2019 - JAMB Mathematics Past Questions and Answers - page 4
If P varies inversely as the square root of q, where p = 3 and q = 16, find the value of q when p = 4.
12
8
9
16
\(p \propto \frac{1}{\sqrt{q}}\)
\(\implies p = \frac{k}{\sqrt{q}}\)
when p = 3, q = 16.
\(3 = \frac{k}{\sqrt{16}}\)
\(k = 3 \times 4 = 12\)
\(\therefore p = \frac{12}{\sqrt{q}}\)
at p = 4,
\(4 = \frac{12}{\sqrt{q}} \implies \sqrt{q} = \frac{12}{4}\)
\(\sqrt{q} = 3 \implies q = 3^2 \)
\(q = 9\)
Tade bought 200 mangoes at 4 for ₦2.50. 30 out of the mangoes got spoilt and the remaining were sold at 2 for ₦2.40. Find the percentage profit or loss.
43.6% loss
35% profit
63.2% profit
28% loss
For 200 mangoes @4 for N2.50
it \(\implies\) that the total cost price = \(\frac{200}{4} \times N 2.50\)
= N 125.00
Since there are 30 mangoes that got spoilt, \(\implies\) Left over = 200 - 30
= 170 mangoes
170 mangoes at 2 for N 2.40
\(\implies\) Total selling point = \(\frac{170}{2} \times N 2.40\)
= N 204.00
Profit : N (204.00 - 125.00) = N 79.00
% profit = \(\frac{79}{125} \times 100%\)
profit = 63.2%.
The simple interest on ₦8550 for 3 years at x% per annum is ₦4890. Calculate the value of x to the nearest whole number.
19%
20%
25%
16.3%
the S.I = \(\frac{PRT}{100}\)
\(\implies\) N 4890 = \(\frac{8550 \times 3 \times x}{100}\)
\(x = \frac{4890 \times 100}{8550 \times 3}\)
\(x = 19.06%\)
\(x \approxeq 19%\)
Simplify 81\(^{\frac{-3}{4}}\) x 25\(^{\frac{1}{2}}\) x 243\(^{\frac{2}{5}}\)
81\(^{\frac{-3}{4}}\) x 25\(^{\frac{1}{2}}\) x 243\(^{\frac{2}{5}}\)
= \((\sqrt[4]{81})^{-3} \times \sqrt{25} \times (\sqrt[5]{243})^2\)
= \(\frac{5 \times 3^2}{3^{-3}}\)
= \(\frac{5}{3}\)
Find the value of \(\frac{(0.5436)^3}{0.017 \times 0.219}\) to 3 significant figures.
(\frac{(0.5436)^3}{0.017 \times 0.219}\)
= \(\frac{0.16063}{0.017 \times 0.219}\)
= 43.1 (to 3 s.f)
If S = (4t + 3)(t - 2), find ds/dt when t = 5 secs.
50 units per sec
35 units per sec
22 units per sec
13 units per sec
\(s = (4t + 3)(t - 2)\)
\(\frac{\mathrm d s}{\mathrm d t} = (4t + 3)(1) + (t - 2)(4)\)
= \(4t + 3 + 4t - 8\)
= 8t - 5
\(\frac{\mathrm d s}{\mathrm d t} (t = 5 secs) = 8(5) - 5\)
= 40 - 5
= 35 units per second
The angles of a polygon are given by 2x, 5x, x and 4x respectively. The value of x is
31°
30°
26°
48°
given that there are 4 angles, it means that the polygon is a quadrilateral.
The sum of the angles in a quadrilateral = 360°
\(\therefore\) 2x + 5x + x + 4x = 360°
12x = 360°
x = 30°
The weight of a day-old chick was measured to be 0.21g. If the actual weight of the chick is 0.18g, what was the percentage error in the measurement?
15.5%
18.2%
14.8%
16.7%
Actual weight = 0.18g
Error = 0.21g - 0.18g = 0.03g
% error = \(\frac{0.03}{0.18} \times 100%\) = 16.7%
% error = 16.7%
Evaluate \((\frac{6}{0.32} \div \frac{2}{0.084})^{-1}\) correct to 1 decimal place.
\((\frac{6}{0.32} \div \frac{2}{0.084})^{-1}\)
= \((\frac{600}{32} \div \frac{2000}{84})^{-1}\)
= \((\frac{600}{32} \times \frac{84}{2000})^{-1}\)
= \((\frac{63}{80})^{-1}\)
= \(\frac{80}{63}\)
= 1.3 (to 1 decimal place)
If 2\(^{x + y}\) = 16 and 4\(^{x - y} = \frac{1}{32}\), find the values of x and y.
x = \(\frac{3}{4}\), y = \(\frac{11}{4}\)
x = \(\frac{3}{4}\), y = \(\frac{13}{4}\)
x = \(\frac{2}{3}\), y = \(\frac{4}{5}\)
x = \(\frac{2}{3}\), y = \(\frac{13}{4}\)
2\(^{x + y}\) = 16 ; 4\(^{x - y}\) = \(\frac{1}{32}\).
\(\implies 2^{x + y} = 2^4\)
\(x + y = 4 ... (1)\)
\(2^{2(x - y)} = 2^{-5} \)
\(2^{2x - 2y} = 2^{-5}\)
\(\implies 2x - 2y = -5 ... (2)\)
Solving the equations (1) and (2) simultaneously gives:
x = \(\frac{3}{4}\) and y = \(\frac{13}{4}\)