Mathematics (Core), 1982, JAMB Exam, Exam, Paper 1 | Objectives

Paper Info

Year :

1982

Title :

Mathematics (Core)

Exam :

JAMB Exam

Paper 1 | Objectives

21 - 30 of 48 Questions

#	Question	Ans
21.	Find the values of x for which the expression \(\frac{(x - 3)(x - 2)}{x^2 + x - 2}\) A. 1, -2 B. -1, 2 C. 2, 3 D. -2 E. -2, -3 Show Content Detailed Solution to find the values of x for which the expression is underlined, let x² + x - 2 = 0 By factorizing, we have (x + 2)(x - 1) = 0 when x + 2 = 0, when x - 1 = 0, x = -2 or x = 1 The two values are -2 and 1	A
22.	A stone Q is tied to a point P vertically above Q by an inelastic string of length 2 meters. How high does the stone rise when the string is inclined at an angle 60^o to the vertical? A. It does not rise B. 2\(\sqrt{3}\) meters C. 3 meters D. 1 meters E. 3 Show Content Detailed Solution Cos 60^o = \(\frac{PD}{2}\) Cos 60^o x 2 = 0.5 x 2 = 1m	D
23.	Express 130 kilometers per second in meters per hour A. 7.8 x 10^-5 B. 4.68 x 10⁶ C. 7,800,000 D. 4.68 x 10⁸ E. 7.80 x 10⁵ Show Content Detailed Solution 1km = 1000m 60sec. = 1 mins 60 mins. = 1 hr 130000m per sec = 130000 x 3600 = 468000000m/hr = 468 x 108 m/hr	D
24.	The quantity y is partly constant and partly varies inversely as the square of x. With P and Q as constants, a possible relationship between x and y is A. y = Q + \(\frac{P}{x^2}\) B. y = Q + px C. y = \(\frac{PQ}{x^2}\) D. y = Q - \(\frac{P}{x^2}\) Show Content Detailed Solution Given the above statement, \(y = Q + \frac{P}{x^{2}}\)	A
25.	If \(\frac{3e + f}{3f - e}\) = \(\frac{2}{5}\), find the value of \(\frac{e + 3f}{f - 3e}\) A. \(\frac{5}{2}\) B. 1 C. \(\frac{26}{7}\) D. \(\frac{1}{3}\) Show Content Detailed Solution \(\frac{3e + f}{3f - e}\) = \(\frac{2}{5}\) = 3e + f = 2 x 1 \(\frac{-e + 3f}{3e - f}\) = \(\frac{5 \times 3}{2}\) = \(\frac{3e + 9f = 15}{10f = 17}\) f = \(\frac{17}{10}\) Sub. for equ. (1) 3e + \(\frac{17}{10}\) = 2 3e = 2 - \(\frac{17}{10}\) \(\frac{3}{10}\) e = \(\frac{3}{10}\) x \(\frac{1}{3}\) = \(\frac{1}{10}\) = e + 3f = \(\frac{1}{10}\) + \(\frac{3 \times}{10}\) = \(\frac{52}{10}\) f - 3e = \(\frac{17}{10}\) - 3 x \(\frac{1}{10}\) = \(\frac	C
26.	A world congress of mathematicians were held in Nice in 1970 with 800 people participating. There were 300 from Europe, 200 from America, 150 from Asia, 45 from Africa and 105 from Australia. Representing the above on a pie chart, the angle of the sector representing the participants from Asia is? A. 150^o B. 67\(\frac{1}{2}\)^o C. 67^o D. 135^o E. 68^o Show Content Detailed Solution Representing from Asia is 150 \(\frac{150}{800}\) x 360 = \(\frac{135}{2}\) = 67\(\frac{1}{2}\)o	B
27.	The diameter of a metal rod is measured as 23.40 cm to four significant figures. What is the maximum error in the measurement? A. 0.05cm B. 0.5cm C. 0.045cm D. 0.005cm E. 0.004cm Show Content Detailed Solution Maximum error in measurement to 2 decimal places Maximum error = \(\frac{1}{2}\) x 0.001 = 0.005	D
28.	In a regular polygon of n sides, each interior angle is 144o. Find n A. 12 B. 11 C. 10 D. 8 E. 6F Show Content Detailed Solution Formula for an interior angle of a polygon is (2n - 4) x 90 (2n - 4) x 90 = 144n 190n - 360 = 144n n = \(\frac{360}{36}\) = 10	C
29.	Simplify \(\frac{3}{2x - 1}\) + \(\frac{2 - x}{x - 2}\) A. \(\frac{2 - x}{(2x - 1)(x - 2)}\) B. \(\frac{5 - x}{(2x - 1)(x - 2)}\) C. \(\frac{4 - 2x}{2x - 1}\) D. \(\frac{6 - 3x}{(2x - 1)(x - 2)}\) Show Content Detailed Solution \(\frac{3}{2x - 1}\) + \(\frac{2 - x}{x - 2}\) = \(\frac{3}{2x - 1}\) - \(\frac{x - 2}{x - 2}\) = \(\frac{3}{2x - 1}\) - 1 = \(\frac{3 - (2x - 1)}{2x - 1}\) = \(\frac{3 - 2x + 1}{2x - 1}\) = \(\frac{4 - 2x}{2x - 1}\)	C
30.	The solution to the quadratic equation 5 + 3x - 2x² = 0 is A. (\(\frac{5}{2}\), 1) B. (5, 3) C. -(\(\frac{5}{2}\), -1) D. (\(\frac{5}{2}\), -1) Show Content Detailed Solution 5 + 3x - 2x² = 0, (x + 1)(5 - 2x) (expand to check) (x + 1)(5 - 2x) = 0 when x = 1 = 0, x = -1 when 5 - 2x = 0, x = \(\frac{5}{2}\) - 1	D

21.	Find the values of x for which the expression \(\frac{(x - 3)(x - 2)}{x^2 + x - 2}\) A. 1, -2 B. -1, 2 C. 2, 3 D. -2 E. -2, -3 Show Content Detailed Solution to find the values of x for which the expression is underlined, let x² + x - 2 = 0 By factorizing, we have (x + 2)(x - 1) = 0 when x + 2 = 0, when x - 1 = 0, x = -2 or x = 1 The two values are -2 and 1	A
22.	A stone Q is tied to a point P vertically above Q by an inelastic string of length 2 meters. How high does the stone rise when the string is inclined at an angle 60^o to the vertical? A. It does not rise B. 2\(\sqrt{3}\) meters C. 3 meters D. 1 meters E. 3 Show Content Detailed Solution Cos 60^o = \(\frac{PD}{2}\) Cos 60^o x 2 = 0.5 x 2 = 1m	D
23.	Express 130 kilometers per second in meters per hour A. 7.8 x 10^-5 B. 4.68 x 10⁶ C. 7,800,000 D. 4.68 x 10⁸ E. 7.80 x 10⁵ Show Content Detailed Solution 1km = 1000m 60sec. = 1 mins 60 mins. = 1 hr 130000m per sec = 130000 x 3600 = 468000000m/hr = 468 x 108 m/hr	D
24.	The quantity y is partly constant and partly varies inversely as the square of x. With P and Q as constants, a possible relationship between x and y is A. y = Q + \(\frac{P}{x^2}\) B. y = Q + px C. y = \(\frac{PQ}{x^2}\) D. y = Q - \(\frac{P}{x^2}\) Show Content Detailed Solution Given the above statement, \(y = Q + \frac{P}{x^{2}}\)	A
25.	If \(\frac{3e + f}{3f - e}\) = \(\frac{2}{5}\), find the value of \(\frac{e + 3f}{f - 3e}\) A. \(\frac{5}{2}\) B. 1 C. \(\frac{26}{7}\) D. \(\frac{1}{3}\) Show Content Detailed Solution \(\frac{3e + f}{3f - e}\) = \(\frac{2}{5}\) = 3e + f = 2 x 1 \(\frac{-e + 3f}{3e - f}\) = \(\frac{5 \times 3}{2}\) = \(\frac{3e + 9f = 15}{10f = 17}\) f = \(\frac{17}{10}\) Sub. for equ. (1) 3e + \(\frac{17}{10}\) = 2 3e = 2 - \(\frac{17}{10}\) \(\frac{3}{10}\) e = \(\frac{3}{10}\) x \(\frac{1}{3}\) = \(\frac{1}{10}\) = e + 3f = \(\frac{1}{10}\) + \(\frac{3 \times}{10}\) = \(\frac{52}{10}\) f - 3e = \(\frac{17}{10}\) - 3 x \(\frac{1}{10}\) = \(\frac	C

26.	A world congress of mathematicians were held in Nice in 1970 with 800 people participating. There were 300 from Europe, 200 from America, 150 from Asia, 45 from Africa and 105 from Australia. Representing the above on a pie chart, the angle of the sector representing the participants from Asia is? A. 150^o B. 67\(\frac{1}{2}\)^o C. 67^o D. 135^o E. 68^o Show Content Detailed Solution Representing from Asia is 150 \(\frac{150}{800}\) x 360 = \(\frac{135}{2}\) = 67\(\frac{1}{2}\)o	B
27.	The diameter of a metal rod is measured as 23.40 cm to four significant figures. What is the maximum error in the measurement? A. 0.05cm B. 0.5cm C. 0.045cm D. 0.005cm E. 0.004cm Show Content Detailed Solution Maximum error in measurement to 2 decimal places Maximum error = \(\frac{1}{2}\) x 0.001 = 0.005	D
28.	In a regular polygon of n sides, each interior angle is 144o. Find n A. 12 B. 11 C. 10 D. 8 E. 6F Show Content Detailed Solution Formula for an interior angle of a polygon is (2n - 4) x 90 (2n - 4) x 90 = 144n 190n - 360 = 144n n = \(\frac{360}{36}\) = 10	C
29.	Simplify \(\frac{3}{2x - 1}\) + \(\frac{2 - x}{x - 2}\) A. \(\frac{2 - x}{(2x - 1)(x - 2)}\) B. \(\frac{5 - x}{(2x - 1)(x - 2)}\) C. \(\frac{4 - 2x}{2x - 1}\) D. \(\frac{6 - 3x}{(2x - 1)(x - 2)}\) Show Content Detailed Solution \(\frac{3}{2x - 1}\) + \(\frac{2 - x}{x - 2}\) = \(\frac{3}{2x - 1}\) - \(\frac{x - 2}{x - 2}\) = \(\frac{3}{2x - 1}\) - 1 = \(\frac{3 - (2x - 1)}{2x - 1}\) = \(\frac{3 - 2x + 1}{2x - 1}\) = \(\frac{4 - 2x}{2x - 1}\)	C
30.	The solution to the quadratic equation 5 + 3x - 2x² = 0 is A. (\(\frac{5}{2}\), 1) B. (5, 3) C. -(\(\frac{5}{2}\), -1) D. (\(\frac{5}{2}\), -1) Show Content Detailed Solution 5 + 3x - 2x² = 0, (x + 1)(5 - 2x) (expand to check) (x + 1)(5 - 2x) = 0 when x = 1 = 0, x = -1 when 5 - 2x = 0, x = \(\frac{5}{2}\) - 1	D