Mathematics (Core), 2015, WASSCE/WAEC MAY/JUNE, Exam, Paper 1 | Objectives

Paper Info

Year :

2015

Title :

Mathematics (Core)

Exam :

WASSCE/WAEC MAY/JUNE

Paper 1 | Objectives

1 - 10 of 45 Questions

#	Question	Ans
1.	If {X: 2 d- x d- 19; X integer} and 7 + x = 4 (mod 9), find the highest value of x A. 2 B. 5 C. 15 D. 18	C
2.	The sum 11011₂, 1111₂ and 10_m10_n0₂. Find the value of m and n. A. m = 0, n = 0 B. m = 1, n = 0 C. m = 0, n = 1 D. m = 1, n = 1	C
3.	A trader bought an engine for $15,000.00 outside Nigeria. If the exchange rate is $0.075 to N1.00, how much did the engine cost in Naira? A. N250,000.00 B. N200,000.00 C. N150,000.00 D. N100,000.00 Show Content Detailed Solution N1.00 = $0.075 N X = $15,000 X = \(\frac{1.00 \times 15000}{0.075}\) = N200,000.00	B
4.	If \(\frac{27^x \times 3^{1 - x}}{9^{2x}} = 1\), find the value of x. A. 1 B. \(\frac{1}{2}\) C. -\(\frac{1}{2}\) D. -1 Show Content Detailed Solution \(\frac{27^x \times 3^{1 - x}}{9^{2x}} = 1\) \(\frac{3^{3x} \times 3^{1 - x}}{3^{2(2 - x)}} = 3^0\) \(3^{3x} \times 3^{1 - x} \div 3^{4x} = 3^0\) \(3^{(3x + 1 - x - 4x)} = 3^0\) \(3^{(1 - 2x)} = 3^0\) since the bases are equal, 1 - 2x = 0 - 2x = -1 x = \(\frac{1}{2}\)	B
5.	Find the 7^th term of the sequence: 2, 5, 10, 17, 6,... A. 37 B. 48 C. 50 D. 63	C
6.	Given that log_x 64 = 3, evaluate x log₈ A. 6 B. 9 C. 12 D. 24 Show Content Detailed Solution If log_x 64 = 3, then 64 = x³ 4³ = x³ Since the indices are equal, x = 4 Hence, x log₂8 = log₂8^x = log₂8⁴ = log₂(2³)₄ = log₂2¹² = 1 log₂ = 1(1) = 12	C
7.	If 2ⁿ = y, Find 2\(^{(2 + \frac{n}{3})}\) A. 4y\(^\frac{1}{3}\) B. 4y\(^-3\) C. 2y\(^\frac{1}{3}\) D. 2y\(^-3\) Show Content Detailed Solution If 2ⁿ = y, then, 2\(^{(2 + \frac{n}{3})}\) = 2² x 2\(^\frac{n}{3}\) = 4 x (2ⁿ)\(^{\frac{1}{3}}\) But y = 2ⁿ, hence 2\(^{(2 + \frac{n}{3})}\) = 4 x y\(^{\frac{1}{3}}\) = 4y\(^\frac{1}{3}\)	A
8.	Factorize completely: 6ax - 12by - 9ay + 8bx A. (2a - 3b)(4x + 3y) B. (3a + 4b)(2x - 3y) C. (3a - 4b)(2x + 3y) D. (2a + 3b)(4x -3y) Show Content Detailed Solution 6ax - 12by - 9ay + 8bx = 6ax - 9ay + 8bx - 12by = 3a(2x - 3y) + 4b(2x - 3y) = (3a + 4b)(2x - 3y)	B
9.	Find the equation whose roots are \(\frac{3}{4}\) and -4 A. 4x² - 13x + 12 = 0 B. 4x² - 13x - 12 = 0 C. 4x² + 13x - 12 = 0 D. 4x² + 13x + 12 = 0 Show Content Detailed Solution Let x = \(\frac{3}{4}\) or x = -4 i.e. 4x = 3 or x = -4 (4x - 3)(x + 4) = 0 therefore, 4x² + 13x - 12 = 0	C
10.	If m = 4, n = 9 and r = 16., evaluate \(\frac{m}{n}\) - 1\(\frac{7}{9}\) + \(\frac{n}{r}\) A. 1\(\frac{5}{16}\) B. 1\(\frac{1}{16}\) C. \(\frac{5}{16}\) D. - 1\(\frac{37}{48}\) Show Content Detailed Solution If m = 4, n = 9, r = 16, then \(\frac{m}{n}\) - 1\(\frac{7}{9}\) + \(\frac{n}{r}\) = \(\frac{4}{9}\) - \(\frac{16}{9}\) + \(\frac{9}{16}\) = \(\frac{64 - 258 + 81}{144}\) = \(\frac{-111}{144}\) = - 1\(\frac{37}{48}\)	D

1.	If {X: 2 d- x d- 19; X integer} and 7 + x = 4 (mod 9), find the highest value of x A. 2 B. 5 C. 15 D. 18	C
2.	The sum 11011₂, 1111₂ and 10_m10_n0₂. Find the value of m and n. A. m = 0, n = 0 B. m = 1, n = 0 C. m = 0, n = 1 D. m = 1, n = 1	C
3.	A trader bought an engine for $15,000.00 outside Nigeria. If the exchange rate is $0.075 to N1.00, how much did the engine cost in Naira? A. N250,000.00 B. N200,000.00 C. N150,000.00 D. N100,000.00 Show Content Detailed Solution N1.00 = $0.075 N X = $15,000 X = \(\frac{1.00 \times 15000}{0.075}\) = N200,000.00	B
4.	If \(\frac{27^x \times 3^{1 - x}}{9^{2x}} = 1\), find the value of x. A. 1 B. \(\frac{1}{2}\) C. -\(\frac{1}{2}\) D. -1 Show Content Detailed Solution \(\frac{27^x \times 3^{1 - x}}{9^{2x}} = 1\) \(\frac{3^{3x} \times 3^{1 - x}}{3^{2(2 - x)}} = 3^0\) \(3^{3x} \times 3^{1 - x} \div 3^{4x} = 3^0\) \(3^{(3x + 1 - x - 4x)} = 3^0\) \(3^{(1 - 2x)} = 3^0\) since the bases are equal, 1 - 2x = 0 - 2x = -1 x = \(\frac{1}{2}\)	B
5.	Find the 7^th term of the sequence: 2, 5, 10, 17, 6,... A. 37 B. 48 C. 50 D. 63	C

6.	Given that log_x 64 = 3, evaluate x log₈ A. 6 B. 9 C. 12 D. 24 Show Content Detailed Solution If log_x 64 = 3, then 64 = x³ 4³ = x³ Since the indices are equal, x = 4 Hence, x log₂8 = log₂8^x = log₂8⁴ = log₂(2³)₄ = log₂2¹² = 1 log₂ = 1(1) = 12	C
7.	If 2ⁿ = y, Find 2\(^{(2 + \frac{n}{3})}\) A. 4y\(^\frac{1}{3}\) B. 4y\(^-3\) C. 2y\(^\frac{1}{3}\) D. 2y\(^-3\) Show Content Detailed Solution If 2ⁿ = y, then, 2\(^{(2 + \frac{n}{3})}\) = 2² x 2\(^\frac{n}{3}\) = 4 x (2ⁿ)\(^{\frac{1}{3}}\) But y = 2ⁿ, hence 2\(^{(2 + \frac{n}{3})}\) = 4 x y\(^{\frac{1}{3}}\) = 4y\(^\frac{1}{3}\)	A
8.	Factorize completely: 6ax - 12by - 9ay + 8bx A. (2a - 3b)(4x + 3y) B. (3a + 4b)(2x - 3y) C. (3a - 4b)(2x + 3y) D. (2a + 3b)(4x -3y) Show Content Detailed Solution 6ax - 12by - 9ay + 8bx = 6ax - 9ay + 8bx - 12by = 3a(2x - 3y) + 4b(2x - 3y) = (3a + 4b)(2x - 3y)	B
9.	Find the equation whose roots are \(\frac{3}{4}\) and -4 A. 4x² - 13x + 12 = 0 B. 4x² - 13x - 12 = 0 C. 4x² + 13x - 12 = 0 D. 4x² + 13x + 12 = 0 Show Content Detailed Solution Let x = \(\frac{3}{4}\) or x = -4 i.e. 4x = 3 or x = -4 (4x - 3)(x + 4) = 0 therefore, 4x² + 13x - 12 = 0	C
10.	If m = 4, n = 9 and r = 16., evaluate \(\frac{m}{n}\) - 1\(\frac{7}{9}\) + \(\frac{n}{r}\) A. 1\(\frac{5}{16}\) B. 1\(\frac{1}{16}\) C. \(\frac{5}{16}\) D. - 1\(\frac{37}{48}\) Show Content Detailed Solution If m = 4, n = 9, r = 16, then \(\frac{m}{n}\) - 1\(\frac{7}{9}\) + \(\frac{n}{r}\) = \(\frac{4}{9}\) - \(\frac{16}{9}\) + \(\frac{9}{16}\) = \(\frac{64 - 258 + 81}{144}\) = \(\frac{-111}{144}\) = - 1\(\frac{37}{48}\)	D