Mathematics (Core), 2020, JAMB Exam, Exam, Paper 1 | Objectives

Paper Info

Year :

2020

Title :

Mathematics (Core)

Exam :

JAMB Exam

Paper 1 | Objectives

21 - 30 of 40 Questions

#	Question	Ans
21.	Calculate the standard deviation of the following data: 7, 8, 9, 10, 11, 12, 13 A. 2 B. 4 C. 12 D. 17 Show Content Detailed Solution 7 8 9 10 11 12 13 -3 -2 -1 0 1 2 3 9 4 1 1 0 4 9 -------------- 28 S.D = \(\frac{\sqrt\sum (x - x)^2}{N} = \frac{\sum d^2}{N} = \frac{\sqrt{28}}{7}\) = \(\sqrt{4}\) = 2 There is an explanation video available below.	A
22.	A number is selected at random between 20 and 30, both numbers inclusive. Find the probability that the number is a prime. A. \(\frac{2}{11}\) B. \(\frac{5}{11}\) C. \(\frac{6}{11}\) D. \(\frac{8}{11}\) Show Content Detailed Solution Possible outcomes are 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30. Prime numbers have only two factors, itself and 1. The prime numbers among the group are 23, 29. The probability of choosing a prime number = \(\frac{\text{Number of Prime}}{\text{No. of Total Possible Outcome}}\) = \(\frac{2}{11}\) There is an explanation video available below.	A
23.	The equation of the line in the graph is A. 3y = 3x + 12 B. 3y = 3x + 12 C. 3y = -4x + 12 D. 3y = -4x + 9 Show Content Detailed Solution Gradient of line = \(\frac{\text{Change in y}}{\text{Change in x}}\) = \(\frac{y_2 - Y}{x_2 - x}\) y\(_2\) = 0\(_1\) Y\(_1\) = 4 x\(_2\) = 3 and x\(_1\) = 0 \(\frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 4}{3 - 0} = \frac{-4}{3}\) Equation of straight line y = mx + c Where m = gradient and c = y intercept = 4 y = 4x + \(\frac{4}{3}\) multiply through y 3y = 4x + 23 There is an explanation video available below.	C
24.	Express the product of 0.0014 and 0.011 in standard form A. 1.54 x 10\(^{-2}\) B. 1.54 x 10\(^{-3}\) C. 1.54 x 10\(^{-2}\) D. 1.54 x 10\(^{-5}\) Show Content Detailed Solution There is an explanation video available below.	D
25.	A school boy lying on the ground 30m away from the foot of a water tank towel observes that the angle of elevation of the top of the tank is 60\(^o\). Calculate the height of the tank. A. 60\(\sqrt{3m}\) B. 30\(\sqrt{3m}\) C. 20\(\sqrt{3m}\) D. 10\(\sqrt{3m}\) Show Content Detailed Solution h = 30 tan 60 = 30\(\sqrt{3}\) There is an explanation video available below.	B
26.	Find the simple interest rate percent annum at which N1000 accumulates to N1240 in 3 years. A. 6% B. 8% C. 10% D. 12% Show Content Detailed Solution I = \(\frac{PRT}{100}\) = 1 = 1240 - 1000 = 240 R = \(\frac{240 \times 100}{100 \times 3}\) = 8% There is an explanation video available below.	B
27.	The pie chart shows the income of a civil servant in month. If his monthly income is N6,000. Find his monthly basic salary. A. N2,050 B. N2600 C. N3,100 D. N3,450 Show Content Detailed Solution 360\(^o\) - (60\(^o\) + 60\(^o\) + 67 + 50 = 237\(^o\)) 360\(^o\) - 237 = 130\(^o\) B. Salary = \(\frac{123}{360} X \frac{N6000}{1}\) = N2,050 There is an explanation video available below.	A
28.	If x is positive real number, find the range of values for which \(\frac{1}{3x}\) + \(\frac{1}{2}\)x = \(\frac{2 + 3x}{6x}\) > \(\frac{1}{4x}\) A. x > -\(\frac{1}{6}\) B. x > 0 C. 0 < x < 6 D. 0 < x <\(\frac{1}{6}\) Show Content Detailed Solution \(\frac{1}{3x}\) + \(\frac{1}{2}\)x = \(\frac{2 + 3x}{6x}\) > \(\frac{1}{4x}\) = 4(2 + 3x) > 6x = 12x\(^2\) - 2x = 0 = 2x(6x - 1) > 0 = x(6x - 1) > 0 Case 1 (-, -) = x < 0, 6x - 1 > 0 = x < 0, x < \(\frac{1}{6}\) (solution) Case 2 (+, +) = x > 0, 6x - 1 > 0 = x > 0 x > \(\frac{1}{6}\) Combining solutions in cases (1) and (2) = x > 0, x < \(\frac{1}{6}\) = 0 < x < \(\frac{1}{6}\) There is an explanation video available below.	A
29.	Find the value of x if \(\frac{\sqrt{2}}{x + \sqrt{2}}\) = \(\frac{1}{x - \sqrt{2}}\) A. 3\(\sqrt{2}\) + 4 B. 3\(\sqrt{2}\) - 4 C. 3 - 2\(\sqrt{2}\) D. 4 + 2\(\sqrt{2}\) Show Content Detailed Solution \(\frac{\sqrt{2}}{x + 2}\) = x - \(\frac{1}{\sqrt{2}}\) x\(\sqrt{2}\) (x - \(\sqrt{2}\)) = x + \(\sqrt{2}\) (cross multiply) x\(\sqrt{2}\) - 2 = x + \(\sqrt{2}\) = x\(\sqrt{2}\) - x = 2 + \(\sqrt{2}\) x (\(\sqrt{2}\) - 1) = 2 + \(\sqrt{2}\) = \(\frac{2 + \sqrt{2}}{\sqrt{2} - 1} \times \frac{\sqrt{2} + 1}{\sqrt{2} + 1}\) x = \(\frac{2 \sqrt{2} + 2 + 2 + \sqrt{2}}{2 - 1}\) = 3\(\sqrt{2}\) + 4 There is an explanation video available below.	A
30.	A binary operation x is defined by a x b = a\(^b\). If a x 2 = 2 - a, find the possible values of a? A. 1, -2 B. 2, -1 C. 2, -2 D. 1, -1 Show Content Detailed Solution a = b = a\(^2\) a + 2 = a\(^2\).....(i) a + 2 = 2 - a..............(ii) a\(^2\) = 2 - a a\(^2\)+ a - 2 = a\(^2\) + a - 2 = 0 = (a + 2)(a - 1) = 0 a = 1 or - 2 There is an explanation video available below.	A

21.	Calculate the standard deviation of the following data: 7, 8, 9, 10, 11, 12, 13 A. 2 B. 4 C. 12 D. 17 Show Content Detailed Solution 7 8 9 10 11 12 13 -3 -2 -1 0 1 2 3 9 4 1 1 0 4 9 -------------- 28 S.D = \(\frac{\sqrt\sum (x - x)^2}{N} = \frac{\sum d^2}{N} = \frac{\sqrt{28}}{7}\) = \(\sqrt{4}\) = 2 There is an explanation video available below.	A
22.	A number is selected at random between 20 and 30, both numbers inclusive. Find the probability that the number is a prime. A. \(\frac{2}{11}\) B. \(\frac{5}{11}\) C. \(\frac{6}{11}\) D. \(\frac{8}{11}\) Show Content Detailed Solution Possible outcomes are 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30. Prime numbers have only two factors, itself and 1. The prime numbers among the group are 23, 29. The probability of choosing a prime number = \(\frac{\text{Number of Prime}}{\text{No. of Total Possible Outcome}}\) = \(\frac{2}{11}\) There is an explanation video available below.	A
23.	The equation of the line in the graph is A. 3y = 3x + 12 B. 3y = 3x + 12 C. 3y = -4x + 12 D. 3y = -4x + 9 Show Content Detailed Solution Gradient of line = \(\frac{\text{Change in y}}{\text{Change in x}}\) = \(\frac{y_2 - Y}{x_2 - x}\) y\(_2\) = 0\(_1\) Y\(_1\) = 4 x\(_2\) = 3 and x\(_1\) = 0 \(\frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 4}{3 - 0} = \frac{-4}{3}\) Equation of straight line y = mx + c Where m = gradient and c = y intercept = 4 y = 4x + \(\frac{4}{3}\) multiply through y 3y = 4x + 23 There is an explanation video available below.	C
24.	Express the product of 0.0014 and 0.011 in standard form A. 1.54 x 10\(^{-2}\) B. 1.54 x 10\(^{-3}\) C. 1.54 x 10\(^{-2}\) D. 1.54 x 10\(^{-5}\) Show Content Detailed Solution There is an explanation video available below.	D
25.	A school boy lying on the ground 30m away from the foot of a water tank towel observes that the angle of elevation of the top of the tank is 60\(^o\). Calculate the height of the tank. A. 60\(\sqrt{3m}\) B. 30\(\sqrt{3m}\) C. 20\(\sqrt{3m}\) D. 10\(\sqrt{3m}\) Show Content Detailed Solution h = 30 tan 60 = 30\(\sqrt{3}\) There is an explanation video available below.	B

26.	Find the simple interest rate percent annum at which N1000 accumulates to N1240 in 3 years. A. 6% B. 8% C. 10% D. 12% Show Content Detailed Solution I = \(\frac{PRT}{100}\) = 1 = 1240 - 1000 = 240 R = \(\frac{240 \times 100}{100 \times 3}\) = 8% There is an explanation video available below.	B
27.	The pie chart shows the income of a civil servant in month. If his monthly income is N6,000. Find his monthly basic salary. A. N2,050 B. N2600 C. N3,100 D. N3,450 Show Content Detailed Solution 360\(^o\) - (60\(^o\) + 60\(^o\) + 67 + 50 = 237\(^o\)) 360\(^o\) - 237 = 130\(^o\) B. Salary = \(\frac{123}{360} X \frac{N6000}{1}\) = N2,050 There is an explanation video available below.	A
28.	If x is positive real number, find the range of values for which \(\frac{1}{3x}\) + \(\frac{1}{2}\)x = \(\frac{2 + 3x}{6x}\) > \(\frac{1}{4x}\) A. x > -\(\frac{1}{6}\) B. x > 0 C. 0 < x < 6 D. 0 < x <\(\frac{1}{6}\) Show Content Detailed Solution \(\frac{1}{3x}\) + \(\frac{1}{2}\)x = \(\frac{2 + 3x}{6x}\) > \(\frac{1}{4x}\) = 4(2 + 3x) > 6x = 12x\(^2\) - 2x = 0 = 2x(6x - 1) > 0 = x(6x - 1) > 0 Case 1 (-, -) = x < 0, 6x - 1 > 0 = x < 0, x < \(\frac{1}{6}\) (solution) Case 2 (+, +) = x > 0, 6x - 1 > 0 = x > 0 x > \(\frac{1}{6}\) Combining solutions in cases (1) and (2) = x > 0, x < \(\frac{1}{6}\) = 0 < x < \(\frac{1}{6}\) There is an explanation video available below.	A
29.	Find the value of x if \(\frac{\sqrt{2}}{x + \sqrt{2}}\) = \(\frac{1}{x - \sqrt{2}}\) A. 3\(\sqrt{2}\) + 4 B. 3\(\sqrt{2}\) - 4 C. 3 - 2\(\sqrt{2}\) D. 4 + 2\(\sqrt{2}\) Show Content Detailed Solution \(\frac{\sqrt{2}}{x + 2}\) = x - \(\frac{1}{\sqrt{2}}\) x\(\sqrt{2}\) (x - \(\sqrt{2}\)) = x + \(\sqrt{2}\) (cross multiply) x\(\sqrt{2}\) - 2 = x + \(\sqrt{2}\) = x\(\sqrt{2}\) - x = 2 + \(\sqrt{2}\) x (\(\sqrt{2}\) - 1) = 2 + \(\sqrt{2}\) = \(\frac{2 + \sqrt{2}}{\sqrt{2} - 1} \times \frac{\sqrt{2} + 1}{\sqrt{2} + 1}\) x = \(\frac{2 \sqrt{2} + 2 + 2 + \sqrt{2}}{2 - 1}\) = 3\(\sqrt{2}\) + 4 There is an explanation video available below.	A
30.	A binary operation x is defined by a x b = a\(^b\). If a x 2 = 2 - a, find the possible values of a? A. 1, -2 B. 2, -1 C. 2, -2 D. 1, -1 Show Content Detailed Solution a = b = a\(^2\) a + 2 = a\(^2\).....(i) a + 2 = 2 - a..............(ii) a\(^2\) = 2 - a a\(^2\)+ a - 2 = a\(^2\) + a - 2 = 0 = (a + 2)(a - 1) = 0 a = 1 or - 2 There is an explanation video available below.	A