Mathematics (Core), 2019, WASSCE/WAEC MAY/JUNE, Exam, Paper 1 | Objectives

Paper Info

Year :

2019

Title :

Mathematics (Core)

Exam :

WASSCE/WAEC MAY/JUNE

Paper 1 | Objectives

11 - 20 of 50 Questions

#	Question	Ans
11.	If m : n = 2 : 1, evaluate \(\frac{3m^2 - 2n^2}{m^2 + mn}\) A. \(\frac{4}{3}\) B. \(\frac{5}{3}\) C. \(\frac{3}{4}\) D. \(\frac{3}{5}\) Show Content Detailed Solution m = 2, n = 1 \(\frac{3m^2 - 2n^2}{m^2 _ mn}\) = \(\frac{3(2)^2 - 2(1)^2}{2^2 + 2(1)}\) = \(\frac{12 - 2}{4 + 2} = \frac{10}{6}\) = \(\frac{5}{3}\)	B
12.	H varies directly as p and inversely as the square of y. If H = 1, p = 8 and y = 2, find H in terms of p and y. A. H = \(\frac{p}{4y^2}\) B. H = \(\frac{2p}{y^2}\) C. H = \(\frac{p}{2y^2}\) D. H = \(\frac{p}{y^2}\) Show Content Detailed Solution H \(\propto\) \(\frac{p}{y^2}\) H = \(\frac{pk}{y^2}\) 1 = \(\frac{8k}{2^2}\) k = \(\frac{4}{8}\) = \(\frac{1}{2}\) H = \(\frac{p}{2y^2}\)	C
13.	Solve 4x^{2}\) - 16x + 15 = 0. A. x = 1\(\frac{1}{2}\) or x = -2\(\frac{1}{2}\) B. x = 1\(\frac{1}{2}\) or x = 2\(\frac{1}{2}\) C. x = 1\(\frac{1}{2}\) or x = -1\(\frac{1}{2}\) D. x = -1\(\frac{1}{2}\) or x -2\(\frac{1}{2}\) Show Content Detailed Solution 4x\(^2\) - 16x + 15 = 0 (2x - 3)(2x - 5) = 0 x = 1\(\frac{1}{2}\) or x = 2\(\frac{1}{2}\)	B
14.	Simplify: \(\log_{10}\) 6 - 3 log\(_{10}\) 3 + \(\frac{2}{3} \log_{10} 27\) A. 3 \(\log_{10}^2\) B. \(\log_{10}^2\) C. \(\log_{10}^3\) D. 2 \(\log_{10}^3\) Show Content Detailed Solution log\(_{10}\) 6 - log\(_{10}\)3\(^3\) + log\(_{10}\) (\(\sqrt[3]{27}\))\(^2\) = log \(_{10}\) 6 - log \(_{10}\) 27 + log\(_{10}\) 9 = log\(_{10}\) \(\frac{6 \times 9}{27}\) = log\(_{10}\)2	B
15.	Bala sold an article for #6,900.00 and made a profit of 15%. Calculate his percentage profit if he had sold it for N6,600.00. A. 5% B. 10% C. 12% D. 13% Show Content Detailed Solution 15 = (\(\frac{6,900 - C.P \times 100}{C.P}\)) 15 C.P = 690000 - C.P 100 C.P = \(\frac{690000}{115}\) C.P = N6,000 %profit = \(\frac{6,600 - 6,000}{6,000}\) x 100 = \(\frac{600}{6,000}\) x 100 = 10%	B
16.	If 3p = 4q and 9p = 8q - 12, find the value of pq. A. 12 B. 7 C. -7 D. -12 Show Content Detailed Solution 9p = 8q - 12 9p = 2(4q) - 12 9p = 2(3q) - 12 9p = 6p - 12 3p = -12 p = -4 \(\frac{3 \times -4}{4} = \frac{4q}{4}\) q = 13 pq = -3 x -4 = 12	A
17.	If (0.25)\(^y\) = 32, find the value of y. A. y = - \(\frac{5}{2}\) B. y = -\(\frac{3}{2}\) C. y = \(\frac{3}{2}\) D. y = \(\frac{5}{2}\) Show Content Detailed Solution (0.25)\(^y\) = 32 2\(^{-2y}\) = 3\(^{2}\) 2 - 2y = 5 y = - \(\frac{5}{2}\)	A
18.	There are 8 boys and 4 girls in a lift. What is the probability that the first person who steps out of the lift will be a boy? A. \(\frac{1}{6}\) B. \(\frac{1}{4}\) C. \(\frac{2}{3}\) D. \(\frac{1}{2}\) Show Content Detailed Solution Total number of people in the lift = 8 boys + 4 girls = 12 people probability that a boy comes out = \(\frac{8}{12}\) = \(\frac{2}{3}\)	C
19.	Simplify: \(\frac{x^2 - 5x - 14}{x^2 - 9x + 14}\) A. \(\frac{x - 7}{x + 7}\) B. \(\frac{x + 7}{x - 7}\) C. \(\frac{x - 2}{x + 4}\) D. \(\frac{x + 2}{x - 2}\) Show Content Detailed Solution \(\frac{x^2 - 5x - 14}{x^2 - 9x + 14}\) \(\frac{(x - 7)(x + 2)}{(x - 7)(x - 2)}\) = \(\frac{x + 2}{x - 2}\)	D
20.	Which of these values would make \(\frac{3p^-}{p^{2-}}\) undefined? A. 1 B. \(\frac{1}{3}\) C. -\(\frac{1}{3}\) D. -1 Show Content Detailed Solution P\(^2\) - p = 0 p(p - 1) = 0 p = 0 or p = 1	A

11.	If m : n = 2 : 1, evaluate \(\frac{3m^2 - 2n^2}{m^2 + mn}\) A. \(\frac{4}{3}\) B. \(\frac{5}{3}\) C. \(\frac{3}{4}\) D. \(\frac{3}{5}\) Show Content Detailed Solution m = 2, n = 1 \(\frac{3m^2 - 2n^2}{m^2 _ mn}\) = \(\frac{3(2)^2 - 2(1)^2}{2^2 + 2(1)}\) = \(\frac{12 - 2}{4 + 2} = \frac{10}{6}\) = \(\frac{5}{3}\)	B
12.	H varies directly as p and inversely as the square of y. If H = 1, p = 8 and y = 2, find H in terms of p and y. A. H = \(\frac{p}{4y^2}\) B. H = \(\frac{2p}{y^2}\) C. H = \(\frac{p}{2y^2}\) D. H = \(\frac{p}{y^2}\) Show Content Detailed Solution H \(\propto\) \(\frac{p}{y^2}\) H = \(\frac{pk}{y^2}\) 1 = \(\frac{8k}{2^2}\) k = \(\frac{4}{8}\) = \(\frac{1}{2}\) H = \(\frac{p}{2y^2}\)	C
13.	Solve 4x^{2}\) - 16x + 15 = 0. A. x = 1\(\frac{1}{2}\) or x = -2\(\frac{1}{2}\) B. x = 1\(\frac{1}{2}\) or x = 2\(\frac{1}{2}\) C. x = 1\(\frac{1}{2}\) or x = -1\(\frac{1}{2}\) D. x = -1\(\frac{1}{2}\) or x -2\(\frac{1}{2}\) Show Content Detailed Solution 4x\(^2\) - 16x + 15 = 0 (2x - 3)(2x - 5) = 0 x = 1\(\frac{1}{2}\) or x = 2\(\frac{1}{2}\)	B
14.	Simplify: \(\log_{10}\) 6 - 3 log\(_{10}\) 3 + \(\frac{2}{3} \log_{10} 27\) A. 3 \(\log_{10}^2\) B. \(\log_{10}^2\) C. \(\log_{10}^3\) D. 2 \(\log_{10}^3\) Show Content Detailed Solution log\(_{10}\) 6 - log\(_{10}\)3\(^3\) + log\(_{10}\) (\(\sqrt[3]{27}\))\(^2\) = log \(_{10}\) 6 - log \(_{10}\) 27 + log\(_{10}\) 9 = log\(_{10}\) \(\frac{6 \times 9}{27}\) = log\(_{10}\)2	B
15.	Bala sold an article for #6,900.00 and made a profit of 15%. Calculate his percentage profit if he had sold it for N6,600.00. A. 5% B. 10% C. 12% D. 13% Show Content Detailed Solution 15 = (\(\frac{6,900 - C.P \times 100}{C.P}\)) 15 C.P = 690000 - C.P 100 C.P = \(\frac{690000}{115}\) C.P = N6,000 %profit = \(\frac{6,600 - 6,000}{6,000}\) x 100 = \(\frac{600}{6,000}\) x 100 = 10%	B

16.	If 3p = 4q and 9p = 8q - 12, find the value of pq. A. 12 B. 7 C. -7 D. -12 Show Content Detailed Solution 9p = 8q - 12 9p = 2(4q) - 12 9p = 2(3q) - 12 9p = 6p - 12 3p = -12 p = -4 \(\frac{3 \times -4}{4} = \frac{4q}{4}\) q = 13 pq = -3 x -4 = 12	A
17.	If (0.25)\(^y\) = 32, find the value of y. A. y = - \(\frac{5}{2}\) B. y = -\(\frac{3}{2}\) C. y = \(\frac{3}{2}\) D. y = \(\frac{5}{2}\) Show Content Detailed Solution (0.25)\(^y\) = 32 2\(^{-2y}\) = 3\(^{2}\) 2 - 2y = 5 y = - \(\frac{5}{2}\)	A
18.	There are 8 boys and 4 girls in a lift. What is the probability that the first person who steps out of the lift will be a boy? A. \(\frac{1}{6}\) B. \(\frac{1}{4}\) C. \(\frac{2}{3}\) D. \(\frac{1}{2}\) Show Content Detailed Solution Total number of people in the lift = 8 boys + 4 girls = 12 people probability that a boy comes out = \(\frac{8}{12}\) = \(\frac{2}{3}\)	C
19.	Simplify: \(\frac{x^2 - 5x - 14}{x^2 - 9x + 14}\) A. \(\frac{x - 7}{x + 7}\) B. \(\frac{x + 7}{x - 7}\) C. \(\frac{x - 2}{x + 4}\) D. \(\frac{x + 2}{x - 2}\) Show Content Detailed Solution \(\frac{x^2 - 5x - 14}{x^2 - 9x + 14}\) \(\frac{(x - 7)(x + 2)}{(x - 7)(x - 2)}\) = \(\frac{x + 2}{x - 2}\)	D
20.	Which of these values would make \(\frac{3p^-}{p^{2-}}\) undefined? A. 1 B. \(\frac{1}{3}\) C. -\(\frac{1}{3}\) D. -1 Show Content Detailed Solution P\(^2\) - p = 0 p(p - 1) = 0 p = 0 or p = 1	A