Year :
2012
Title :
Mathematics (Core)
Exam :
WASSCE/WAEC MAY/JUNE
Paper 1 | Objectives
21 - 30 of 49 Questions
| # | Question | Ans |
|---|---|---|
| 21. |
Which of these statements about y = 8\(\sqrt{m}\) is correct? A. log y = log 8 x log \(\sqrt{m}\) B. log y = 3 log 2 x \(\frac{1}{2}\) log m C. log y = 3 log 2 - \(\frac{1}{2}\) log m D. log y = 3 log 2 + \(\frac{1}{2}\) log m Detailed Solutiony = 8\(\sqrt{m}\); log y = log 8\(\sqrt{m}\)log y = log 8 + log \(\sqrt{m}\) log y = log 23 + log m\(\frac{1}{2}\) log y = 3 log 3 + \(\frac{1}{2}\) log m |
|
| 22. |
If x + 0.4y = 3 and y = \(\frac{1}{2}\)x, find the value of (x + y) A. 1\(\frac{1}{4}\) B. 2\(\frac{1}{2}\) C. 3\(\frac{3}{4}\) D. 5 Detailed Solutionx + 0.4y = 3...(i)y = \(\frac{1}{2}\)x x = 2y x - 2y = 0....(ii) solve simultaneously; x + 0.4y = 3 - x - 2y = 0 2.4 = 3 y = \(\frac{3 \times 10}{2.4 \times 10} \) = \(\frac{30}{24} = \frac{5}{4}\) x - 2(\(\frac{5}{4}\)) = 0 x - \(\frac{5}{2}\) = 0 x = \(\frac{5}{2}\) x + y = \(\frac{5}{2} + \frac{5}{4}\) \(\frac{10 + 5}{4} = \frac{15}{4}\) = 3\(\frac{3}{4}\) |
|
| 23. |
Express 3 - [\(\frac{x - y}{y}\)] as a single fraction A. \(\frac{3xy}{y}\) B. \(\frac{x - 4y}{y}\) C. \(\frac{4y - x}{y}\) D. 3 - \(\frac{x - y}{y}\) Detailed Solution(\(\frac{x -y}{y}\)); \(\frac{3}{1} - \frac{x y}{y}\)= \(\frac{3y - (x - y)}{y}\) = \(\frac{3y - x + y}{y}\) = \(\frac{4y - x}{y}\) |
|
| 24. |
If p = {prime factors of 210} and Q = {prime less than 10}, find p \(\cap\) Q A. {1,2, 3} B. {2, 3, 5} C. {1, 3, 5,7} D. {2,3,5,7} Detailed Solutionprime factor of 210 = 2, 3, 5, 7prime numbers less than 10 = 2, 3, 5 , 7 |
|
| 25. |
Alfred spent \(\frac{1}{4}\) of his money on food, \(\frac{1}{3}\) on clothing and save the rest. If he saved N72,20.00, how much did he spend on food? A. N43,200.00 B. N43,000.00 C. N42,200.00 D. N40,000.00 Detailed Solutionlet the total amount be Nx i.e (\(\frac{1}{4}\))x + (\(\frac{1}{3}\))x + 72,000 = x\(\frac{x}{4} + \frac{x}{4} + 72,000 = x\) \(\frac{3x + 4x + 86,400}{12} = x\) cross multiply to clear fraction 12x = 3x + 4x + 86,400 12x - 7x = 86,400 5x = 86,400 x - \(\frac{86,400}{5}\) = 172,800 amount spent on food = \(\frac{1}{4} \times 172,800\) = N43,200 |
|
| 26. |
Solve (\(\frac{27}{125}\))-\(\frac{1}{3}\) x (\(\frac{4}{9}\))\(\frac{1}{2}\) A. \(\frac{10}{9}\) B. \(\frac{9}{10}\) C. \(\frac{2}{5}\) D. \(\frac{12}{125}\) Detailed Solution(\(\frac{27}{125}\))-\(\frac{1}{3}\) x (\(\frac{4}{9}\))\(\frac{1}{2}\)= (\(\frac{3^3}{5^3}\))-\(\frac{1}{3}\)-\(\frac{1}{3}\) x (\(\frac{3^2}{3^2}\))\(\frac{1}{2}\) -\(\frac{1}{2}\) = \(\frac{3^{-1}}{3^{-1}} \times \frac{2}{3}\) = \(\frac{\frac{1}{3}}{\frac{1}{5}} \times \frac{2}{3}\) \(\frac{1}{3} \times \frac{5}{1} \times {2}{3} = \frac{10}{9}\) |
|
| 27. |
The sum of the interior angles of regular polygon is 1800o. How many sides has the polygon? A. 16 B. 12 C. 10 D. 8 Detailed SolutionSum = (n - 2)1801800 = (n - 2)180 divide both sides by 180o \(\frac{1800}{180}\) = (n - 2)\(\frac{180}{180}\) 10 = n - 2 10 + 2 = n n = 12 |
|
| 28. |
Find the coefficient of m in the expression of (\(\frac{m}{2} - 1 \frac{1}{2}\)) (m + \(\frac{2}{3}\)) A. -\(\frac{1}{6}\) B. - \(\frac{1}{2}\) C. -1 D. -1\(\frac{1}{6}\) Detailed Solution(\(\frac{m}{2} - 1\frac{1}{4}\))(m + \(\frac{2}{3}\))(\(\frac{m}{2} - \frac{3}{2}\))(\(\frac{m}{1} + \frac{2}{3}\)) = \(\frac{m^2}{3} + \frac{3m}{6} - \frac{6}{6}\) = \(\frac{2m - 9m}{6}\) = \(\frac{-7m}{6}\) = 1\(\frac{1}{6}\) |
|
| 29. |
The volume of a cuboid is 54cm3. If the length, width and height of the cuboid are in the ratio 2:1:1 respectively, find its total surface area A. 108cm2 B. 90cm2 C. 80cm2 D. 72cm2 Detailed SolutionV = L x B x HV = \(2x \times x \times x = 2x^3\) = 54cm3 i.e. 2x3 = 54 x3 = \(\frac{54}{2}\) = 27 x = 3\(\sqrt{27}\) x = 3 L = 2x i.e. 2 x 3 = 6cm B = x i.e. x = 3cm H = x i.e. x = 3cm but A = 2(LB + LH + BH) = 2(6 x 3) + (6 x 3) + (3 x 3) = 2(18 + 18 + 9) = 2(45) = 90cm2 |
|
| 30. |
A side and a diagonal of a rhombus are 10cm and 12cm respectively, Find its area A. 20cm2 B. 24cm2 C. 48cm2 D. 96cm2 |
D |
| 21. |
Which of these statements about y = 8\(\sqrt{m}\) is correct? A. log y = log 8 x log \(\sqrt{m}\) B. log y = 3 log 2 x \(\frac{1}{2}\) log m C. log y = 3 log 2 - \(\frac{1}{2}\) log m D. log y = 3 log 2 + \(\frac{1}{2}\) log m Detailed Solutiony = 8\(\sqrt{m}\); log y = log 8\(\sqrt{m}\)log y = log 8 + log \(\sqrt{m}\) log y = log 23 + log m\(\frac{1}{2}\) log y = 3 log 3 + \(\frac{1}{2}\) log m |
|
| 22. |
If x + 0.4y = 3 and y = \(\frac{1}{2}\)x, find the value of (x + y) A. 1\(\frac{1}{4}\) B. 2\(\frac{1}{2}\) C. 3\(\frac{3}{4}\) D. 5 Detailed Solutionx + 0.4y = 3...(i)y = \(\frac{1}{2}\)x x = 2y x - 2y = 0....(ii) solve simultaneously; x + 0.4y = 3 - x - 2y = 0 2.4 = 3 y = \(\frac{3 \times 10}{2.4 \times 10} \) = \(\frac{30}{24} = \frac{5}{4}\) x - 2(\(\frac{5}{4}\)) = 0 x - \(\frac{5}{2}\) = 0 x = \(\frac{5}{2}\) x + y = \(\frac{5}{2} + \frac{5}{4}\) \(\frac{10 + 5}{4} = \frac{15}{4}\) = 3\(\frac{3}{4}\) |
|
| 23. |
Express 3 - [\(\frac{x - y}{y}\)] as a single fraction A. \(\frac{3xy}{y}\) B. \(\frac{x - 4y}{y}\) C. \(\frac{4y - x}{y}\) D. 3 - \(\frac{x - y}{y}\) Detailed Solution(\(\frac{x -y}{y}\)); \(\frac{3}{1} - \frac{x y}{y}\)= \(\frac{3y - (x - y)}{y}\) = \(\frac{3y - x + y}{y}\) = \(\frac{4y - x}{y}\) |
|
| 24. |
If p = {prime factors of 210} and Q = {prime less than 10}, find p \(\cap\) Q A. {1,2, 3} B. {2, 3, 5} C. {1, 3, 5,7} D. {2,3,5,7} Detailed Solutionprime factor of 210 = 2, 3, 5, 7prime numbers less than 10 = 2, 3, 5 , 7 |
|
| 25. |
Alfred spent \(\frac{1}{4}\) of his money on food, \(\frac{1}{3}\) on clothing and save the rest. If he saved N72,20.00, how much did he spend on food? A. N43,200.00 B. N43,000.00 C. N42,200.00 D. N40,000.00 Detailed Solutionlet the total amount be Nx i.e (\(\frac{1}{4}\))x + (\(\frac{1}{3}\))x + 72,000 = x\(\frac{x}{4} + \frac{x}{4} + 72,000 = x\) \(\frac{3x + 4x + 86,400}{12} = x\) cross multiply to clear fraction 12x = 3x + 4x + 86,400 12x - 7x = 86,400 5x = 86,400 x - \(\frac{86,400}{5}\) = 172,800 amount spent on food = \(\frac{1}{4} \times 172,800\) = N43,200 |
| 26. |
Solve (\(\frac{27}{125}\))-\(\frac{1}{3}\) x (\(\frac{4}{9}\))\(\frac{1}{2}\) A. \(\frac{10}{9}\) B. \(\frac{9}{10}\) C. \(\frac{2}{5}\) D. \(\frac{12}{125}\) Detailed Solution(\(\frac{27}{125}\))-\(\frac{1}{3}\) x (\(\frac{4}{9}\))\(\frac{1}{2}\)= (\(\frac{3^3}{5^3}\))-\(\frac{1}{3}\)-\(\frac{1}{3}\) x (\(\frac{3^2}{3^2}\))\(\frac{1}{2}\) -\(\frac{1}{2}\) = \(\frac{3^{-1}}{3^{-1}} \times \frac{2}{3}\) = \(\frac{\frac{1}{3}}{\frac{1}{5}} \times \frac{2}{3}\) \(\frac{1}{3} \times \frac{5}{1} \times {2}{3} = \frac{10}{9}\) |
|
| 27. |
The sum of the interior angles of regular polygon is 1800o. How many sides has the polygon? A. 16 B. 12 C. 10 D. 8 Detailed SolutionSum = (n - 2)1801800 = (n - 2)180 divide both sides by 180o \(\frac{1800}{180}\) = (n - 2)\(\frac{180}{180}\) 10 = n - 2 10 + 2 = n n = 12 |
|
| 28. |
Find the coefficient of m in the expression of (\(\frac{m}{2} - 1 \frac{1}{2}\)) (m + \(\frac{2}{3}\)) A. -\(\frac{1}{6}\) B. - \(\frac{1}{2}\) C. -1 D. -1\(\frac{1}{6}\) Detailed Solution(\(\frac{m}{2} - 1\frac{1}{4}\))(m + \(\frac{2}{3}\))(\(\frac{m}{2} - \frac{3}{2}\))(\(\frac{m}{1} + \frac{2}{3}\)) = \(\frac{m^2}{3} + \frac{3m}{6} - \frac{6}{6}\) = \(\frac{2m - 9m}{6}\) = \(\frac{-7m}{6}\) = 1\(\frac{1}{6}\) |
|
| 29. |
The volume of a cuboid is 54cm3. If the length, width and height of the cuboid are in the ratio 2:1:1 respectively, find its total surface area A. 108cm2 B. 90cm2 C. 80cm2 D. 72cm2 Detailed SolutionV = L x B x HV = \(2x \times x \times x = 2x^3\) = 54cm3 i.e. 2x3 = 54 x3 = \(\frac{54}{2}\) = 27 x = 3\(\sqrt{27}\) x = 3 L = 2x i.e. 2 x 3 = 6cm B = x i.e. x = 3cm H = x i.e. x = 3cm but A = 2(LB + LH + BH) = 2(6 x 3) + (6 x 3) + (3 x 3) = 2(18 + 18 + 9) = 2(45) = 90cm2 |
|
| 30. |
A side and a diagonal of a rhombus are 10cm and 12cm respectively, Find its area A. 20cm2 B. 24cm2 C. 48cm2 D. 96cm2 |
D |