Mathematics (Core), 2014, WASSCE/WAEC MAY/JUNE, Exam, Paper 1 | Objectives

Paper Info

Year :

2014

Title :

Mathematics (Core)

Exam :

WASSCE/WAEC MAY/JUNE

Paper 1 | Objectives

21 - 30 of 49 Questions

#	Question	Ans
21.	If x : y = 3 : 2 and y : z = 5 : 4, find the value of x in the ratio x : y : z A. 8 B. 10 C. 15 D. 20	C
22.	Given that cos x = \(\frac{12}{13}\), evaluate \(\frac{1 - \tan x}{\tan x}\) A. \(\frac{5}{13}\) B. \(\frac{5}{7}\) C. \(\frac{7}{5}\) D. \(\frac{13}{5}\) Show Content Detailed Solution cos x\(\frac{12}{13}\) 13² = 12² + a² 169 = 144 + a² a² = 169 - 144 a² = 25 a \(\sqrt{25}\) a = 5 tan x = \(\frac{5}{12}\) \(\frac{1 - \tan x}{\tan x} = \frac{1 - \frac{5}{12}}{\frac{5}{12}}\) \(\frac{\frac{1 - \frac{5}{12}}{12 - 5}}{12} = \frac{\frac{7}{12}}{\frac{5}{12}}\) = \(\frac{7}{2} \div \frac{5}{12}\) = \(\frac{7}{12} \times \frac{12}{5} = \frac{7}{5}\)	C
23.	Approximate 0.0033780 to 3 significant figures A. 338 B. 0.338 C. 0.00338 D. 0.003	C
24.	Simplify \(\frac{\sqrt{8^2 \times 4^{n + 1}}}{2^{2n} \times 16}\) A. 16 B. 8 C. 4 D. 1 Show Content Detailed Solution \(\frac{\sqrt{8^2 \times 4^{n + 1}}}{2^{2n} \times 16}\) = \(\frac{\sqrt{2^{3(2)} \times 2^{2(n + 1)}}}{2^{2n} \times 2^4}\) = \(\frac{\sqrt{2^6 \times 2^{2n + 2)}}}{2^{2n} + 4}\) = \(\frac{\sqrt{2^6 + 2^{2n + 2)}}}{2^{2n} + 4}\) = \(\frac{\sqrt{2^{2n + 8}}}{2^{2n} + 4}\) = \(\sqrt{2^{2n + 8} \div 2^{2n} + 4}\) = \(\sqrt{2^{2n - 2n} + 8 - 4}\) = \(\sqrt{2^4}\) = \(\sqrt{16}\) = 4	C
25.	If \(\frac{2}{x - 3} - \frac{3}{x - 2}\) is equal to \(\frac{p}{(x - 3)(x - 2)}\), find p A. -x - 5 B. -(x + 3) C. 5x - 13 D. 5 - x Show Content Detailed Solution \(\frac{2}{x - 3} - \frac{3}{x - 2}\) = \(\frac{p}{(x - 3)(x - 2)}\) \(\frac{2(x - 2) - 3(x - 3)}{(x - 3)(x - 2)}\) = \(\frac{p}{(x - 3)(x - 2)}\) = \(\frac{2x - 4 - 3x + 9}{(x - 3)(x - 2)}\) = \(\frac{p}{(x - 3)(x - 2)}\) \(\frac{-x + 5}{(x - 3)(x - 2)} = \frac{p}{(x - 3)(x - 2)}\) p(x - 3)(x - 2) = -x + 5(x - 3)(x - 2) p = -x + 5 or p = 5 - x	D
26.	Subtract \(\frac{1}{2}\)(a - b - c) from the sum of \(\frac{1}{2}\)(a - b + c) and \(\frac{1}{2}\) (a + b - c) A. \(\frac{1}{2}\) (a + b + c) B. \(\frac{1}{2}\) (a - b - c) C. \(\frac{1}{2}\) (a - b + c) D. \(\frac{1}{2}\) (a + b - c) Show Content Detailed Solution \(\frac{1}{2}\)(a - b + c) + \(\frac{1}{2}\)(a + b - c) - [\(\frac{1}{2}\) (a - b - c)] \(\frac{1}{2}a - \frac{1}{2}b + \frac{1}{2}c + \frac{1}{2}a + \frac{1}{2}b - \frac{1}{2}c - \frac{1}{2}a + \frac{1}{2}b + \frac{1}{2}c\) = \(\frac{1}{2}a + \frac{1}{2}b + \frac{1}{2}c\) = \(\frac{1}{2}(a + b + c)\)	A
27.	A man's eye level is 1.7m above the horizontal ground and 13m from a vertical pole. If the pole is 8.3m high, calculate, correct to the nearest degree, the angle of elevation of the top of the pole from his eyes. A. 33^o B. 32^o C. 27^o D. 26^o Show Content Detailed Solution tan \(\theta = \frac{opp}{adj} = \frac{6.6}{13}\) tan \(\theta = 0.5077\) \(\theta\) = tan^-1 0.5077 \(\theta = 27^o\)	C
28.	A chord subtends an angle of 120^o at the centre of a circle of radius 3.5cm. Find the perimeter of the minor sector containing the chord, [Take \(\pi = \frac{22}{7}\)] A. 14\(\frac{1}{3}\)cm B. 12\(\frac{5}{6}\)cm C. 8\(\frac{1}{7}\)cm D. 7\(\frac{1}{3}\)cm Show Content Detailed Solution perimeter of minor sector 2r + \(\frac{\theta}{360} \times 2 \pi r\) = 2 x 3.5 + \(\frac{120^o}{360^o} \times 2 \frac{22}{7} \times 3.5\) = 7 + \(\frac{154}{21}\) = 7 + 7.33 = 14.33 = 14\(\frac{1}{3}\)cm	A
29.	In parallelogram PQRS, QR is produced to M such that \|QR\| = \|RM\|. What fraction of the area of PQMS is the area of PRMS? A. \(\frac{1}{4}\) B. \(\frac{1}{3}\) C. \(\frac{2}{3}\) D. \(\frac{3}{4}\) Show Content Detailed Solution There are 3 triangles: \(\bigtriangleup\)MRS, \(\bigtriangleup\) and \(\bigtriangleup\) PRQ Area PRMS has 2 triangles: \(\bigtriangleup\) MRS and \(\bigtriangleup\) RSP the fraction = \(\frac{2}{3}\)	C
30.	In a cumulative frequency graph, the lower quartile is 18 years while the 60th percentile is 48 years. What percentage of the distribution is at most 18 years or greater than 48 years? A. 15% B. 35% C. 65% D. 85%	C

21.	If x : y = 3 : 2 and y : z = 5 : 4, find the value of x in the ratio x : y : z A. 8 B. 10 C. 15 D. 20	C
22.	Given that cos x = \(\frac{12}{13}\), evaluate \(\frac{1 - \tan x}{\tan x}\) A. \(\frac{5}{13}\) B. \(\frac{5}{7}\) C. \(\frac{7}{5}\) D. \(\frac{13}{5}\) Show Content Detailed Solution cos x\(\frac{12}{13}\) 13² = 12² + a² 169 = 144 + a² a² = 169 - 144 a² = 25 a \(\sqrt{25}\) a = 5 tan x = \(\frac{5}{12}\) \(\frac{1 - \tan x}{\tan x} = \frac{1 - \frac{5}{12}}{\frac{5}{12}}\) \(\frac{\frac{1 - \frac{5}{12}}{12 - 5}}{12} = \frac{\frac{7}{12}}{\frac{5}{12}}\) = \(\frac{7}{2} \div \frac{5}{12}\) = \(\frac{7}{12} \times \frac{12}{5} = \frac{7}{5}\)	C
23.	Approximate 0.0033780 to 3 significant figures A. 338 B. 0.338 C. 0.00338 D. 0.003	C
24.	Simplify \(\frac{\sqrt{8^2 \times 4^{n + 1}}}{2^{2n} \times 16}\) A. 16 B. 8 C. 4 D. 1 Show Content Detailed Solution \(\frac{\sqrt{8^2 \times 4^{n + 1}}}{2^{2n} \times 16}\) = \(\frac{\sqrt{2^{3(2)} \times 2^{2(n + 1)}}}{2^{2n} \times 2^4}\) = \(\frac{\sqrt{2^6 \times 2^{2n + 2)}}}{2^{2n} + 4}\) = \(\frac{\sqrt{2^6 + 2^{2n + 2)}}}{2^{2n} + 4}\) = \(\frac{\sqrt{2^{2n + 8}}}{2^{2n} + 4}\) = \(\sqrt{2^{2n + 8} \div 2^{2n} + 4}\) = \(\sqrt{2^{2n - 2n} + 8 - 4}\) = \(\sqrt{2^4}\) = \(\sqrt{16}\) = 4	C
25.	If \(\frac{2}{x - 3} - \frac{3}{x - 2}\) is equal to \(\frac{p}{(x - 3)(x - 2)}\), find p A. -x - 5 B. -(x + 3) C. 5x - 13 D. 5 - x Show Content Detailed Solution \(\frac{2}{x - 3} - \frac{3}{x - 2}\) = \(\frac{p}{(x - 3)(x - 2)}\) \(\frac{2(x - 2) - 3(x - 3)}{(x - 3)(x - 2)}\) = \(\frac{p}{(x - 3)(x - 2)}\) = \(\frac{2x - 4 - 3x + 9}{(x - 3)(x - 2)}\) = \(\frac{p}{(x - 3)(x - 2)}\) \(\frac{-x + 5}{(x - 3)(x - 2)} = \frac{p}{(x - 3)(x - 2)}\) p(x - 3)(x - 2) = -x + 5(x - 3)(x - 2) p = -x + 5 or p = 5 - x	D

26.	Subtract \(\frac{1}{2}\)(a - b - c) from the sum of \(\frac{1}{2}\)(a - b + c) and \(\frac{1}{2}\) (a + b - c) A. \(\frac{1}{2}\) (a + b + c) B. \(\frac{1}{2}\) (a - b - c) C. \(\frac{1}{2}\) (a - b + c) D. \(\frac{1}{2}\) (a + b - c) Show Content Detailed Solution \(\frac{1}{2}\)(a - b + c) + \(\frac{1}{2}\)(a + b - c) - [\(\frac{1}{2}\) (a - b - c)] \(\frac{1}{2}a - \frac{1}{2}b + \frac{1}{2}c + \frac{1}{2}a + \frac{1}{2}b - \frac{1}{2}c - \frac{1}{2}a + \frac{1}{2}b + \frac{1}{2}c\) = \(\frac{1}{2}a + \frac{1}{2}b + \frac{1}{2}c\) = \(\frac{1}{2}(a + b + c)\)	A
27.	A man's eye level is 1.7m above the horizontal ground and 13m from a vertical pole. If the pole is 8.3m high, calculate, correct to the nearest degree, the angle of elevation of the top of the pole from his eyes. A. 33^o B. 32^o C. 27^o D. 26^o Show Content Detailed Solution tan \(\theta = \frac{opp}{adj} = \frac{6.6}{13}\) tan \(\theta = 0.5077\) \(\theta\) = tan^-1 0.5077 \(\theta = 27^o\)	C
28.	A chord subtends an angle of 120^o at the centre of a circle of radius 3.5cm. Find the perimeter of the minor sector containing the chord, [Take \(\pi = \frac{22}{7}\)] A. 14\(\frac{1}{3}\)cm B. 12\(\frac{5}{6}\)cm C. 8\(\frac{1}{7}\)cm D. 7\(\frac{1}{3}\)cm Show Content Detailed Solution perimeter of minor sector 2r + \(\frac{\theta}{360} \times 2 \pi r\) = 2 x 3.5 + \(\frac{120^o}{360^o} \times 2 \frac{22}{7} \times 3.5\) = 7 + \(\frac{154}{21}\) = 7 + 7.33 = 14.33 = 14\(\frac{1}{3}\)cm	A
29.	In parallelogram PQRS, QR is produced to M such that \|QR\| = \|RM\|. What fraction of the area of PQMS is the area of PRMS? A. \(\frac{1}{4}\) B. \(\frac{1}{3}\) C. \(\frac{2}{3}\) D. \(\frac{3}{4}\) Show Content Detailed Solution There are 3 triangles: \(\bigtriangleup\)MRS, \(\bigtriangleup\) and \(\bigtriangleup\) PRQ Area PRMS has 2 triangles: \(\bigtriangleup\) MRS and \(\bigtriangleup\) RSP the fraction = \(\frac{2}{3}\)	C
30.	In a cumulative frequency graph, the lower quartile is 18 years while the 60th percentile is 48 years. What percentage of the distribution is at most 18 years or greater than 48 years? A. 15% B. 35% C. 65% D. 85%	C