Mathematics (Core), 2008, WASSCE/WAEC MAY/JUNE, Exam, Paper 1 | Objectives

Paper Info

Year :

2008

Title :

Mathematics (Core)

Exam :

WASSCE/WAEC MAY/JUNE

Paper 1 | Objectives

21 - 30 of 45 Questions

#	Question	Ans
21.	If x \(\alpha\) (45 + \(\frac{1}{2}y\)), which of the following is true>? A. x varies directly as y B. x varies inversely as y C. x is partly constant and partly varies as y D. x vries jointly as 45 and directly as y	C
22.	Simplify \(\frac{\log \sqrt{8}}{\log 4 - \log 2}\) A. \(\frac{2}{3}\) B. \(\frac{1}{2} \log 2\) C. \(\frac{3}{2}\) D. \(\log 2\) Show Content Detailed Solution \(\frac{\log\sqrt{8}}{\log 4 - \log 2} = \frac{\log 8\frac{1}{2}}{\log (\frac{4}{2})}\) = \(\frac{8 \frac{1}{2}}{\log (\frac{4}{2})}\) = \(\frac{\frac{1}{2} \log 2^3}{\log 2}\) = \(\frac{3}{2} \frac{\log 2}{\log 2}\) = \(\frac{3}{2}\)	C
23.	A train travels 60km in M minutes. If its average speed is 400km per hour, find the value of M A. 15 B. 12 C. 10 D. 9 Show Content Detailed Solution Average speed = \(\frac{Distance}{Time}\) \(\frac{400km}{hr} = \frac{60km}{Time}\) Time = \(\frac{60km}{400 km/hr}\) = \(\frac{60hr}{400}\) M = \(\frac{60hr}{400} \times \frac{60min}{1hr}\) = 9 minutes	D
24.	An arc of a circle, radius 14cm, is 18.33cm long. Calculate to the nearest degree, the angle which the arc subtends at the centre of the circle. [T = \(\frac{22}{7}\)] A. 11^o B. 20^o C. 22^o D. 75^o Show Content Detailed Solution Length of an arc = \(\frac{\theta}{360} \times 2\pi r\) 18.33 = \(\frac{\theta}{360} \times 2 \times \frac{22}{7} \times 14\) \(\theta = \frac{18.33 \times 360 \times 17}{2 \times 22 \times 14}\) = 75^o (approx.)	D
25.	What is the length of an edge of a cube whose total surface area is X cm² and whose total surface area is \(\frac{X}{2}\)cm³? A. 3 B. 6 C. 9 D. 12 Show Content Detailed Solution Total surface area of cube = 6s² 6s² = x s² = x = \(\frac{x}{6}\).....(1) volume of a cube = s² = \(\frac{x}{2}\) s² = \(\frac{x}{2}\)......(2) put(1) into (2) s(\(\frac{x}{6}\)) = \(\frac{x}{2}\) s = \(\frac{x}{2} \times \frac{6}{x}\) = 3cm	A
26.	XY is a chord of circle centre O and radius 7cm. The chord XY which is 8cm long subtends an angle of 120^o at the centre of the circle. Calculate the perimeter of the minor segment. [Take \(\pi = \frac{22}{7}\)] A. 14.67cm B. 22.67cm C. 29.33cm D. 37.33cm Show Content Detailed Solution perimeter of minor segment = Length of arc xy + chord xy where lxy = \(\frac{120}{360} \times 2x \times \frac{22}{7} \times 7\) = 14.67cm perimeter of minor segment = 14.67 + 8 = 22.67cm	B
27.	If p = \(\frac{1}{2}\) and \(\frac{1}{p - 1} = \frac{2}{p + x}\), find the value of x A. -2\(\frac{1}{2}\) B. -1\(\frac{1}{2}\) C. 1\(\frac{1}{2}\) D. 2\(\frac{1}{2}\) Show Content Detailed Solution p = \(\frac{1}{2}; \frac{1}{p - 1} = \frac{2}{p + x}\) \(\frac{1}{\frac{1}{2} - 1} = \frac{2}{\frac{1}{2} + x}\) \(\frac{1}{\frac{1 - 2}{2}} = \frac{2}{\frac{1 + 2x}{2}}\) \(\frac{1}{-\frac{1}{2}} = \frac{2}{\frac{1 + 2x}{2}}\) -2 = \(\frac{4}{1 + 2x} -2(1 + 2x) = 4\) 1 + 2x = \(\frac{4}{-2}\) 1 + 2x = -2 2x = -2 - 1 2x = -3 x = -\(\frac{3}{2}\) x = -1\(\frac{1}{2}\)	B
28.	Find the quadratic equation whose roots are c and -c A. x² - c² = 0 B. x² + 2cx = 0 C. x² + 2cx + c² = 0 D. x² - 2cx + c² = 0 Show Content Detailed Solution Roots; x and -c sum of roots = c + (-c) = 0 product of roots = c x -c = -c² Equation; x² - (sum of roots) x = product of roots = 0 x² - (0)x + (-c²) = 0 x² - c² = 0	A
29.	Solve the inequality 1 - 2x < - \(\frac{1}{3}\) A. x < \(\frac{2}{3}\) B. x < -\(\frac{2}{3}\) C. x > \(\frac{2}{3}\) D. x > -\(\frac{2}{3}\) Show Content Detailed Solution 1 - 2x < - \(\frac{1}{3}\); -2x < -\(\frac{1}{3}\) - 1 -2x < - \(\frac{1- 3}{3}\) -2x < - \(\frac{4}{-6}\) 3x -2x < -4; -8x < -4 x > -\(\frac{4}{-6}\) = x > \(\frac{2}{3}\)	C
30.	Given the sets A = [2, 4, 6, 8] and B = [2, 3, 5, 9]. If a number is selected at random from set B, what is the probability that the number is prime? A. 1 B. \(\frac{3}{4}\) C. \(\frac{1}{2}\) D. \(\frac{1}{4}\) Show Content Detailed Solution A = [2, 4, 6, 8} B = {2, 3, 5, 9} Pr = (Prime in B) = \(\frac{3}{4}\)	B

21.	If x \(\alpha\) (45 + \(\frac{1}{2}y\)), which of the following is true>? A. x varies directly as y B. x varies inversely as y C. x is partly constant and partly varies as y D. x vries jointly as 45 and directly as y	C
22.	Simplify \(\frac{\log \sqrt{8}}{\log 4 - \log 2}\) A. \(\frac{2}{3}\) B. \(\frac{1}{2} \log 2\) C. \(\frac{3}{2}\) D. \(\log 2\) Show Content Detailed Solution \(\frac{\log\sqrt{8}}{\log 4 - \log 2} = \frac{\log 8\frac{1}{2}}{\log (\frac{4}{2})}\) = \(\frac{8 \frac{1}{2}}{\log (\frac{4}{2})}\) = \(\frac{\frac{1}{2} \log 2^3}{\log 2}\) = \(\frac{3}{2} \frac{\log 2}{\log 2}\) = \(\frac{3}{2}\)	C
23.	A train travels 60km in M minutes. If its average speed is 400km per hour, find the value of M A. 15 B. 12 C. 10 D. 9 Show Content Detailed Solution Average speed = \(\frac{Distance}{Time}\) \(\frac{400km}{hr} = \frac{60km}{Time}\) Time = \(\frac{60km}{400 km/hr}\) = \(\frac{60hr}{400}\) M = \(\frac{60hr}{400} \times \frac{60min}{1hr}\) = 9 minutes	D
24.	An arc of a circle, radius 14cm, is 18.33cm long. Calculate to the nearest degree, the angle which the arc subtends at the centre of the circle. [T = \(\frac{22}{7}\)] A. 11^o B. 20^o C. 22^o D. 75^o Show Content Detailed Solution Length of an arc = \(\frac{\theta}{360} \times 2\pi r\) 18.33 = \(\frac{\theta}{360} \times 2 \times \frac{22}{7} \times 14\) \(\theta = \frac{18.33 \times 360 \times 17}{2 \times 22 \times 14}\) = 75^o (approx.)	D
25.	What is the length of an edge of a cube whose total surface area is X cm² and whose total surface area is \(\frac{X}{2}\)cm³? A. 3 B. 6 C. 9 D. 12 Show Content Detailed Solution Total surface area of cube = 6s² 6s² = x s² = x = \(\frac{x}{6}\).....(1) volume of a cube = s² = \(\frac{x}{2}\) s² = \(\frac{x}{2}\)......(2) put(1) into (2) s(\(\frac{x}{6}\)) = \(\frac{x}{2}\) s = \(\frac{x}{2} \times \frac{6}{x}\) = 3cm	A

26.	XY is a chord of circle centre O and radius 7cm. The chord XY which is 8cm long subtends an angle of 120^o at the centre of the circle. Calculate the perimeter of the minor segment. [Take \(\pi = \frac{22}{7}\)] A. 14.67cm B. 22.67cm C. 29.33cm D. 37.33cm Show Content Detailed Solution perimeter of minor segment = Length of arc xy + chord xy where lxy = \(\frac{120}{360} \times 2x \times \frac{22}{7} \times 7\) = 14.67cm perimeter of minor segment = 14.67 + 8 = 22.67cm	B
27.	If p = \(\frac{1}{2}\) and \(\frac{1}{p - 1} = \frac{2}{p + x}\), find the value of x A. -2\(\frac{1}{2}\) B. -1\(\frac{1}{2}\) C. 1\(\frac{1}{2}\) D. 2\(\frac{1}{2}\) Show Content Detailed Solution p = \(\frac{1}{2}; \frac{1}{p - 1} = \frac{2}{p + x}\) \(\frac{1}{\frac{1}{2} - 1} = \frac{2}{\frac{1}{2} + x}\) \(\frac{1}{\frac{1 - 2}{2}} = \frac{2}{\frac{1 + 2x}{2}}\) \(\frac{1}{-\frac{1}{2}} = \frac{2}{\frac{1 + 2x}{2}}\) -2 = \(\frac{4}{1 + 2x} -2(1 + 2x) = 4\) 1 + 2x = \(\frac{4}{-2}\) 1 + 2x = -2 2x = -2 - 1 2x = -3 x = -\(\frac{3}{2}\) x = -1\(\frac{1}{2}\)	B
28.	Find the quadratic equation whose roots are c and -c A. x² - c² = 0 B. x² + 2cx = 0 C. x² + 2cx + c² = 0 D. x² - 2cx + c² = 0 Show Content Detailed Solution Roots; x and -c sum of roots = c + (-c) = 0 product of roots = c x -c = -c² Equation; x² - (sum of roots) x = product of roots = 0 x² - (0)x + (-c²) = 0 x² - c² = 0	A
29.	Solve the inequality 1 - 2x < - \(\frac{1}{3}\) A. x < \(\frac{2}{3}\) B. x < -\(\frac{2}{3}\) C. x > \(\frac{2}{3}\) D. x > -\(\frac{2}{3}\) Show Content Detailed Solution 1 - 2x < - \(\frac{1}{3}\); -2x < -\(\frac{1}{3}\) - 1 -2x < - \(\frac{1- 3}{3}\) -2x < - \(\frac{4}{-6}\) 3x -2x < -4; -8x < -4 x > -\(\frac{4}{-6}\) = x > \(\frac{2}{3}\)	C
30.	Given the sets A = [2, 4, 6, 8] and B = [2, 3, 5, 9]. If a number is selected at random from set B, what is the probability that the number is prime? A. 1 B. \(\frac{3}{4}\) C. \(\frac{1}{2}\) D. \(\frac{1}{4}\) Show Content Detailed Solution A = [2, 4, 6, 8} B = {2, 3, 5, 9} Pr = (Prime in B) = \(\frac{3}{4}\)	B