Paper 1  Objectives  40 Questions
JAMB Exam
Year: 2021
Level: SHS
Time:
Type: Question Paper
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#  Question  Ans 

1. 
Solve the following equation: \(\frac{2}{(2r  1)}\)  \(\frac{5}{3}\) = \(\frac{1}{(r + 2)}\) A. ( 1,\(\frac{5}{2}\) ) B. ( 1,  \(\frac{5}{2}\) ) C. ( \(\frac{5}{2}\), 1 ) D. (2,1)
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Detailed Solution\(\frac{2}{(2r  1)}\)  \(\frac{5}{3}\) = \(\frac{1}{(r + 2)}\)\(\frac{2}{(2r  1)}\)  \(\frac{1}{(r + 2)}\) = \(\frac{5}{3}\) The L.C.M.: (2r  1) (r + 2) \(\frac{2(r + 2)  1(2r  1)}{(2r  1) (r + 2)}\) = \(\frac{5}{3}\) \(\frac{2r + 4  2r + 1}{ (2r  1) (r + 2)}\) = \(\frac{5}{3}\) cross multiply the solution 3 = (2r  1) (r + 2) or 2r\(^2\) + 3r  2 (when expanded) collect like terms 2r\(^2\) + 3r  2  3 = 0 2r\(^2\) + 3r  5 = 0 Factorize to get x = 1 or  \(\frac{5}{2}\) There is an explanation video available below. 

2. 
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
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Detailed Solution\(In\hspace{1mm} ^{5}C_{2}\hspace{1mm}ways\hspace{1mm}=\frac{5!}{(52)!2!}\\=\frac{5!}{3!2!}\\=\frac{5\times4\times3!}{3!\times2\times1}\\=10\hspace{1mm}ways\)There is an explanation video available below. 

3. 
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
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Detailed Solution\(V = \frac{2}{3} \pi r^{3}\)\(\frac{\mathrm d V}{\mathrm d r} = 2\pi r^{2}\) \(\frac{\mathrm d V}{\mathrm d r} (r = 2) = 2\pi (2)^{2}\) = \(8\pi\) There is an explanation video available below. 

4. 
Determine the maximum value of y=3x\(^2\) + 5x  3 A. 6 B. 0 C. 2 D. No correct option 

5. 
A trapezium has two parallel sides of lengths 5cm and 9cm. If the area is 91cm\(^2\), find the distance between the parallel sides A. 13 cm B. 4 cm C. 6 cm D. 7 cm
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Detailed SolutionArea of Trapezium = 1/2(sum of parallel sides) * h91 = \(\frac{1}{2}\) (5 + 9)h cross multiply 91 = 7h h = \(\frac{91}{7}\) h = 13cm There is an explanation video available below. 

6. 
Find the value of p if the line which passes through (1, p) and (2,2) is parallel to the line 2y+8x17=0? A. \(\frac{2}{7}\) B. \(\frac{7}{6}\) C. \(\frac{6}{7}\) D. 2
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Detailed SolutionLine: 2y+8x17=0recall y = mx + c 2y = 8x + 17 y = 4x + \(\frac{17}{2}\) Slope m\(_1\) = 4 parallel lines: m\(_1\). m\(_2\) = 4 where Slope ( 4) = \(\frac{y_2  y_1}{x_2  x_1}\) at points (1, p) and (2,2) 4( \(x_2  x_1\) ) = \(y_2  y_1\) 4 ( 2  1) = 2  p p = 4  2 = 2 There is an explanation video available below. 

7. 
The ratio of the length of two similar rectangular blocks is 2 : 3. If the volume of the larger block is 351cm\(^3\), then the volume of the other block is? A. 234.00 cm^{3} B. 526.50 cm^{3} C. 166.00 cm^{3} D. 687cm^{3}
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Detailed SolutionLet x represent total vol. 2 : 3 = 2 + 3 = 5\(\frac{3}{5}\)x = 351 x = \(\frac{351 \times 5}{3}\) = 585 Volume of smaller block = \(\frac{2}{5}\) x 585 = 234.00cm\(^3\) There is an explanation video available below. 

8. 
Find the derivative of the function y = 2x\(^2\)(2x  1) at the point x = 1? A. 18 B. 16 C. 4 D. 6
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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 There is an explanation video available below. 
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