Mathematics (Core), 1992, WASSCE/WAEC MAY/JUNE, Exam, Paper 1 | Objectives

Paper Info

Year :

1992

Title :

Mathematics (Core)

Exam :

WASSCE/WAEC MAY/JUNE

Paper 1 | Objectives

1 - 10 of 48 Questions

#	Question	Ans
1.	Let U = {1, 2, 3, 4}, P = {2, 3} and Q = {2, 4}. What is (P∩Q)'? A. (1, 2, 3) B. (1, 3, 4) C. (2, 3) D. (1, 3) E. (1, 4) Show Content Detailed Solution U = {1,2,3,4}; P = {2,3}; Q = {2,4}; P∩Q = {2} (P∩Q)' = {1,3,4}	B
2.	Simplify (³/₄ + ¹/₃) x 4¹/₃ + 3¹/₄ A. 1/2 B. 13/12 C. 10/9 D. 17/12 E. 13/9 Show Content Detailed Solution (³/₄ + ¹/₃) x 4¹/₃ \(\div\) 3¹₄ \(\begin{pmatrix} 9 + 4 \\ 12 \end{pmatrix}\) x \(\frac{13}{3}\) \(\frac{4}{13}\) = 1⁴₉	E
3.	If x varies over the set of real numbers, which of the following is illustrated in the diagram above? A. -3 B. -3≤x<2 C. -3 D. -3≤x≤2 E. x≥2	B
4.	Convert 77 to a number in base two A. 1001 101 B. 111001 C. 100110 D. 10101 E. 10011 Show Content Detailed Solution \(\begin{array}{c\|c} 2 & 77 \\ \hline 2 & 38 R1 \\ 2 & 19 R0 \\ 2 & 9 R1 \\ 2 & 4 R1 \\ 2 & 2 R0 \\ 2 & 1 R0 \\ & 0 R1\end{array}\) 77_ten = 1001101_two	A
5.	A bricklayer measured the length of a wall and obtained 4.10m. If the actual length of the wall is 4.25m, find his percentage error. A. 3 9/17% B. 3 27/41% C. 15% D. 35 5/17% E. 36 24/41% Show Content Detailed Solution Error = 4.25 - 4.10 = 0.15 % error = \(\frac{0.15}{4.25} \times 100%\) = \(\frac{15}{\frac{17}{4}} = \frac{15 \times 4}{17}\) = \(3\frac{9}{17} %\)	A
6.	The nth term of a sequence is given by 3.2\(^{n-2}\). Write down the first three terms of the sequence. A. 2/3, 0, 6 B. 3/2, 3, 6, C. 2/3, 3, 8/3 D. 2/3, ³/₄, 6 E. 2/3, 3, 1/3 Show Content Detailed Solution \(T_n = 3. 2^{n - 2} \\ T_{1} = 3. 2^{1 - 2} = 3. 2^{-1} \\ T_1 = \frac{3}{2} \) \(T_2 = 3. 2^{2 - 2} \\ T_2 = 3. 2^0 = 3\) \(T_3 = 3. 2^{3 - 2} = 3. 2^1 \\ T_3 = 6\) The first 3 terms of the sequence are \(\frac{3}{2}\), 3 and 6.	B
7.	Simplify: \((\frac{16}{81})^{\frac{1}{4}}\) A. 8/27 B. 1/3 C. 4/9 D. 2/3 E. -4/3 Show Content Detailed Solution \((\frac{16}{81})^{\frac{1}{4}}\) = \(((\frac{2}{3})^{4})^{\frac{1}{4}}\) = \(\frac{2}{3}\)	D
8.	Evaluate \(\log_{10} 25 + \log_{10} 32 - \log_{10} 8\) A. 0.2 B. 2 C. 100 D. 409 E. 490 Show Content Detailed Solution \(\log_{10} 25 + \log_{10} 32 - \log_{10} 8\) = \(\log_{10} (\frac{25 \times 32}{8})\) = \(\log_{10} 100 \) = 2	B
9.	Factorize the expression 2y\(^2\) + xy - 3x\(^2\) A. 2y (y + x) - 3x² B. (2y - x)(2y + x) C. (3x - 2y(x - y) D. (2y + 3x)(y - x) E. (x – y)(2y + 3x) Show Content Detailed Solution 2y\(^2\) + xy - 3x\(^2\) 2y\(^2\) + 3xy - 2xy - 3x\(^2\) y(2y + 3x) - x(2y + 3x) = (y - x)(2y + 3x)	D
10.	Construct a quadratic equation whose roots are \(-\frac{1}{2}\) and 2. A. 3x²-3x+2=0 B. 3x²+3x-2=0 C. 2x²+3x-2=0 D. 2x²-3x+2=0 E. 2x²-3x-2=0 Show Content Detailed Solution If x = \(-\frac{1}{2}\) and 2; then \(x + \frac{1}{2} = 0\) and \(x - 2 = 0\) \(\implies (x + \frac{1}{2})(x - 2) = 0\) \(x^2 - 2x + \frac{1}{2}x - 1 = 0\) \(x^2 - \frac{3}{2}x - 1 = 0\) \(2x^2 - 3x - 2 = 0\)	E

1.	Let U = {1, 2, 3, 4}, P = {2, 3} and Q = {2, 4}. What is (P∩Q)'? A. (1, 2, 3) B. (1, 3, 4) C. (2, 3) D. (1, 3) E. (1, 4) Show Content Detailed Solution U = {1,2,3,4}; P = {2,3}; Q = {2,4}; P∩Q = {2} (P∩Q)' = {1,3,4}	B
2.	Simplify (³/₄ + ¹/₃) x 4¹/₃ + 3¹/₄ A. 1/2 B. 13/12 C. 10/9 D. 17/12 E. 13/9 Show Content Detailed Solution (³/₄ + ¹/₃) x 4¹/₃ \(\div\) 3¹₄ \(\begin{pmatrix} 9 + 4 \\ 12 \end{pmatrix}\) x \(\frac{13}{3}\) \(\frac{4}{13}\) = 1⁴₉	E
3.	If x varies over the set of real numbers, which of the following is illustrated in the diagram above? A. -3 B. -3≤x<2 C. -3 D. -3≤x≤2 E. x≥2	B
4.	Convert 77 to a number in base two A. 1001 101 B. 111001 C. 100110 D. 10101 E. 10011 Show Content Detailed Solution \(\begin{array}{c\|c} 2 & 77 \\ \hline 2 & 38 R1 \\ 2 & 19 R0 \\ 2 & 9 R1 \\ 2 & 4 R1 \\ 2 & 2 R0 \\ 2 & 1 R0 \\ & 0 R1\end{array}\) 77_ten = 1001101_two	A
5.	A bricklayer measured the length of a wall and obtained 4.10m. If the actual length of the wall is 4.25m, find his percentage error. A. 3 9/17% B. 3 27/41% C. 15% D. 35 5/17% E. 36 24/41% Show Content Detailed Solution Error = 4.25 - 4.10 = 0.15 % error = \(\frac{0.15}{4.25} \times 100%\) = \(\frac{15}{\frac{17}{4}} = \frac{15 \times 4}{17}\) = \(3\frac{9}{17} %\)	A

6.	The nth term of a sequence is given by 3.2\(^{n-2}\). Write down the first three terms of the sequence. A. 2/3, 0, 6 B. 3/2, 3, 6, C. 2/3, 3, 8/3 D. 2/3, ³/₄, 6 E. 2/3, 3, 1/3 Show Content Detailed Solution \(T_n = 3. 2^{n - 2} \\ T_{1} = 3. 2^{1 - 2} = 3. 2^{-1} \\ T_1 = \frac{3}{2} \) \(T_2 = 3. 2^{2 - 2} \\ T_2 = 3. 2^0 = 3\) \(T_3 = 3. 2^{3 - 2} = 3. 2^1 \\ T_3 = 6\) The first 3 terms of the sequence are \(\frac{3}{2}\), 3 and 6.	B
7.	Simplify: \((\frac{16}{81})^{\frac{1}{4}}\) A. 8/27 B. 1/3 C. 4/9 D. 2/3 E. -4/3 Show Content Detailed Solution \((\frac{16}{81})^{\frac{1}{4}}\) = \(((\frac{2}{3})^{4})^{\frac{1}{4}}\) = \(\frac{2}{3}\)	D
8.	Evaluate \(\log_{10} 25 + \log_{10} 32 - \log_{10} 8\) A. 0.2 B. 2 C. 100 D. 409 E. 490 Show Content Detailed Solution \(\log_{10} 25 + \log_{10} 32 - \log_{10} 8\) = \(\log_{10} (\frac{25 \times 32}{8})\) = \(\log_{10} 100 \) = 2	B
9.	Factorize the expression 2y\(^2\) + xy - 3x\(^2\) A. 2y (y + x) - 3x² B. (2y - x)(2y + x) C. (3x - 2y(x - y) D. (2y + 3x)(y - x) E. (x – y)(2y + 3x) Show Content Detailed Solution 2y\(^2\) + xy - 3x\(^2\) 2y\(^2\) + 3xy - 2xy - 3x\(^2\) y(2y + 3x) - x(2y + 3x) = (y - x)(2y + 3x)	D
10.	Construct a quadratic equation whose roots are \(-\frac{1}{2}\) and 2. A. 3x²-3x+2=0 B. 3x²+3x-2=0 C. 2x²+3x-2=0 D. 2x²-3x+2=0 E. 2x²-3x-2=0 Show Content Detailed Solution If x = \(-\frac{1}{2}\) and 2; then \(x + \frac{1}{2} = 0\) and \(x - 2 = 0\) \(\implies (x + \frac{1}{2})(x - 2) = 0\) \(x^2 - 2x + \frac{1}{2}x - 1 = 0\) \(x^2 - \frac{3}{2}x - 1 = 0\) \(2x^2 - 3x - 2 = 0\)	E