Year :
2004
Title :
Mathematics (Core)
Exam :
JAMB Exam
Paper 1 | Objectives
11 - 20 of 45 Questions
| # | Question | Ans |
|---|---|---|
| 11. |
Find the derivatives of (2 + 3x)(1 - x) with respect to x A. 6 B. -3 C. 1 - 6x D. 6x - 1 Detailed Solutiony = (2 + 3x)(1 - x)y = 2 - 2x + 3x - 3x2 y = 2 + x - 3x2 dy/dx = 1 - 6x |
|
| 12. |
What is the rate of change of the volume V of a hemisphere with respect to its radius r when r = 2? A. 8π B. 16π C. 2π D. 4π Detailed Solution\(V = \frac{2}{3} \pi r^{3}\)\(\frac{\mathrm d V}{\mathrm d r} = 2\pi r^{2}\) \(\frac{\mathrm d V}{\mathrm d r} (r = 2) = 2\pi (2)^{2}\) = \(8\pi\) |
|
| 13. |
Find the derivatives of the function y = 2x\(^2\)(2x - 1) at the point x = -1? A. 18 B. 16 C. -4 D. -6 Detailed Solutiony = 2x\(^2\)(2x - 1)y = 4x\(^3\) - 2x\(^2\) dy/dx = 12x\(^2\) - 4x at x = -1 dy/dx = 12(-1)\(^2\) - 4(-1) = 12 + 4 = 16 |
|
| 14. |
Evaluate \(\int_{1}^{3}(x^2 - 1)dx\) A. \(\frac{2}{3}\) B. \(-\frac{2}{3}\) C. \(-6\frac{2}{3}\) D. \(6\frac{2}{3}\) Detailed Solution\(\int_{1}^{3}(x^2 - 1)dx = \left[\frac{1}{3}x^2 - x\right] ^{3}_{1}\\ =(9-3)-(\frac{1}{3}-1)\\ =6-\left(-\frac{2}{3}\right)\\ =6+\frac{2}{3}=6\frac{2}{3}\) |
|
| 15. |
Some white balls put in a basket containing twelve red balls and sixteen black balls. If the probability of picking a white balls from the baskets is 3/7, how many white balls were introduced? A. 12 B. 21 C. 28 D. 32 Detailed SolutionNumber of white balls = xNumber of red balls = 12 Number of black balls = 16 Total number of balls = 28 + x P(white balls) = 3/7 But P(white balls) \(= \frac{x}{28+x}\\ = \frac{3}{7} = \frac{x}{28+x}\\ 3(28 + x) = 7x\\ 84 + 3x = 7x\\ 7x - 3x = 84\\ 4x = 84\\ x = 21\) |
|
| 16. |
Find the mean deviation of 1, 2, 3 and 4 A. 2.5 B. 2.0 C. 1.0 D. 1.5 Detailed SolutionX = 1, 2, 3, 4; ∑X = 10x = ∑X/n = 10/4 = 2.5 X - x = -1.5, -0.5, 0.5, 1.5 lX - xl = 1.5, 0.5, 0.5, 1.5; ∑lX - xl = 4.0 mean deviation = (∑lX - xl)/n = 4.0/4 = 1.0 |
|
| 17. |
 An unbiased die is rolled 100 times and the outcome is tabulated above. A. 1/5 B. 1/2 C. 1/6 D. 1/4 Detailed SolutionNumber of times 5 was obtained = 20P(obtaining 5) = 20/100 = 1/5 |
|
| 18. |
 The pie chart above shows the distribution of the crops harvested from a farmland in a year. If 3000 tonnes of millet is harvested, what amount of beans is harvested A. 6000 tonnes B. 1500 tonnes C. 1200 tonnes D. 9000 tonnes Detailed SolutionSectorial angle of beans = 360 - (150 + 90 + 60)= 360 -300 = 60o if 150o represents 3000 tonnes 1o 3000/150 60o will represents (3000/150) * (60/1) = 1200 tonnes |
|
| 19. |
In how many ways can 2 students be selected from a group of 5 students in a debating competition? A. 25 ways B. 10 ways C. 15 ways D. 20 ways Detailed Solution\(In\hspace{1mm} ^{5}C_{2}\hspace{1mm}ways\hspace{1mm}=\frac{5!}{(5-2)!2!}\\=\frac{5!}{3!2!}\\=\frac{5\times4\times3!}{3!\times2\times1}\\=10\hspace{1mm}ways\) |
|
| 20. |
The mean age of a group of students is 15 years. When the age of a teacher, 45 years old, is added to the age of the students, the mean of their ages becomes 18 years. Find the number of the students in the group A. 9 B. 7 C. 42 D. 15 Detailed SolutionLet the number of students = xTotal age of the students = 15x Total age including age of the teacher = 15x + 45 Mean of their ages; (15x + 45)/(x + 1) = 18 15x + 45 = 18(x + 1) 15x + 45 = 18x + 18 18x - 15x = 45 - 18 3x = 27 x = 9 |
| 11. |
Find the derivatives of (2 + 3x)(1 - x) with respect to x A. 6 B. -3 C. 1 - 6x D. 6x - 1 Detailed Solutiony = (2 + 3x)(1 - x)y = 2 - 2x + 3x - 3x2 y = 2 + x - 3x2 dy/dx = 1 - 6x |
|
| 12. |
What is the rate of change of the volume V of a hemisphere with respect to its radius r when r = 2? A. 8π B. 16π C. 2π D. 4π Detailed Solution\(V = \frac{2}{3} \pi r^{3}\)\(\frac{\mathrm d V}{\mathrm d r} = 2\pi r^{2}\) \(\frac{\mathrm d V}{\mathrm d r} (r = 2) = 2\pi (2)^{2}\) = \(8\pi\) |
|
| 13. |
Find the derivatives of the function y = 2x\(^2\)(2x - 1) at the point x = -1? A. 18 B. 16 C. -4 D. -6 Detailed Solutiony = 2x\(^2\)(2x - 1)y = 4x\(^3\) - 2x\(^2\) dy/dx = 12x\(^2\) - 4x at x = -1 dy/dx = 12(-1)\(^2\) - 4(-1) = 12 + 4 = 16 |
|
| 14. |
Evaluate \(\int_{1}^{3}(x^2 - 1)dx\) A. \(\frac{2}{3}\) B. \(-\frac{2}{3}\) C. \(-6\frac{2}{3}\) D. \(6\frac{2}{3}\) Detailed Solution\(\int_{1}^{3}(x^2 - 1)dx = \left[\frac{1}{3}x^2 - x\right] ^{3}_{1}\\ =(9-3)-(\frac{1}{3}-1)\\ =6-\left(-\frac{2}{3}\right)\\ =6+\frac{2}{3}=6\frac{2}{3}\) |
|
| 15. |
Some white balls put in a basket containing twelve red balls and sixteen black balls. If the probability of picking a white balls from the baskets is 3/7, how many white balls were introduced? A. 12 B. 21 C. 28 D. 32 Detailed SolutionNumber of white balls = xNumber of red balls = 12 Number of black balls = 16 Total number of balls = 28 + x P(white balls) = 3/7 But P(white balls) \(= \frac{x}{28+x}\\ = \frac{3}{7} = \frac{x}{28+x}\\ 3(28 + x) = 7x\\ 84 + 3x = 7x\\ 7x - 3x = 84\\ 4x = 84\\ x = 21\) |
| 16. |
Find the mean deviation of 1, 2, 3 and 4 A. 2.5 B. 2.0 C. 1.0 D. 1.5 Detailed SolutionX = 1, 2, 3, 4; ∑X = 10x = ∑X/n = 10/4 = 2.5 X - x = -1.5, -0.5, 0.5, 1.5 lX - xl = 1.5, 0.5, 0.5, 1.5; ∑lX - xl = 4.0 mean deviation = (∑lX - xl)/n = 4.0/4 = 1.0 |
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| 17. |
An unbiased die is rolled 100 times and the outcome is tabulated above. A. 1/5 B. 1/2 C. 1/6 D. 1/4 Detailed SolutionNumber of times 5 was obtained = 20P(obtaining 5) = 20/100 = 1/5 |
|
| 18. |
The pie chart above shows the distribution of the crops harvested from a farmland in a year. If 3000 tonnes of millet is harvested, what amount of beans is harvested A. 6000 tonnes B. 1500 tonnes C. 1200 tonnes D. 9000 tonnes Detailed SolutionSectorial angle of beans = 360 - (150 + 90 + 60)= 360 -300 = 60o if 150o represents 3000 tonnes 1o 3000/150 60o will represents (3000/150) * (60/1) = 1200 tonnes |
|
| 19. |
In how many ways can 2 students be selected from a group of 5 students in a debating competition? A. 25 ways B. 10 ways C. 15 ways D. 20 ways Detailed Solution\(In\hspace{1mm} ^{5}C_{2}\hspace{1mm}ways\hspace{1mm}=\frac{5!}{(5-2)!2!}\\=\frac{5!}{3!2!}\\=\frac{5\times4\times3!}{3!\times2\times1}\\=10\hspace{1mm}ways\) |
|
| 20. |
The mean age of a group of students is 15 years. When the age of a teacher, 45 years old, is added to the age of the students, the mean of their ages becomes 18 years. Find the number of the students in the group A. 9 B. 7 C. 42 D. 15 Detailed SolutionLet the number of students = xTotal age of the students = 15x Total age including age of the teacher = 15x + 45 Mean of their ages; (15x + 45)/(x + 1) = 18 15x + 45 = 18(x + 1) 15x + 45 = 18x + 18 18x - 15x = 45 - 18 3x = 27 x = 9 |