Year :
2021
Title :
Mathematics (Core)
Exam :
JAMB Exam
Paper 1 | Objectives
21 - 30 of 40 Questions
| # | Question | Ans |
|---|---|---|
| 21. |
The locus of a point which moves so that it is equidistant from two intersecting straight lines is the? A. perpendicular bisector of the two lines B. angle bisector of the two lines C. bisector of the two lines D. line parallel to the two lines |
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| 22. |
4, 16, 30, 20, 10, 14 and 26 are represented on a pie chart. Find the sum of the angles of the bisectors representing all numbers equals to or greater than 16 A. 48o B. 84o C. 92o D. 276o Detailed SolutionGiven that 4, 16, 30, 20, 10, 14 and 26Adding up = 120 nos \(\geq\) 16 are 16 + 30 + 20 + 26 = 92 The requires sum of angles = \(\frac{92}{120}\) x \(\frac{360^o}{1}\) = 276o There is an explanation video available below. |
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| 23. |
The mean of ten positive numbers is 16. When another number is added, the mean becomes 18. Find the eleventh number A. 3 B. 16 C. 38 D. 30 Detailed SolutionMean of 10 numbers = 16The total sum of numbers = 16 x 10 = 160 Mean of 11 numbers = 18 Total sum of numbers = 11 x 18 = 198 The 11th no. = 198 - 160 = 38 There is an explanation video available below. |
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| 24. |
Two numbers are removed at random from the numbers 1, 2, 3 and 4. What is the probability that the sum of the numbers removed is even? A. \(\frac{2}{3}\) B. \(\frac{1}{2}\) C. \(\frac{1}{3}\) D. \(\frac{1}{4}\) Detailed Solution\(\begin{array}{c|c} 1 & 2 & 3 & 4\\\hline 1(1, 1) & (1, 2) & (1, 3) & (1, 4)\\ \hline 2(2, 1) & (2 , 2) & (2, 3) & (2, 4) \\ \hline 3(3, 1) & (3, 2) & (3, 3) & (3, 4)\\ \hline 4(4, 1) & (4, 2) & (4, 3) & (4, 4)\end{array}\)sample space = 16 sum of nos. removed are (2), 3, (4), 5 3, (4), 5, (6) (4), 5, (6), 7 (5), 6, 7, (8) Even nos. = 8 of them Pr(even sum) = \(\frac{8}{16}\) = \(\frac{1}{2}\) There is an explanatio |
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| 25. |
Find the probability that a number selected at random from 41 to 56 is a multiple of 9 A. \(\frac{1}{8}\) B. \(\frac{2}{15}\) C. \(\frac{3}{16}\) D. \(\frac{7}{8}\) Detailed SolutionGiven from 41 to 5641, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56 The nos multiple of 9 are: 45, 54 P(multiple of 9) = \(\frac{2}{16}\) = \(\frac{1}{8}\) There is an explanation video available below. |
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| 26. |
Musa borrows N10.00 at 2% per month simple interest and repays N8.00 after 4 months. How much does he still owe? A. N10.80 B. N10.67 C. N2.80 D. N2.67 Detailed SolutionI = \(\frac{PRT}{100}\)= \(\frac{10 \times 2 \times 4}{100}\) = \(\frac{4}{5}\) = 0.8 Total amount = N10.80 He pays N8.00 Remainder = 10.80 - 8.00 = N2.80 There is an explanation video available below. |
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| 27. |
Simplify 2log \(\frac{2}{5}\) - log\(\frac{72}{125}\) + log 9 A. 1 - 4 log3 B. -1 + 2 log 3 C. -1 + 5 log2 D. 1 - 2log 2 Detailed Solution2log \(\frac{2}{5}\) - log\(\frac{72}{125}\) + log 9[\(\frac{2}{5}\))2 x 9] = log \(\frac{4}{25}\) x \(\frac{9}{1}\) x \(\frac{125}{72}\) = log \(\frac{72}{125}\) = log \(\frac{5}{2}\) = log \(\frac{10}{4}\) = log 10 - log 4 = log10 - log2\(^2\) = 1 - 2 log2 There is an explanation video available below. |
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| 28. |
A car travels from calabar to Enugu, a distance of P km with an average speed of U km per hour and continues to benin, a distance of Q km, with an average speed of Wkm per hour. Find its average speed from Calabar to Benin A. \(\frac{(p + q)}{pw + qu}\) B. \(\frac{uw(p + q)}{pw + qu}\) C. \(\frac{uw(p + q)}{pw}\) D. \(\frac{uw}{pw + qu}\) Detailed SolutionAverage speed = \(\frac{total Distance}{Total Time}\)from Calabar to Enugu in time t1, hence t1 = \(\frac{P}{U}\) Also from Enugu to Benin t2 \(\frac{q}{w}\) Av. speed = \(\frac{p + q}{t_1 + t_2}\) = \(\frac{p + q}{p/u + q/w}\) = p + q x \(\frac{uw}{pw + qu}\) = \(\frac{uw(p + q)}{pw + qu}\) There is an explanation video available below. |
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| 29. |
If w varies inversely as \(\frac{uv}{u + v}\) and w = 8 when A. uvw = 16(u + v) B. 16uv = 3w(u + v) C. uvw = 12(u + v) D. 12uvw = u + v Detailed SolutionW \(\alpha\) \(\frac{\frac{1}{uv}}{u + v}\)∴ w = \(\frac{\frac{k}{uv}}{u + v}\) = \(\frac{k(u + v)}{uv}\) w = \(\frac{k(u + v)}{uv}\) w = 8, u = 2 and v = 6 8 = \(\frac{k(2 + 6)}{2(6)}\) = \(\frac{k(8)}{12}\) k = 12 i.e 12 ( u + v) = uwv There is an explanation video available below. |
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| 30. |
If g(x) = x\(^2\) + 3x find g(x + 1) - g(x) A. (x + 2) B. 2(x + 2) C. (2x + 1) D. (x2 + 4) Detailed Solutiong(x) = x2 + 3xWhen g(x + 1) = (x + 1)^2 + 3(x + 1) = x\(^2\) + 1 + 2x + 3x + 3 = x\(^2\) + 5x + 4 g(x + 1) - g(x) = x2 + 5x + 8 - (x\(^2\) + 3x) = x\(^2\) + 5x + 4 - x2 -3x = 2x + 4 or 2(x + 4) = 2(x + 2) There is an explanation video available below. |
| 21. |
The locus of a point which moves so that it is equidistant from two intersecting straight lines is the? A. perpendicular bisector of the two lines B. angle bisector of the two lines C. bisector of the two lines D. line parallel to the two lines |
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| 22. |
4, 16, 30, 20, 10, 14 and 26 are represented on a pie chart. Find the sum of the angles of the bisectors representing all numbers equals to or greater than 16 A. 48o B. 84o C. 92o D. 276o Detailed SolutionGiven that 4, 16, 30, 20, 10, 14 and 26Adding up = 120 nos \(\geq\) 16 are 16 + 30 + 20 + 26 = 92 The requires sum of angles = \(\frac{92}{120}\) x \(\frac{360^o}{1}\) = 276o There is an explanation video available below. |
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| 23. |
The mean of ten positive numbers is 16. When another number is added, the mean becomes 18. Find the eleventh number A. 3 B. 16 C. 38 D. 30 Detailed SolutionMean of 10 numbers = 16The total sum of numbers = 16 x 10 = 160 Mean of 11 numbers = 18 Total sum of numbers = 11 x 18 = 198 The 11th no. = 198 - 160 = 38 There is an explanation video available below. |
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| 24. |
Two numbers are removed at random from the numbers 1, 2, 3 and 4. What is the probability that the sum of the numbers removed is even? A. \(\frac{2}{3}\) B. \(\frac{1}{2}\) C. \(\frac{1}{3}\) D. \(\frac{1}{4}\) Detailed Solution\(\begin{array}{c|c} 1 & 2 & 3 & 4\\\hline 1(1, 1) & (1, 2) & (1, 3) & (1, 4)\\ \hline 2(2, 1) & (2 , 2) & (2, 3) & (2, 4) \\ \hline 3(3, 1) & (3, 2) & (3, 3) & (3, 4)\\ \hline 4(4, 1) & (4, 2) & (4, 3) & (4, 4)\end{array}\)sample space = 16 sum of nos. removed are (2), 3, (4), 5 3, (4), 5, (6) (4), 5, (6), 7 (5), 6, 7, (8) Even nos. = 8 of them Pr(even sum) = \(\frac{8}{16}\) = \(\frac{1}{2}\) There is an explanatio |
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| 25. |
Find the probability that a number selected at random from 41 to 56 is a multiple of 9 A. \(\frac{1}{8}\) B. \(\frac{2}{15}\) C. \(\frac{3}{16}\) D. \(\frac{7}{8}\) Detailed SolutionGiven from 41 to 5641, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56 The nos multiple of 9 are: 45, 54 P(multiple of 9) = \(\frac{2}{16}\) = \(\frac{1}{8}\) There is an explanation video available below. |
| 26. |
Musa borrows N10.00 at 2% per month simple interest and repays N8.00 after 4 months. How much does he still owe? A. N10.80 B. N10.67 C. N2.80 D. N2.67 Detailed SolutionI = \(\frac{PRT}{100}\)= \(\frac{10 \times 2 \times 4}{100}\) = \(\frac{4}{5}\) = 0.8 Total amount = N10.80 He pays N8.00 Remainder = 10.80 - 8.00 = N2.80 There is an explanation video available below. |
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| 27. |
Simplify 2log \(\frac{2}{5}\) - log\(\frac{72}{125}\) + log 9 A. 1 - 4 log3 B. -1 + 2 log 3 C. -1 + 5 log2 D. 1 - 2log 2 Detailed Solution2log \(\frac{2}{5}\) - log\(\frac{72}{125}\) + log 9[\(\frac{2}{5}\))2 x 9] = log \(\frac{4}{25}\) x \(\frac{9}{1}\) x \(\frac{125}{72}\) = log \(\frac{72}{125}\) = log \(\frac{5}{2}\) = log \(\frac{10}{4}\) = log 10 - log 4 = log10 - log2\(^2\) = 1 - 2 log2 There is an explanation video available below. |
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| 28. |
A car travels from calabar to Enugu, a distance of P km with an average speed of U km per hour and continues to benin, a distance of Q km, with an average speed of Wkm per hour. Find its average speed from Calabar to Benin A. \(\frac{(p + q)}{pw + qu}\) B. \(\frac{uw(p + q)}{pw + qu}\) C. \(\frac{uw(p + q)}{pw}\) D. \(\frac{uw}{pw + qu}\) Detailed SolutionAverage speed = \(\frac{total Distance}{Total Time}\)from Calabar to Enugu in time t1, hence t1 = \(\frac{P}{U}\) Also from Enugu to Benin t2 \(\frac{q}{w}\) Av. speed = \(\frac{p + q}{t_1 + t_2}\) = \(\frac{p + q}{p/u + q/w}\) = p + q x \(\frac{uw}{pw + qu}\) = \(\frac{uw(p + q)}{pw + qu}\) There is an explanation video available below. |
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| 29. |
If w varies inversely as \(\frac{uv}{u + v}\) and w = 8 when A. uvw = 16(u + v) B. 16uv = 3w(u + v) C. uvw = 12(u + v) D. 12uvw = u + v Detailed SolutionW \(\alpha\) \(\frac{\frac{1}{uv}}{u + v}\)∴ w = \(\frac{\frac{k}{uv}}{u + v}\) = \(\frac{k(u + v)}{uv}\) w = \(\frac{k(u + v)}{uv}\) w = 8, u = 2 and v = 6 8 = \(\frac{k(2 + 6)}{2(6)}\) = \(\frac{k(8)}{12}\) k = 12 i.e 12 ( u + v) = uwv There is an explanation video available below. |
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| 30. |
If g(x) = x\(^2\) + 3x find g(x + 1) - g(x) A. (x + 2) B. 2(x + 2) C. (2x + 1) D. (x2 + 4) Detailed Solutiong(x) = x2 + 3xWhen g(x + 1) = (x + 1)^2 + 3(x + 1) = x\(^2\) + 1 + 2x + 3x + 3 = x\(^2\) + 5x + 4 g(x + 1) - g(x) = x2 + 5x + 8 - (x\(^2\) + 3x) = x\(^2\) + 5x + 4 - x2 -3x = 2x + 4 or 2(x + 4) = 2(x + 2) There is an explanation video available below. |