Year :
2019
Title :
Mathematics (Core)
Exam :
JAMB Exam
Paper 1 | Objectives
31 - 40 of 80 Questions
| # | Question | Ans |
|---|---|---|
| 31. |
If P varies inversely as the square root of q, where p = 3 and q = 16, find the value of q when p = 4. A. 12 B. 8 C. 9 D. 16 Detailed Solution\(p \propto \frac{1}{\sqrt{q}}\)\(\implies p = \frac{k}{\sqrt{q}}\) when p = 3, q = 16. \(3 = \frac{k}{\sqrt{16}}\) \(k = 3 \times 4 = 12\) \(\therefore p = \frac{12}{\sqrt{q}}\) when p = 4, \(4 = \frac{12}{\sqrt{q}} \implies \sqrt{q} = \frac{12}{4}\) \(\sqrt{q} = 3 \implies q = 3^2 \) \(q = 9\) There is an explanation video available below. |
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| 32. |
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. A. 43.6% loss B. 35% profit C. 63.2% profit D. 28% loss Detailed Solution200 mangoes at 4 for N2.50\(\implies\) Total cost price = \(\frac{200}{4} \times N 2.50\) = N 125.00 Since 30 mangoes 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 = \(\frac{79}{125} \times 100%\) = 63.2% profit. There is an explanation video available below. |
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| 33. |
The simple interest on ₦8550 for 3 years at x% per annum is ₦4890. Calculate the value of x to the nearest whole number. A. 19% B. 20% C. 25% D. 16.3% Detailed SolutionS.I = \(\frac{PRT}{100}\)\(\implies\) N 4890 = \(\frac{8550 \times 3 \times x}{100}\) \(x = \frac{4890 \times 100}{8550 \times 3}\) \(x = 19.06%\) \(x \approxeq 19%\) There is an explanation video available below. |
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| 34. |
Simplify 81\(^{\frac{-3}{4}}\) x 25\(^{\frac{1}{2}}\) x 243\(^{\frac{2}{5}}\) A. \(\frac{2}{5}\) B. \(\frac{3}{5}\) C. \(\frac{5}{2}\) D. \(\frac{5}{3}\) Detailed Solution81\(^{\frac{-3}{4}}\) x 25\(^{\frac{1}{2}}\) x 243\(^{\frac{2}{5}}\)= \((\sqrt[4]{81})^{-3} \times \sqrt{25} \times (\sqrt[5]{243})^2\) = \(\frac{5 \times 3^2}{3^{3}}\) = \(\frac{5}{3}\) There is an explanation video available below. |
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| 35. |
Find the value of \(\frac{(0.5436)^3}{0.017 \times 0.219}\) to 3 significant figures. A. 46.2 B. 43.1 C. 534 D. 431 Detailed Solution(\frac{(0.5436)^3}{0.017 \times 0.219}\)= \(\frac{0.16063}{0.017 \times 0.219}\) = 43.1 (to 3 s.f) There is an explanation video available below. |
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| 36. |
If S = (4t + 3)(t - 2), find ds/dt when t = 5 secs. A. 50 units per sec B. 35 units per sec C. 22 units per sec D. 13 units per sec Detailed Solution\(s = (4t + 3)(t - 2)\)\(\frac{\mathrm d s}{\mathrm d t} = (4t + 3)(1) + (t - 2)(4)\) = \(4t + 3 + 4t - 8\) = 8t - 5 \(\frac{\mathrm d s}{\mathrm d t} (t = 5 secs) = 8(5) - 5\) = 40 - 5 = 35 units per sec There is an explanation video available below. |
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| 37. |
The angles of a polygon are given by 2x, 5x, x and 4x respectively. The value of x is A. 31° B. 30° C. 26° D. 48° Detailed SolutionSince there are 4 angles given, the polygon is a quadrilateral.Sum of angle in a quadrilateral = 360° \(\therefore\) 2x + 5x + x + 4x = 360° 12x = 360° x = 30° There is an explanation video available below. |
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| 38. |
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? A. 15.5% B. 18.2% C. 14.8% D. 16.7% Detailed SolutionActual weight = 0.18gError = 0.21g - 0.18g = 0.03g % error = \(\frac{0.03}{0.18} \times 100%\) = 16.7% There is an explanation video available below. |
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| 39. |
Evaluate \((\frac{6}{0.32} \div \frac{2}{0.084})^{-1}\) correct to 1 decimal place. A. 1.3 B. 2.5 C. 4.6 D. 3.2 Detailed Solution\((\frac{6}{0.32} \div \frac{2}{0.084})^{-1}\)= \((\frac{600}{32} \div \frac{2000}{84})^{-1}\) = \((\frac{600}{32} \times \frac{84}{2000})^{-1}\) = \((\frac{63}{80})^{-1}\) = \(\frac{80}{63}\) = 1.3 (to 1 decimal place) There is an explanation video available below. |
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| 40. |
If 2\(^{x + y}\) = 16 and 4\(^{x - y} = \frac{1}{32}\), find the values of x and y. A. x = \(\frac{3}{4}\), y = \(\frac{11}{4}\) B. x = \(\frac{3}{4}\), y = \(\frac{13}{4}\) C. x = \(\frac{2}{3}\), y = \(\frac{4}{5}\) D. x = \(\frac{2}{3}\), y = \(\frac{13}{4}\) Detailed Solution2\(^{x + y}\) = 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, we have x = \(\frac{3}{4}\) and y = \(\frac{13}{4}\) There is an explanation video available below. |
| 31. |
If P varies inversely as the square root of q, where p = 3 and q = 16, find the value of q when p = 4. A. 12 B. 8 C. 9 D. 16 Detailed Solution\(p \propto \frac{1}{\sqrt{q}}\)\(\implies p = \frac{k}{\sqrt{q}}\) when p = 3, q = 16. \(3 = \frac{k}{\sqrt{16}}\) \(k = 3 \times 4 = 12\) \(\therefore p = \frac{12}{\sqrt{q}}\) when p = 4, \(4 = \frac{12}{\sqrt{q}} \implies \sqrt{q} = \frac{12}{4}\) \(\sqrt{q} = 3 \implies q = 3^2 \) \(q = 9\) There is an explanation video available below. |
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| 32. |
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. A. 43.6% loss B. 35% profit C. 63.2% profit D. 28% loss Detailed Solution200 mangoes at 4 for N2.50\(\implies\) Total cost price = \(\frac{200}{4} \times N 2.50\) = N 125.00 Since 30 mangoes 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 = \(\frac{79}{125} \times 100%\) = 63.2% profit. There is an explanation video available below. |
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| 33. |
The simple interest on ₦8550 for 3 years at x% per annum is ₦4890. Calculate the value of x to the nearest whole number. A. 19% B. 20% C. 25% D. 16.3% Detailed SolutionS.I = \(\frac{PRT}{100}\)\(\implies\) N 4890 = \(\frac{8550 \times 3 \times x}{100}\) \(x = \frac{4890 \times 100}{8550 \times 3}\) \(x = 19.06%\) \(x \approxeq 19%\) There is an explanation video available below. |
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| 34. |
Simplify 81\(^{\frac{-3}{4}}\) x 25\(^{\frac{1}{2}}\) x 243\(^{\frac{2}{5}}\) A. \(\frac{2}{5}\) B. \(\frac{3}{5}\) C. \(\frac{5}{2}\) D. \(\frac{5}{3}\) Detailed Solution81\(^{\frac{-3}{4}}\) x 25\(^{\frac{1}{2}}\) x 243\(^{\frac{2}{5}}\)= \((\sqrt[4]{81})^{-3} \times \sqrt{25} \times (\sqrt[5]{243})^2\) = \(\frac{5 \times 3^2}{3^{3}}\) = \(\frac{5}{3}\) There is an explanation video available below. |
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| 35. |
Find the value of \(\frac{(0.5436)^3}{0.017 \times 0.219}\) to 3 significant figures. A. 46.2 B. 43.1 C. 534 D. 431 Detailed Solution(\frac{(0.5436)^3}{0.017 \times 0.219}\)= \(\frac{0.16063}{0.017 \times 0.219}\) = 43.1 (to 3 s.f) There is an explanation video available below. |
| 36. |
If S = (4t + 3)(t - 2), find ds/dt when t = 5 secs. A. 50 units per sec B. 35 units per sec C. 22 units per sec D. 13 units per sec Detailed Solution\(s = (4t + 3)(t - 2)\)\(\frac{\mathrm d s}{\mathrm d t} = (4t + 3)(1) + (t - 2)(4)\) = \(4t + 3 + 4t - 8\) = 8t - 5 \(\frac{\mathrm d s}{\mathrm d t} (t = 5 secs) = 8(5) - 5\) = 40 - 5 = 35 units per sec There is an explanation video available below. |
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| 37. |
The angles of a polygon are given by 2x, 5x, x and 4x respectively. The value of x is A. 31° B. 30° C. 26° D. 48° Detailed SolutionSince there are 4 angles given, the polygon is a quadrilateral.Sum of angle in a quadrilateral = 360° \(\therefore\) 2x + 5x + x + 4x = 360° 12x = 360° x = 30° There is an explanation video available below. |
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| 38. |
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? A. 15.5% B. 18.2% C. 14.8% D. 16.7% Detailed SolutionActual weight = 0.18gError = 0.21g - 0.18g = 0.03g % error = \(\frac{0.03}{0.18} \times 100%\) = 16.7% There is an explanation video available below. |
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| 39. |
Evaluate \((\frac{6}{0.32} \div \frac{2}{0.084})^{-1}\) correct to 1 decimal place. A. 1.3 B. 2.5 C. 4.6 D. 3.2 Detailed Solution\((\frac{6}{0.32} \div \frac{2}{0.084})^{-1}\)= \((\frac{600}{32} \div \frac{2000}{84})^{-1}\) = \((\frac{600}{32} \times \frac{84}{2000})^{-1}\) = \((\frac{63}{80})^{-1}\) = \(\frac{80}{63}\) = 1.3 (to 1 decimal place) There is an explanation video available below. |
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| 40. |
If 2\(^{x + y}\) = 16 and 4\(^{x - y} = \frac{1}{32}\), find the values of x and y. A. x = \(\frac{3}{4}\), y = \(\frac{11}{4}\) B. x = \(\frac{3}{4}\), y = \(\frac{13}{4}\) C. x = \(\frac{2}{3}\), y = \(\frac{4}{5}\) D. x = \(\frac{2}{3}\), y = \(\frac{13}{4}\) Detailed Solution2\(^{x + y}\) = 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, we have x = \(\frac{3}{4}\) and y = \(\frac{13}{4}\) There is an explanation video available below. |