Mathematics (Core), 2011, WASSCE/WAEC MAY/JUNE, Exam, Paper 1 | Objectives

Paper Info

Year :

2011

Title :

Mathematics (Core)

Exam :

WASSCE/WAEC MAY/JUNE

Paper 1 | Objectives

11 - 20 of 49 Questions

#	Question	Ans
11.	From the equation whose roots are x = \(\frac{1}{2}\) and -\(\frac{2}{3}\) A. 6x² - x + 2 = 0 B. 6x² - x - 2 = 0 C. 6x² + x + 2 = 0 D. 6x² + x - 2 = 0 Show Content Detailed Solution x = \(\frac{1}{2}\) and x = \(\frac{-2}{3}\) expand (x - \(\frac{1}{2}\))(x + \(\frac{2}{3}\)) = 0 x(x + \(\frac{2}{3}\)) - \(\frac{1}{2}(x + \frac{2}{3}\)) = 0 x² + \(\frac{4x - 3x}{6} - \frac{2}{6} = 0\) \(x^2 + \frac{x}{6} - 2 = 0\) 6x² + x - 2 = 0	D
12.	Simplify \(\frac{\log \sqrt{27}}{\log \sqrt{81}}\) A. 3 B. 2 C. \(\frac{3}{2}\) D. \(\frac{3}{4}\) Show Content Detailed Solution \(\frac{\log \sqrt{27}}{\log \sqrt{81}}\) = \(\frac{\log 27\frac{1}{2}}{81\frac{1}{2}}\) = \(\frac{\log 3\frac{1}{2}}{\log 3^2}\) \(\frac{\frac{3}{2} \log 3}{2 \log 3} = \frac{3}{2} \div \frac{2}{1}\) = \(\frac{3}{2} \times \frac{1}{2}\) = \(\frac{3}{4}\)	D
13.	Which of these angles can be constructed using ruler and a pair of compasses only? A. 115^o B. 125^o C. 135^o D. 145^o	C
14.	The perimeter of a sector of a circle of radius 4cm is (\(\pi + 8\))cm. Calculate the anle of the sector A. 45^o B. 60^o C. 75^o D. 90^o Show Content Detailed Solution Perimeter of sector = 2r + \(\frac{\theta}{360^o} \times 2\pi r\) \(\pi + 8 = 2 \times 4 + \frac{\theta}{3360^o} \times 2 \pi \times 4\) \(\pi + 8 + \frac{\theta}{360^o} \times 8 \pi\) P + 8 - 8 = \(\frac{\theta \pi}{456o}\) \(\pi = \frac{\theta \pi}{45^o}\) \(\theta \pi = 45^o\)	A
15.	The length of a piece of stick is 1.75m. A girl measured it as 1.80m. Find the percentage error A. \(\frac{28}{7}\)% B. \(\frac{29}{7}\)% C. 5% D. \(\frac{20}{7}\)% Show Content Detailed Solution Error = 1.80m - 1.75m = 0.05m %error = \(\frac{\text{error}}{\text{true measurement}}\) x 100%	D
16.	What is the value of 3 in the number 42.7531? A. \(\frac{3}{10000}\) B. \(\frac{3}{1000}\) C. \(\frac{3}{100}\) D. \(\frac{1}{10}\)	B
17.	The height of a cylinder is equal to its radius. If the volume is 0.216 \(\pi\) m\(^3\). Calculate the radius. A. 0.46m B. 0.60m C. 0.87m D. 1.80m Show Content Detailed Solution volume of cylinder = \(\pi r^2\)h 0.216\(\pi\) m\(^3\) = \(\pi \times r^2 \times h\) Since r = h, 0.216 = r\(^3\) r\(^3\) = 0.216 r = \(\sqrt[3]{0.216}\) = 0.6	B
18.	The height of a cylinder is equal to its radius. If the volume is 0.216 \(\pi m^3\) Calculate the radius. A. 0.46m B. 0.60m C. 0.87m D. 1.80m Show Content Detailed Solution volume of cylinder = \(\pi r^2\)h 0.216\(\pi m^3 = \pi \times r^2 \times 1m\) assumed that h = 1m 0.216 = r² r² = 0.216 r = \(\sqrt{0.216}\) = 0.46	A
19.	What is the value of 3 in the number 42.7531? A. \(\frac{3}{10000}\) B. \(\frac{3}{1000}\) C. \(\frac{3}{100}\) D. \(\frac{1}{10}\)	B
20.	Factorize the expression: am + bn - an - bm A. (a - b)(m + n) B. (a - b)(m - n) C. (a + b)(m - n) D. (a + b)(m + n) Show Content Detailed Solution am + bn - an - bm am - an - bm + bn a(m - n) - b(m - n) (a - b)(m - n)	B

11.	From the equation whose roots are x = \(\frac{1}{2}\) and -\(\frac{2}{3}\) A. 6x² - x + 2 = 0 B. 6x² - x - 2 = 0 C. 6x² + x + 2 = 0 D. 6x² + x - 2 = 0 Show Content Detailed Solution x = \(\frac{1}{2}\) and x = \(\frac{-2}{3}\) expand (x - \(\frac{1}{2}\))(x + \(\frac{2}{3}\)) = 0 x(x + \(\frac{2}{3}\)) - \(\frac{1}{2}(x + \frac{2}{3}\)) = 0 x² + \(\frac{4x - 3x}{6} - \frac{2}{6} = 0\) \(x^2 + \frac{x}{6} - 2 = 0\) 6x² + x - 2 = 0	D
12.	Simplify \(\frac{\log \sqrt{27}}{\log \sqrt{81}}\) A. 3 B. 2 C. \(\frac{3}{2}\) D. \(\frac{3}{4}\) Show Content Detailed Solution \(\frac{\log \sqrt{27}}{\log \sqrt{81}}\) = \(\frac{\log 27\frac{1}{2}}{81\frac{1}{2}}\) = \(\frac{\log 3\frac{1}{2}}{\log 3^2}\) \(\frac{\frac{3}{2} \log 3}{2 \log 3} = \frac{3}{2} \div \frac{2}{1}\) = \(\frac{3}{2} \times \frac{1}{2}\) = \(\frac{3}{4}\)	D
13.	Which of these angles can be constructed using ruler and a pair of compasses only? A. 115^o B. 125^o C. 135^o D. 145^o	C
14.	The perimeter of a sector of a circle of radius 4cm is (\(\pi + 8\))cm. Calculate the anle of the sector A. 45^o B. 60^o C. 75^o D. 90^o Show Content Detailed Solution Perimeter of sector = 2r + \(\frac{\theta}{360^o} \times 2\pi r\) \(\pi + 8 = 2 \times 4 + \frac{\theta}{3360^o} \times 2 \pi \times 4\) \(\pi + 8 + \frac{\theta}{360^o} \times 8 \pi\) P + 8 - 8 = \(\frac{\theta \pi}{456o}\) \(\pi = \frac{\theta \pi}{45^o}\) \(\theta \pi = 45^o\)	A
15.	The length of a piece of stick is 1.75m. A girl measured it as 1.80m. Find the percentage error A. \(\frac{28}{7}\)% B. \(\frac{29}{7}\)% C. 5% D. \(\frac{20}{7}\)% Show Content Detailed Solution Error = 1.80m - 1.75m = 0.05m %error = \(\frac{\text{error}}{\text{true measurement}}\) x 100%	D

16.	What is the value of 3 in the number 42.7531? A. \(\frac{3}{10000}\) B. \(\frac{3}{1000}\) C. \(\frac{3}{100}\) D. \(\frac{1}{10}\)	B
17.	The height of a cylinder is equal to its radius. If the volume is 0.216 \(\pi\) m\(^3\). Calculate the radius. A. 0.46m B. 0.60m C. 0.87m D. 1.80m Show Content Detailed Solution volume of cylinder = \(\pi r^2\)h 0.216\(\pi\) m\(^3\) = \(\pi \times r^2 \times h\) Since r = h, 0.216 = r\(^3\) r\(^3\) = 0.216 r = \(\sqrt[3]{0.216}\) = 0.6	B
18.	The height of a cylinder is equal to its radius. If the volume is 0.216 \(\pi m^3\) Calculate the radius. A. 0.46m B. 0.60m C. 0.87m D. 1.80m Show Content Detailed Solution volume of cylinder = \(\pi r^2\)h 0.216\(\pi m^3 = \pi \times r^2 \times 1m\) assumed that h = 1m 0.216 = r² r² = 0.216 r = \(\sqrt{0.216}\) = 0.46	A
19.	What is the value of 3 in the number 42.7531? A. \(\frac{3}{10000}\) B. \(\frac{3}{1000}\) C. \(\frac{3}{100}\) D. \(\frac{1}{10}\)	B
20.	Factorize the expression: am + bn - an - bm A. (a - b)(m + n) B. (a - b)(m - n) C. (a + b)(m - n) D. (a + b)(m + n) Show Content Detailed Solution am + bn - an - bm am - an - bm + bn a(m - n) - b(m - n) (a - b)(m - n)	B