Year :
1983
Title :
Mathematics (Core)
Exam :
JAMB Exam
Paper 1 | Objectives
21 - 30 of 48 Questions
| # | Question | Ans |
|---|---|---|
| 21. |
Find the angle of the sectors representing each item in pie chart of the following data 6, 10, 14, 16, 26 A. 15o, 25o, 35o, 40o, 65o B. 60o, 100o, 140o, 160o, 260o C. 6o, 10o, 14o, 16o, 26o D. 30o, 50o, 70o, 80o, 130o E. none of the above Detailed Solution6 + 10 + 14 + 16 + 26 = 72\(\frac{6}{72}\) x 360 = 30o Similarly others give 30o, 50o, 70o, 80o and 130o respectively |
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| 22. |
The scores of 16 students in a Mathematics test are 65, 65, 55, 60, 60, 65, 60, 70, 75, 70, 65, 70, 60, 65, 65, 70. What is the sum of the median and modal scores? A. 125 B. 130 C. 140 D. 150 E. 137.5 Detailed Solution\(\begin{array}{c|c} Scores & Frequency \\\hline 55 & 1\\ 60 & 4\\ 65 & 6\\ 70 & 4\\ 75 & 1 \end{array}\)Median = 65(middle number) Mode = 65(most common) Median + Mode = 65 + 65 = 130 |
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| 23. |
The letters of the word MATRICULATION are cut and put into a box. One letter is drawn at random from the box. Find the probability of drawing a vowel A. \(\frac{7}{13}\) B. \(\frac{5}{13}\) C. \(\frac{6}{13}\) D. \(\frac{8}{13}\) E. \(\frac{4}{13}\) Detailed SolutionVowels of letters are 6 in numbersprob. of vowel = \(\frac{6}{13}\) |
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| 24. |
Correct each of the numbers 59.81798 and 0.0746829 to three significant figures and multiply them, giving your answer to three significant figures A. 4.46 B. 4.48 C. 4.47 D. 4.49 E. 4.50 Detailed Solution59.81798 = 59.8(3 s.f)0.0746829 = 0.0747 59.8 x 0.0747 = 4.46706 = 4.47(3s.f) |
|
| 25. |
If a rod of length 250cm is measured as 255cm long in error, what is the percentage error in the measurement? A. 55 B. 10 C. 5 D. 4 E. 2 Detailed Solution% error = \(\frac{\text{Actual error}}{\text{real value}}\) x 100= \(\frac{5}{250}\) x 100 = 2% |
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| 26. |
If \((\frac{2}{3})^{m} (\frac{3}{4})^{n} = \frac{256}{729}\), find the values of m and n. A. m = 4, n = 2 B. m = -4, n = -2 C. m = -4, n =2 D. m = 4, n = -2 E. m = -2, n = 4 Detailed Solution(\(\frac{2}{3}\))m (\(\frac{3}{4}\))n = \(\frac{256}{729}\)\(\frac{2^m}{4^n}\) x \(\frac{3^n}{3^m}\) = \(\frac{2^{8}}{3^{6}}\) \(2^{m} \div 2^{2n} = 2^{8}; 3^{n} \div 3^{m} = 3^{-6}\) m - 2n = 8........(i) -m + n = -6........(ii) Solving the equations simultaneously m = 4, n = -2 |
|
| 27. |
Without using tables find the numerical value of log749 + log7(\(\frac{1}{7}\)) A. 1 B. 2 C. 3 D. 7 E. 9 Detailed Solutionlog749 + log7\(\frac{1}{7}\)= log77 = 1 |
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| 28. |
Factorize completely 81a\(^4\) - 16b\(^4\) A. (3a + 2b)(2a - 3b)(9a2 + 4b2) B. (3a - 2b)(2a - 3b)(4a2 - 9b2) C. (3a - 2b)(3a + 2b)(9a2 + 4b2) D. (6a - 2b)(8a - 3b)(4a3 - 9b2) Detailed Solution81a\(^4\) - 16b\(^4\) = (9a\(^2\))\(^2\) - (4b\(^2\))\(^2\)= (9a\(^2\) + 4b\(^2\))(9a\(^2\) - 4b\(^2\)) N:B 9a\(^2\) - 4b\(^2\) = (3a - 2b)(3a + 2b) |
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| 29. |
One interior angle of a convex hexagon is 170o and each of the remaining interior angles is equal to xo. Find x A. 120o B. 110o C. 105o D. 102o E. 100o Detailed SolutionAn hexagon polygon is a six sided polygonn = 6 sum of all interior angles of hexagon polygon will be (2n - 4) x 90o = [2 x 6 - 4] x 90 = 720o If one angle is 170o and each of the remaining five angles is 5xo 5xo + 170o = 720o = 5x + 550 x = \(\frac{550}{5}\) = 110o |
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| 30. |
A ship H leaves a port P and sails 30 km due south. Then it sails 50km due west. What is the bearing of H from P? A. 20o 34' B. 243o 26' C. 116o 34' D. 63o 26' E. 240o 56' Detailed Solution Let the bearing of H from P be represented by x°. \(\tan \theta = \frac{30}{60} = 0.5\) \(\theta = \tan^{-1} (0.5) = 26.565°\) \(x = 180° + (90 - 26.565)\) \(x = 180 + 63.435 = 243.435°\) = \(243° 26'\) |
| 21. |
Find the angle of the sectors representing each item in pie chart of the following data 6, 10, 14, 16, 26 A. 15o, 25o, 35o, 40o, 65o B. 60o, 100o, 140o, 160o, 260o C. 6o, 10o, 14o, 16o, 26o D. 30o, 50o, 70o, 80o, 130o E. none of the above Detailed Solution6 + 10 + 14 + 16 + 26 = 72\(\frac{6}{72}\) x 360 = 30o Similarly others give 30o, 50o, 70o, 80o and 130o respectively |
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| 22. |
The scores of 16 students in a Mathematics test are 65, 65, 55, 60, 60, 65, 60, 70, 75, 70, 65, 70, 60, 65, 65, 70. What is the sum of the median and modal scores? A. 125 B. 130 C. 140 D. 150 E. 137.5 Detailed Solution\(\begin{array}{c|c} Scores & Frequency \\\hline 55 & 1\\ 60 & 4\\ 65 & 6\\ 70 & 4\\ 75 & 1 \end{array}\)Median = 65(middle number) Mode = 65(most common) Median + Mode = 65 + 65 = 130 |
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| 23. |
The letters of the word MATRICULATION are cut and put into a box. One letter is drawn at random from the box. Find the probability of drawing a vowel A. \(\frac{7}{13}\) B. \(\frac{5}{13}\) C. \(\frac{6}{13}\) D. \(\frac{8}{13}\) E. \(\frac{4}{13}\) Detailed SolutionVowels of letters are 6 in numbersprob. of vowel = \(\frac{6}{13}\) |
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| 24. |
Correct each of the numbers 59.81798 and 0.0746829 to three significant figures and multiply them, giving your answer to three significant figures A. 4.46 B. 4.48 C. 4.47 D. 4.49 E. 4.50 Detailed Solution59.81798 = 59.8(3 s.f)0.0746829 = 0.0747 59.8 x 0.0747 = 4.46706 = 4.47(3s.f) |
|
| 25. |
If a rod of length 250cm is measured as 255cm long in error, what is the percentage error in the measurement? A. 55 B. 10 C. 5 D. 4 E. 2 Detailed Solution% error = \(\frac{\text{Actual error}}{\text{real value}}\) x 100= \(\frac{5}{250}\) x 100 = 2% |
| 26. |
If \((\frac{2}{3})^{m} (\frac{3}{4})^{n} = \frac{256}{729}\), find the values of m and n. A. m = 4, n = 2 B. m = -4, n = -2 C. m = -4, n =2 D. m = 4, n = -2 E. m = -2, n = 4 Detailed Solution(\(\frac{2}{3}\))m (\(\frac{3}{4}\))n = \(\frac{256}{729}\)\(\frac{2^m}{4^n}\) x \(\frac{3^n}{3^m}\) = \(\frac{2^{8}}{3^{6}}\) \(2^{m} \div 2^{2n} = 2^{8}; 3^{n} \div 3^{m} = 3^{-6}\) m - 2n = 8........(i) -m + n = -6........(ii) Solving the equations simultaneously m = 4, n = -2 |
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| 27. |
Without using tables find the numerical value of log749 + log7(\(\frac{1}{7}\)) A. 1 B. 2 C. 3 D. 7 E. 9 Detailed Solutionlog749 + log7\(\frac{1}{7}\)= log77 = 1 |
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| 28. |
Factorize completely 81a\(^4\) - 16b\(^4\) A. (3a + 2b)(2a - 3b)(9a2 + 4b2) B. (3a - 2b)(2a - 3b)(4a2 - 9b2) C. (3a - 2b)(3a + 2b)(9a2 + 4b2) D. (6a - 2b)(8a - 3b)(4a3 - 9b2) Detailed Solution81a\(^4\) - 16b\(^4\) = (9a\(^2\))\(^2\) - (4b\(^2\))\(^2\)= (9a\(^2\) + 4b\(^2\))(9a\(^2\) - 4b\(^2\)) N:B 9a\(^2\) - 4b\(^2\) = (3a - 2b)(3a + 2b) |
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| 29. |
One interior angle of a convex hexagon is 170o and each of the remaining interior angles is equal to xo. Find x A. 120o B. 110o C. 105o D. 102o E. 100o Detailed SolutionAn hexagon polygon is a six sided polygonn = 6 sum of all interior angles of hexagon polygon will be (2n - 4) x 90o = [2 x 6 - 4] x 90 = 720o If one angle is 170o and each of the remaining five angles is 5xo 5xo + 170o = 720o = 5x + 550 x = \(\frac{550}{5}\) = 110o |
|
| 30. |
A ship H leaves a port P and sails 30 km due south. Then it sails 50km due west. What is the bearing of H from P? A. 20o 34' B. 243o 26' C. 116o 34' D. 63o 26' E. 240o 56' Detailed SolutionLet the bearing of H from P be represented by x°. \(\tan \theta = \frac{30}{60} = 0.5\) \(\theta = \tan^{-1} (0.5) = 26.565°\) \(x = 180° + (90 - 26.565)\) \(x = 180 + 63.435 = 243.435°\) = \(243° 26'\) |