Mathematics (Core), 1991, WASSCE/WAEC MAY/JUNE, Exam, Paper 1 | Objectives

Paper Info

Year :

1991

Title :

Mathematics (Core)

Exam :

WASSCE/WAEC MAY/JUNE

Paper 1 | Objectives

1 - 10 of 50 Questions

#	Question	Ans
1.	Express 0.0462 in standard form A. 0.462 x 10^-1 B. 0.462 x 10^-2 C. 4.62 x 10^-1 D. 4.62 x 10^-2 E. 4.62 x 10³ Show Content Detailed Solution 4.62 x 10^-2	D
2.	The population of a village is 5846. Express this number to three significant figures A. 5850 B. 5846 C. 5840 D. 585 E. 584 Show Content Detailed Solution 5846 \(\approxeq\) 5850 (to 3 s.f.)	A
3.	Simplify: log6 + log2 - log12 A. -4 B. -1 D. 1 E. 4 Show Content Detailed Solution log 6 + log 2 - log 12 = \(\log (\frac{6 \times 2}{12})\) = \(\log 1\) = 0	C
4.	Find the number whose logarithm to base 10 is 2.6025 A. 400.4 B. 0.4004 C. 0.04004 D. 0.004004 E. 0.0004004 Show Content Detailed Solution For the log to be 2.6025, there must be three digits before the decimal point.	A
5.	Simplify: \((\frac{1}{4})^{-1\frac{1}{2}}\) A. 1/8 B. 1/4 C. 2 D. 4 E. 8 Show Content Detailed Solution \((\frac{1}{4})^{-1\frac{1}{2}}\) = \((\frac{1}{4})^{-\frac{3}{2}}\) = \((\sqrt{\frac{1}{4}})^{-3}\) = \((\frac{1}{2})^{-3}\) = \(2^3\) = 8	E
6.	For what value of y is the expression \(\frac{y + 2}{y^{2} - 3y - 10}\) undefined? A. y = 0 B. y = 2 C. y = 3 D. y = 5 E. y = 10 Show Content Detailed Solution \(\frac{y + 2}{y^2 - 3y - 10}\) \(y^2 - 3y - 10 = 0 \implies y^2 - 5y + 2y - 10 = 0\) \(y(y - 5) + 2(y - 5) = 0\) \((y - 5)(y + 2) = 0\) \(\frac{y + 2}{(y - 5)(y + 2)} = \frac{1}{y - 5}\) \(\therefore\) At y = 5, the expression \(\frac{y + 2}{y^2 - 3y - 10}\) is undefined.	D
7.	Factorize 3a\(^2\) - 11a + 6 A. (3a - 2)(a - 3) B. (2a -2)(a - 3) C. (3a - 2)(a + 3) D. (3a + 2)(a - 3) E. (2a-3)(a + 2) Show Content Detailed Solution 3a\(^2\) - 11a + 6 3a\(^2\) - 9a - 2a + 6 3a(a - 3) - 2(a - 3) = (3a - 2)(a - 3)	A
8.	Solve the equation: 3a + 10 = a\(^2\) A. a = 5 or a = 2 B. a = -5 or a = 2 C. a = 10 or a = 0 D. a = 5 or a = 0 E. a = 5 or a = -2 Show Content Detailed Solution 3a + 10 = a\(^2\) a\(^2\) - 3a - 10 = 0 a\(^2\) - 5a + 2a - 10 = 0 a(a - 5) + 2(a - 5) = 0 (a - 5)(a + 2) = 0 a = 5 or a = -2.	E
9.	Simplify \((\frac{3}{x} + \frac{15}{2y}) \div \frac{6}{xy}\) A. \(\frac{2y - 5x}{4}\) B. \(\frac{9(2x - 5x)}{x^2y^2}\) C. \(\frac{5x - 2y}{2}\) D. \(\frac{c^2y^2}{18y - 45x}\) E. \(\frac{4}{2y - 5x}\) Show Content Detailed Solution \((\frac{3}{x} - \frac{15}{2y}) \div \frac{6}{xy}\) = \((\frac{6y - 15x}{2xy}) \div \frac{6}{xy}\) = \(\frac{6y - 15x}{2xy} \times \frac{xy}{6}\) = \(\frac{3(2y - 5x)}{2xy} \times \frac{xy}{6}\) = \(\frac{2y - 5x}{4}\)	A
10.	Simplify: ¹/₄(2ⁿ - 2ⁿ⁺²) A. 2ⁿ² - 2ⁿ B. 2^n-2(1-2ⁿ) C. 2ⁿ + 2²ⁿ + 2 D. 2²ⁿ Show Content Detailed Solution ¹/₄(2ⁿ - 2ⁿ⁺²) = 2^-2(2ⁿ - 2ⁿ x 2²) = 2ⁿ x ^-2(1 - 2²)= 2^2n-2 (2⁰ - 2²) = 2^2n-2 - 2ⁿ	A

1.	Express 0.0462 in standard form A. 0.462 x 10^-1 B. 0.462 x 10^-2 C. 4.62 x 10^-1 D. 4.62 x 10^-2 E. 4.62 x 10³ Show Content Detailed Solution 4.62 x 10^-2	D
2.	The population of a village is 5846. Express this number to three significant figures A. 5850 B. 5846 C. 5840 D. 585 E. 584 Show Content Detailed Solution 5846 \(\approxeq\) 5850 (to 3 s.f.)	A
3.	Simplify: log6 + log2 - log12 A. -4 B. -1 D. 1 E. 4 Show Content Detailed Solution log 6 + log 2 - log 12 = \(\log (\frac{6 \times 2}{12})\) = \(\log 1\) = 0	C
4.	Find the number whose logarithm to base 10 is 2.6025 A. 400.4 B. 0.4004 C. 0.04004 D. 0.004004 E. 0.0004004 Show Content Detailed Solution For the log to be 2.6025, there must be three digits before the decimal point.	A
5.	Simplify: \((\frac{1}{4})^{-1\frac{1}{2}}\) A. 1/8 B. 1/4 C. 2 D. 4 E. 8 Show Content Detailed Solution \((\frac{1}{4})^{-1\frac{1}{2}}\) = \((\frac{1}{4})^{-\frac{3}{2}}\) = \((\sqrt{\frac{1}{4}})^{-3}\) = \((\frac{1}{2})^{-3}\) = \(2^3\) = 8	E

6.	For what value of y is the expression \(\frac{y + 2}{y^{2} - 3y - 10}\) undefined? A. y = 0 B. y = 2 C. y = 3 D. y = 5 E. y = 10 Show Content Detailed Solution \(\frac{y + 2}{y^2 - 3y - 10}\) \(y^2 - 3y - 10 = 0 \implies y^2 - 5y + 2y - 10 = 0\) \(y(y - 5) + 2(y - 5) = 0\) \((y - 5)(y + 2) = 0\) \(\frac{y + 2}{(y - 5)(y + 2)} = \frac{1}{y - 5}\) \(\therefore\) At y = 5, the expression \(\frac{y + 2}{y^2 - 3y - 10}\) is undefined.	D
7.	Factorize 3a\(^2\) - 11a + 6 A. (3a - 2)(a - 3) B. (2a -2)(a - 3) C. (3a - 2)(a + 3) D. (3a + 2)(a - 3) E. (2a-3)(a + 2) Show Content Detailed Solution 3a\(^2\) - 11a + 6 3a\(^2\) - 9a - 2a + 6 3a(a - 3) - 2(a - 3) = (3a - 2)(a - 3)	A
8.	Solve the equation: 3a + 10 = a\(^2\) A. a = 5 or a = 2 B. a = -5 or a = 2 C. a = 10 or a = 0 D. a = 5 or a = 0 E. a = 5 or a = -2 Show Content Detailed Solution 3a + 10 = a\(^2\) a\(^2\) - 3a - 10 = 0 a\(^2\) - 5a + 2a - 10 = 0 a(a - 5) + 2(a - 5) = 0 (a - 5)(a + 2) = 0 a = 5 or a = -2.	E
9.	Simplify \((\frac{3}{x} + \frac{15}{2y}) \div \frac{6}{xy}\) A. \(\frac{2y - 5x}{4}\) B. \(\frac{9(2x - 5x)}{x^2y^2}\) C. \(\frac{5x - 2y}{2}\) D. \(\frac{c^2y^2}{18y - 45x}\) E. \(\frac{4}{2y - 5x}\) Show Content Detailed Solution \((\frac{3}{x} - \frac{15}{2y}) \div \frac{6}{xy}\) = \((\frac{6y - 15x}{2xy}) \div \frac{6}{xy}\) = \(\frac{6y - 15x}{2xy} \times \frac{xy}{6}\) = \(\frac{3(2y - 5x)}{2xy} \times \frac{xy}{6}\) = \(\frac{2y - 5x}{4}\)	A
10.	Simplify: ¹/₄(2ⁿ - 2ⁿ⁺²) A. 2ⁿ² - 2ⁿ B. 2^n-2(1-2ⁿ) C. 2ⁿ + 2²ⁿ + 2 D. 2²ⁿ Show Content Detailed Solution ¹/₄(2ⁿ - 2ⁿ⁺²) = 2^-2(2ⁿ - 2ⁿ x 2²) = 2ⁿ x ^-2(1 - 2²)= 2^2n-2 (2⁰ - 2²) = 2^2n-2 - 2ⁿ	A