Mathematics (Core), 1996, WASSCE/WAEC MAY/JUNE, Exam, Paper 1 | Objectives

Paper Info

Year :

1996

Title :

Mathematics (Core)

Exam :

WASSCE/WAEC MAY/JUNE

Paper 1 | Objectives

1 - 10 of 49 Questions

#	Question	Ans
1.	The 6th term of a G.P is \(\frac{-2}{27}\) and its first term is 18. What is the common ratio? A. -¹/₂ B. -1/3 C. 1/4 D. 2 E. 3 Show Content Detailed Solution a, ar, ar\(^2\), ar\(^3\), ar\(^4\), ar\(^5\) 6th term = ar\(^5\) = \(\frac{-2}{27}\) 1st term = a = 18 => ar\(^5\) = 18r\(^5\) =\(\frac{-2}{27}\) r\(^5\) = \(\frac{-2}{27 * 18}\) → \(\frac{-1}{27 * 9}\) r\(^5\) = \(\frac{-1}{243}\) r = \(^5\)√[\(\frac{-1}{243}\)] r = \(\frac{-1}{3}\)	B
2.	Convert the decimal number 89 to a binary number A. 101101 B. 111001 C. 1001001 D. 1001101 E. 1011001 Show Content Detailed Solution 89\(_{10}\) = 1011001\(_{2}\)	E
3.	Simplify: \((2\frac{1}{6} - 1\frac{2}{3}) \div 2\frac{2}{3}\). A. 3/16 B. 7/16 C. 1 13/24 D. 2 11/24 E. 10 2/5 Show Content Detailed Solution \((2\frac{1}{6} - 1\frac{2}{3}) \div 2\frac{2}{3}\) = \((\frac{13}{6} - \frac{5}{3}) \div \frac{8}{3}\) = \(\frac{3}{6} \times \frac{3}{8}\) = \(\frac{3}{16}\)	A
4.	Simplify 56x\(^{-4}\) \(\div\) 14x\(^{-8}\) A. 2x^-12 B. 3x^-3 C. 4x^-4 D. 4x^-3 E. 4x⁴ Show Content Detailed Solution \(56x^{-4} \div 14x^{-8}\) = \(4x^{- 4 - (-8)}\) = \(4x^{4}\)	E
5.	Simplufy Log₁₀4 + Log₁₀25 A. 1 B. 2 C. 3 D. 4 E. 5 Show Content Detailed Solution Log₁₀4 + Log₁₀25 = Log₁₀(4 + 25) = Log₁₀100 = Log₁₀10² = 2Log₁₀10 = 2 x 1 = 2	B
6.	A boy measured the length and breath of a rectangular lawn as 59.6m and 40.3m respectively instead of 60m and 40m. What is the percentage error in his calculation of the perimeter of the lawn? A. 10% B. 1.4% C. 7% D. 0.2% E. 0.1% Show Content Detailed Solution Length = 59.6m Breath = 40.3m Perimeter = (59.6m + 40.3m) x 2 = 99.9 x 2 = 199.8m Actual measurement Perimeter = (60 + 40) x 2 = 100 x 2 = 200m Error = 200m - 199.8m = 0.2 Error =0.2/200 x 100/1 = 0.1%	E
7.	Find the 9th term of the arithmetic progression 18, 12, 6, 0, -6 ......... A. -54 B. -30 C. 30 D. 42 E. 66 Show Content Detailed Solution 18, 12, 6, 0, -6, 12, -18, 24, -30 9th term = -30	B
8.	Expand (2x - 5)(x - 3) A. x² - 1x -15 B. 2x² - 11x + 15 C. 2² - 5x - 8 D. x² - 5x - 15 E. 2x² - 6x + 15 Show Content Detailed Solution (2x - 5)(x - 3) 2x\(^2\) - 5x - 6x + 15 2x\(^2\) - 11x + 15	B
9.	Simplify: \(\frac{5}{x - y} - \frac{4}{y - x}\) A. 9/x - y B. 9/y - x C. 1/x - y D. 1/y - x E. y - 9x/x - y Show Content Detailed Solution \(\frac{5}{x - y} - \frac{4}{y - x}\) = \(\frac{5(y - x) - 4(x - y)}{(x - y)(y - x)}\) = \(\frac{5y - 5x - 4x + 4y}{(x - y)(y - x)}\) = \(\frac{9y - 9x}{(x - y)(y - x)}\) = \(\frac{9(y - x)}{(x - y)(y - x)}\) = \(\frac{9}{x - y}\)	A
10.	If 3p - q = 6 and 2p + 3q = 4, find q A. o B. ¹/₂ C. 2/3 D. 1 E. 3³/₇ Show Content Detailed Solution 3p - q = 6 ........ 1 2p + 3q = 4 ....... 2 Multiply eqn 1 by 3 9p - 3q = 18 ........ 3 2p - 3q = 4 ......... 2 Add eqn3 and eqn2 11p = 22 => p = ²²/₁₁ = 2 Substitute for p =2 in eqn1 3p - q = 6 3x2 - q = 6 => 6 - q = 6 => -q = 6 - 6 q = 0	A

1.	The 6th term of a G.P is \(\frac{-2}{27}\) and its first term is 18. What is the common ratio? A. -¹/₂ B. -1/3 C. 1/4 D. 2 E. 3 Show Content Detailed Solution a, ar, ar\(^2\), ar\(^3\), ar\(^4\), ar\(^5\) 6th term = ar\(^5\) = \(\frac{-2}{27}\) 1st term = a = 18 => ar\(^5\) = 18r\(^5\) =\(\frac{-2}{27}\) r\(^5\) = \(\frac{-2}{27 * 18}\) → \(\frac{-1}{27 * 9}\) r\(^5\) = \(\frac{-1}{243}\) r = \(^5\)√[\(\frac{-1}{243}\)] r = \(\frac{-1}{3}\)	B
2.	Convert the decimal number 89 to a binary number A. 101101 B. 111001 C. 1001001 D. 1001101 E. 1011001 Show Content Detailed Solution 89\(_{10}\) = 1011001\(_{2}\)	E
3.	Simplify: \((2\frac{1}{6} - 1\frac{2}{3}) \div 2\frac{2}{3}\). A. 3/16 B. 7/16 C. 1 13/24 D. 2 11/24 E. 10 2/5 Show Content Detailed Solution \((2\frac{1}{6} - 1\frac{2}{3}) \div 2\frac{2}{3}\) = \((\frac{13}{6} - \frac{5}{3}) \div \frac{8}{3}\) = \(\frac{3}{6} \times \frac{3}{8}\) = \(\frac{3}{16}\)	A
4.	Simplify 56x\(^{-4}\) \(\div\) 14x\(^{-8}\) A. 2x^-12 B. 3x^-3 C. 4x^-4 D. 4x^-3 E. 4x⁴ Show Content Detailed Solution \(56x^{-4} \div 14x^{-8}\) = \(4x^{- 4 - (-8)}\) = \(4x^{4}\)	E
5.	Simplufy Log₁₀4 + Log₁₀25 A. 1 B. 2 C. 3 D. 4 E. 5 Show Content Detailed Solution Log₁₀4 + Log₁₀25 = Log₁₀(4 + 25) = Log₁₀100 = Log₁₀10² = 2Log₁₀10 = 2 x 1 = 2	B

6.	A boy measured the length and breath of a rectangular lawn as 59.6m and 40.3m respectively instead of 60m and 40m. What is the percentage error in his calculation of the perimeter of the lawn? A. 10% B. 1.4% C. 7% D. 0.2% E. 0.1% Show Content Detailed Solution Length = 59.6m Breath = 40.3m Perimeter = (59.6m + 40.3m) x 2 = 99.9 x 2 = 199.8m Actual measurement Perimeter = (60 + 40) x 2 = 100 x 2 = 200m Error = 200m - 199.8m = 0.2 Error =0.2/200 x 100/1 = 0.1%	E
7.	Find the 9th term of the arithmetic progression 18, 12, 6, 0, -6 ......... A. -54 B. -30 C. 30 D. 42 E. 66 Show Content Detailed Solution 18, 12, 6, 0, -6, 12, -18, 24, -30 9th term = -30	B
8.	Expand (2x - 5)(x - 3) A. x² - 1x -15 B. 2x² - 11x + 15 C. 2² - 5x - 8 D. x² - 5x - 15 E. 2x² - 6x + 15 Show Content Detailed Solution (2x - 5)(x - 3) 2x\(^2\) - 5x - 6x + 15 2x\(^2\) - 11x + 15	B
9.	Simplify: \(\frac{5}{x - y} - \frac{4}{y - x}\) A. 9/x - y B. 9/y - x C. 1/x - y D. 1/y - x E. y - 9x/x - y Show Content Detailed Solution \(\frac{5}{x - y} - \frac{4}{y - x}\) = \(\frac{5(y - x) - 4(x - y)}{(x - y)(y - x)}\) = \(\frac{5y - 5x - 4x + 4y}{(x - y)(y - x)}\) = \(\frac{9y - 9x}{(x - y)(y - x)}\) = \(\frac{9(y - x)}{(x - y)(y - x)}\) = \(\frac{9}{x - y}\)	A
10.	If 3p - q = 6 and 2p + 3q = 4, find q A. o B. ¹/₂ C. 2/3 D. 1 E. 3³/₇ Show Content Detailed Solution 3p - q = 6 ........ 1 2p + 3q = 4 ....... 2 Multiply eqn 1 by 3 9p - 3q = 18 ........ 3 2p - 3q = 4 ......... 2 Add eqn3 and eqn2 11p = 22 => p = ²²/₁₁ = 2 Substitute for p =2 in eqn1 3p - q = 6 3x2 - q = 6 => 6 - q = 6 => -q = 6 - 6 q = 0	A