Mathematics (Core), 1979, JAMB Exam, Exam, Paper 1 | Objectives

Paper Info

Year :

1979

Title :

Mathematics (Core)

Exam :

JAMB Exam

Paper 1 | Objectives

31 - 40 of 51 Questions

#	Question	Ans
31.	Simplify \(\frac{1 - x^2}{x - x^2}\), where x \(\neq\) 0 A. \(\frac{1}{x}\) B. \(\frac{1 - x}{x}\) C. \(\frac{1 + x}{x}\) D. \(\frac{1}{x - 1}\) E. \(\frac{-x - 1}{1}\) Show Content Detailed Solution \(\frac{1 - x^2}{x - x^2}\), where x = \(\neq\) 0 \(\frac{1^2 - x^2}{x - x^2}\) = \(\frac{(1 + x)(1 - x)}{x(1 - x)}\) = \(\frac{1 + x}{x}\)	C
32.	A cylinder of height h and radius r is open at one end. Its surface area is A. 2\(\pi\)rh B. \(\pi\)r²h C. 2\(\pi\)rh + \(\pi\)r² D. 2\(\pi\)rh + 2\(\pi\)r² Show Content Detailed Solution A cylinder of height h ans radius r is open at one end, its surface area is 2\(\pi\)rh + \(\pi\)r²	C
33.	An arc of circle of radius 2cm subtends an angle of 60^o at the centre. Find the area of the sector A. \(\frac{2 \pi}{3}\)cm² B. \(\frac{\pi}{2}\)cm² C. \(\frac{\pi}{3}\)cm² D. \(\pi\)cm² Show Content Detailed Solution Area of a sector \(\frac{\theta}{360}\) x 2\(\pi\)r = \(\frac{60^o}{360^o}\) x 2\(\pi\)r = \(\frac{2 \pi}{3}\)cm²	A
34.	What is the greatest straight line distance between two vertices (corners) of a cube whose sides are 2239cm long? A. \(\sqrt{2239cm}\) B. \(\sqrt{2}\) x 2239cm C. \(\frac{\sqrt{3}}{2}\) 2239cm D. \(\sqrt{3}\) x 2239cm E. 4478cm Show Content Detailed Solution x = \(\sqrt{-2239^2 + 2239^2}\) = -\(\sqrt{10026242}\) = 3166.42 y = -\(\sqrt{10026242 + 5013121}\) = -\(\sqrt{15039363}\) = 3878 = \(\sqrt{3}\) x 2239	D
35.	What is log₇(49^a) - log₁₀(0.01)? A. \(\frac{49^a}{100}\) B. \(\frac{a}{2}\) + 2 C. 7^2a + 2 D. 2a + 2 E. \(\frac{2a}{2}\) Show Content Detailed Solution log₇(49^a) - log₁₀(0.01) = log₇(7²)^a - log₁₀100 log₇7^2a - log₁₀1 - log₁₀ 10² = 2a - 2 = 2a + a	D
36.	The size of a quantity first doubles and then increases by a further 16%. After a short time its size decreases by 16%. What is the net increases in size of the quantity? A. \(\frac{59300}{625}\) B. \(\frac{50900}{625}\) C. 200% D. +100% Show Content Detailed Solution Let x rept. the size of the quantity 2x + \(\frac{116}{100}\) x \(\frac{-84}{100}\) = 200%	C
37.	The following table relates the number of objects f corresponding to a certain size x. What is the average size of an object? \(\begin{array}{c\|c} f & 1 & 2 & 3 & 4 & 5 \\ \hline x & 1 & 2 & 4 & 8 & 16\end{array}\) A. \(\frac{31}{15}\) B. \(\frac{31}{5}\) C. \(\frac{129}{5}\) D. \(\frac{43}{5}\) E. \(\frac{16}{5}\) Show Content Detailed Solution F = 1, 2, 3, 4, 5 x = 1, 2, 4, 8, 16 fx = 1, 4, 12, 32, 80, 3f = 15 (average size) = \(\frac{\sum fx}{\sum f}\) = \(\frac{129}{15}\) = \(\frac{43}{5}\)	D
38.	If y = x² - 2x - 3, Find the least value of y and corresponding value of x A. x = 3, y = 3 B. x = 1, y = -3 C. x = 4, y = 1 D. x = 1, y = -4 E. x = 2, y = -3 Show Content Detailed Solution If the graph of eqn. y = x² - 2x - 3 is plot and drawn, the lease value of y = -4 while the corresponding value of x = 1 x = 1, y = -4	D
39.	A father is now three times as old as his son. Twelve years ago he was six times as old as his son. How old are the son and the father? A. 20 and 45 B. 100 and 150 C. 45 and 65 D. 35 and 75 E. 20 and 60 Show Content Detailed Solution Son = x, Father = 3x, 12 yrs ago son = x - 12, father = 3x - 12 3x - 12 = 6(x - 12) 3x - 12 = 6x - 72 3x = 60 x = 20	E
40.	If \(\sqrt{3^{\frac{1}{x}}}\) = \(\sqrt{9}\) then the value of x is: A. \(\frac{3}{4}\) B. \(\frac{4}{3}\) C. \(\frac{1}{3}\) D. \(\frac{2}{3}\) E. \(\frac{1}{2}\) Show Content Detailed Solution \(\sqrt{3^{\frac{1}{x}}}\) = \(\sqrt{9}\) 3\(^{\frac{1}{2x}}\) = \(9^{\frac{1}{2}}\) 3\(^{\frac{1}{2x}}\) = 3\(^{2 \times \frac{1}{2}}\) 3\(\frac{1}{2x}\) = 3\(\frac{2}{2}\) = 3 \(3^{\frac{1}{2x}}\) = \(3^{1}\) \(\frac{1}{2x}\) = \(\frac{1}{1}\) x = \(\frac{1}{2}\)	E

31.	Simplify \(\frac{1 - x^2}{x - x^2}\), where x \(\neq\) 0 A. \(\frac{1}{x}\) B. \(\frac{1 - x}{x}\) C. \(\frac{1 + x}{x}\) D. \(\frac{1}{x - 1}\) E. \(\frac{-x - 1}{1}\) Show Content Detailed Solution \(\frac{1 - x^2}{x - x^2}\), where x = \(\neq\) 0 \(\frac{1^2 - x^2}{x - x^2}\) = \(\frac{(1 + x)(1 - x)}{x(1 - x)}\) = \(\frac{1 + x}{x}\)	C
32.	A cylinder of height h and radius r is open at one end. Its surface area is A. 2\(\pi\)rh B. \(\pi\)r²h C. 2\(\pi\)rh + \(\pi\)r² D. 2\(\pi\)rh + 2\(\pi\)r² Show Content Detailed Solution A cylinder of height h ans radius r is open at one end, its surface area is 2\(\pi\)rh + \(\pi\)r²	C
33.	An arc of circle of radius 2cm subtends an angle of 60^o at the centre. Find the area of the sector A. \(\frac{2 \pi}{3}\)cm² B. \(\frac{\pi}{2}\)cm² C. \(\frac{\pi}{3}\)cm² D. \(\pi\)cm² Show Content Detailed Solution Area of a sector \(\frac{\theta}{360}\) x 2\(\pi\)r = \(\frac{60^o}{360^o}\) x 2\(\pi\)r = \(\frac{2 \pi}{3}\)cm²	A
34.	What is the greatest straight line distance between two vertices (corners) of a cube whose sides are 2239cm long? A. \(\sqrt{2239cm}\) B. \(\sqrt{2}\) x 2239cm C. \(\frac{\sqrt{3}}{2}\) 2239cm D. \(\sqrt{3}\) x 2239cm E. 4478cm Show Content Detailed Solution x = \(\sqrt{-2239^2 + 2239^2}\) = -\(\sqrt{10026242}\) = 3166.42 y = -\(\sqrt{10026242 + 5013121}\) = -\(\sqrt{15039363}\) = 3878 = \(\sqrt{3}\) x 2239	D
35.	What is log₇(49^a) - log₁₀(0.01)? A. \(\frac{49^a}{100}\) B. \(\frac{a}{2}\) + 2 C. 7^2a + 2 D. 2a + 2 E. \(\frac{2a}{2}\) Show Content Detailed Solution log₇(49^a) - log₁₀(0.01) = log₇(7²)^a - log₁₀100 log₇7^2a - log₁₀1 - log₁₀ 10² = 2a - 2 = 2a + a	D

36.	The size of a quantity first doubles and then increases by a further 16%. After a short time its size decreases by 16%. What is the net increases in size of the quantity? A. \(\frac{59300}{625}\) B. \(\frac{50900}{625}\) C. 200% D. +100% Show Content Detailed Solution Let x rept. the size of the quantity 2x + \(\frac{116}{100}\) x \(\frac{-84}{100}\) = 200%	C
37.	The following table relates the number of objects f corresponding to a certain size x. What is the average size of an object? \(\begin{array}{c\|c} f & 1 & 2 & 3 & 4 & 5 \\ \hline x & 1 & 2 & 4 & 8 & 16\end{array}\) A. \(\frac{31}{15}\) B. \(\frac{31}{5}\) C. \(\frac{129}{5}\) D. \(\frac{43}{5}\) E. \(\frac{16}{5}\) Show Content Detailed Solution F = 1, 2, 3, 4, 5 x = 1, 2, 4, 8, 16 fx = 1, 4, 12, 32, 80, 3f = 15 (average size) = \(\frac{\sum fx}{\sum f}\) = \(\frac{129}{15}\) = \(\frac{43}{5}\)	D
38.	If y = x² - 2x - 3, Find the least value of y and corresponding value of x A. x = 3, y = 3 B. x = 1, y = -3 C. x = 4, y = 1 D. x = 1, y = -4 E. x = 2, y = -3 Show Content Detailed Solution If the graph of eqn. y = x² - 2x - 3 is plot and drawn, the lease value of y = -4 while the corresponding value of x = 1 x = 1, y = -4	D
39.	A father is now three times as old as his son. Twelve years ago he was six times as old as his son. How old are the son and the father? A. 20 and 45 B. 100 and 150 C. 45 and 65 D. 35 and 75 E. 20 and 60 Show Content Detailed Solution Son = x, Father = 3x, 12 yrs ago son = x - 12, father = 3x - 12 3x - 12 = 6(x - 12) 3x - 12 = 6x - 72 3x = 60 x = 20	E
40.	If \(\sqrt{3^{\frac{1}{x}}}\) = \(\sqrt{9}\) then the value of x is: A. \(\frac{3}{4}\) B. \(\frac{4}{3}\) C. \(\frac{1}{3}\) D. \(\frac{2}{3}\) E. \(\frac{1}{2}\) Show Content Detailed Solution \(\sqrt{3^{\frac{1}{x}}}\) = \(\sqrt{9}\) 3\(^{\frac{1}{2x}}\) = \(9^{\frac{1}{2}}\) 3\(^{\frac{1}{2x}}\) = 3\(^{2 \times \frac{1}{2}}\) 3\(\frac{1}{2x}\) = 3\(\frac{2}{2}\) = 3 \(3^{\frac{1}{2x}}\) = \(3^{1}\) \(\frac{1}{2x}\) = \(\frac{1}{1}\) x = \(\frac{1}{2}\)	E