Mathematics (Core), 1995, WASSCE/WAEC MAY/JUNE, Exam, Paper 1 | Objectives

Paper Info

Year :

1995

Title :

Mathematics (Core)

Exam :

WASSCE/WAEC MAY/JUNE

Paper 1 | Objectives

1 - 10 of 48 Questions

#	Question	Ans
1.	Find (101\(_2\))\(^2\), expressing the answer in base 2. A. 10101 B. 11001 C. 10010 D. 11101 E. 10110 Show Content Detailed Solution You can convert it to base 10 and square, then re-convert it after the operation. OR You can multiply it straight applying the rules of binary multiplication.	B
2.	If three children shares N10.50 among themselves in ratio 6:7:8, how much is the largest share? A. N3.00 B. N3.50 C. N4.00 D. N4.50 E. N5.00 Show Content Detailed Solution Ratio = 6 + 7 + 8 = 21 21 = N10.50 1 = 1050K/21 = 50K 6 = 6 x 50K = N3.00 7 = 7 x 50K = N3.50 8 = 8 x 50K = N4.00 the Largest share = N4.00	C
3.	Express 0.000834 in standard form A. 8.34 x 10^-4 B. 8.34 x 10^-3 C. 8.34 x 10³ D. 8.34 x 10⁴ E. 8.34 x 10⁶	A
4.	Given that log₂a = log₈4, find a A. 2^1/3 B. 4^2/3 C. 4^2/3 D. 2^2/3 E. 2³ Show Content Detailed Solution Log₂a = Log₈4 Log₂a = Log₈8^2/3 → 2/3Log₈8 → 2/3 x 1 Log₂a = 2/3 Recall; If Log_ax = y ∴ ay = x Log₂a = 2/3 2^2/3 = a	D
5.	By selling some crates of soft drinks for N600.00, a dealer makes a profit of 50%. How much did the dealer pay for the drinks? A. N1,200.00 B. N900.00 C. N450.00 D. N400.00 E. N200.00 Show Content Detailed Solution S.P = N600.00 (100 + 50)% = N600 150% = N600 1% = \(\frac{600}{150}\) 100% = \(\frac{600}{150} \times 100%\) = N400	D
6.	Find the nth term Un of the A.P., 11, 4, -3,....... . A. Un=19+7n B. Un=19-7n C. Un=18+7n D. Un= 18-7n E. Un= 17-7n Show Content Detailed Solution A.P 11, 4, -3 1st term = 11 A.P = a, a + d, a + 2d ...... a + (n - 1)d If a = 11 a + d = 4 d = 4 - 11 = -7 nth term = a + (n-1)d = 11 + (n-1)(-7) = 11 - 7n + 7 = 18 - 7n	D
7.	Lf 16/9 , x, 1, y are in Geometric Progression (GP), find the product of x and y. A. 9/16 B. 3/4 C. 1 D. 4/3 E. 16/6 Show Content Detailed Solution 16/9, x, 1, y => a, ar, ar², ar³ ar² = 1 => 16r²/9 = 1 => 16r² 9 => r² = 9/16 => r = 3/4 ar² = y = ar² x r = 1 x 3/4 = 3/4 x xy = 4/3 x 3/4 = 1	C
8.	If R = [2, 4, 6, 7] and S = [1, 2, 4, 8], then R∪S equal A. [1,2,4,6,7,8] B. [1,2,4,7,8] C. [1,4.7,8] D. [2.6.7] E. [2.4] Show Content Detailed Solution R = {2, 4, 6, 7}; S = {1, 2, 4, 8} R \(\cup\) S = {1, 2, 4, 6, 7, 8}	A
9.	Find the value(s) of x for which the expression is undefined: \(\frac{6x - 1}{x^2 + 4x - 5}\) A. +4 or+1 B. -5 or +1 C. -5 or -1 D. +5 or -1 E. \(\frac{1}{6}\) Show Content Detailed Solution \(\frac{6x - 1}{x^2 + 4x - 5}\) The expression is undefined when \(x^2 + 4x - 5 = 0\) \(x^2 + 5x - x - 5 = 0\) \(x(x + 5) - 1(x + 5) = 0\) \((x - 1)(x + 5) = 0\) The expression is undefined when x = 1 or -5.	B
10.	Which of the following could be the inequality illustrated in the sketch graph above? A. y≥2x+3 B. y≤-3x+3 C. y < 3x+2 D. y≤x +3 E. y≥3x+2. Show Content Detailed Solution Gradient of the line = \(\frac{3 - 0}{0 - 1}\) = -3 y = -3x + b. Using (1,0), we have 0 = -3(1) + b 0 = -3 + b b = 3 y = -3x + 3 \(\therefore\) The graph illustrates y \(\leq\) -3x + 3.	B

1.	Find (101\(_2\))\(^2\), expressing the answer in base 2. A. 10101 B. 11001 C. 10010 D. 11101 E. 10110 Show Content Detailed Solution You can convert it to base 10 and square, then re-convert it after the operation. OR You can multiply it straight applying the rules of binary multiplication.	B
2.	If three children shares N10.50 among themselves in ratio 6:7:8, how much is the largest share? A. N3.00 B. N3.50 C. N4.00 D. N4.50 E. N5.00 Show Content Detailed Solution Ratio = 6 + 7 + 8 = 21 21 = N10.50 1 = 1050K/21 = 50K 6 = 6 x 50K = N3.00 7 = 7 x 50K = N3.50 8 = 8 x 50K = N4.00 the Largest share = N4.00	C
3.	Express 0.000834 in standard form A. 8.34 x 10^-4 B. 8.34 x 10^-3 C. 8.34 x 10³ D. 8.34 x 10⁴ E. 8.34 x 10⁶	A
4.	Given that log₂a = log₈4, find a A. 2^1/3 B. 4^2/3 C. 4^2/3 D. 2^2/3 E. 2³ Show Content Detailed Solution Log₂a = Log₈4 Log₂a = Log₈8^2/3 → 2/3Log₈8 → 2/3 x 1 Log₂a = 2/3 Recall; If Log_ax = y ∴ ay = x Log₂a = 2/3 2^2/3 = a	D
5.	By selling some crates of soft drinks for N600.00, a dealer makes a profit of 50%. How much did the dealer pay for the drinks? A. N1,200.00 B. N900.00 C. N450.00 D. N400.00 E. N200.00 Show Content Detailed Solution S.P = N600.00 (100 + 50)% = N600 150% = N600 1% = \(\frac{600}{150}\) 100% = \(\frac{600}{150} \times 100%\) = N400	D

6.	Find the nth term Un of the A.P., 11, 4, -3,....... . A. Un=19+7n B. Un=19-7n C. Un=18+7n D. Un= 18-7n E. Un= 17-7n Show Content Detailed Solution A.P 11, 4, -3 1st term = 11 A.P = a, a + d, a + 2d ...... a + (n - 1)d If a = 11 a + d = 4 d = 4 - 11 = -7 nth term = a + (n-1)d = 11 + (n-1)(-7) = 11 - 7n + 7 = 18 - 7n	D
7.	Lf 16/9 , x, 1, y are in Geometric Progression (GP), find the product of x and y. A. 9/16 B. 3/4 C. 1 D. 4/3 E. 16/6 Show Content Detailed Solution 16/9, x, 1, y => a, ar, ar², ar³ ar² = 1 => 16r²/9 = 1 => 16r² 9 => r² = 9/16 => r = 3/4 ar² = y = ar² x r = 1 x 3/4 = 3/4 x xy = 4/3 x 3/4 = 1	C
8.	If R = [2, 4, 6, 7] and S = [1, 2, 4, 8], then R∪S equal A. [1,2,4,6,7,8] B. [1,2,4,7,8] C. [1,4.7,8] D. [2.6.7] E. [2.4] Show Content Detailed Solution R = {2, 4, 6, 7}; S = {1, 2, 4, 8} R \(\cup\) S = {1, 2, 4, 6, 7, 8}	A
9.	Find the value(s) of x for which the expression is undefined: \(\frac{6x - 1}{x^2 + 4x - 5}\) A. +4 or+1 B. -5 or +1 C. -5 or -1 D. +5 or -1 E. \(\frac{1}{6}\) Show Content Detailed Solution \(\frac{6x - 1}{x^2 + 4x - 5}\) The expression is undefined when \(x^2 + 4x - 5 = 0\) \(x^2 + 5x - x - 5 = 0\) \(x(x + 5) - 1(x + 5) = 0\) \((x - 1)(x + 5) = 0\) The expression is undefined when x = 1 or -5.	B
10.	Which of the following could be the inequality illustrated in the sketch graph above? A. y≥2x+3 B. y≤-3x+3 C. y < 3x+2 D. y≤x +3 E. y≥3x+2. Show Content Detailed Solution Gradient of the line = \(\frac{3 - 0}{0 - 1}\) = -3 y = -3x + b. Using (1,0), we have 0 = -3(1) + b 0 = -3 + b b = 3 y = -3x + 3 \(\therefore\) The graph illustrates y \(\leq\) -3x + 3.	B