n}\)
140 = \(\frac{(n - 2)180}{n}\)
140n = 180n - 360
40n = 360
n = 9 sides
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.
153\(\pi\)cm3
207\(\pi\)cm3
15 300\(\pi\)cm3
20 700\(\pi\)cm3
Volume of a cylinder = πr\(^2\)h
Convert 3m to cm by multiplying by 100
Volume of exterior = \(π \times 13^2 \times 300\)
Volume of interior = \(π \times 10^2 \times 300\)
Difference: volume of the external cylinder - volume of the internal cylinder
Total volume (v) = \(π (169 - 100) \times 300\)
V = \(π \times 69 \times 300\)
V = 20700πcm\(^3\)