Mathematics (Core), 2020, WASSCE/WAEC MAY/JUNE, Exam, Paper 1 | Objectives

Paper Info

Year :

2020

Title :

Mathematics (Core)

Exam :

WASSCE/WAEC MAY/JUNE

Paper 1 | Objectives

11 - 20 of 50 Questions

#	Question	Ans
11.	The first term of a geometric progression (G.P) is 3 and the 5th term is 48. Find the common ratio. A. 2 B. 4 C. 8 D. 16 Show Content Detailed Solution T\(_5\) = ar\(^4\) \(\frac{48}{3} = \frac{3r^4}{3}\) 16 = r\(^4\) r = \(4\sqrt{16}\) = 2	A
12.	Solve \(\frac{1}{3}\)(5 - 3x) < \(\frac{2}{5}\)(3 - 7x) A. x > \(\frac{7}{22}\) B. x < \(\frac{7}{22}\) C. x > \(\frac{-7}{27}\) D. x < \(\frac{-7}{27}\) Show Content Detailed Solution \(\frac{1}{3}\)(5 - 3x) < \(\frac{2}{5}\)(3 - 7x) 5(5 - 3x) < 6(3 - 7x) 25 - 15x < 18 - 42x - 15x + 42x < 18 - 25 \(\frac{27x}{27}\) < \(\frac{-7}{27}\) x < \(\frac{-7}{27}\)	C
13.	Make m the subject of the relation k = \(\frac{m - y}{m + 1}\) A. m = \(\frac{y + k^2}{k^2 + 1}\) B. m = \(\frac{y + k^2}{1 - k^2}\) C. m = \(\frac{y - k^2}{k^2 + 1}\) D. m = \(\frac{y - k^2}{1 - k^2}\) Show Content Detailed Solution k = \(\frac{m - y}{m + 1}\) k\(^2\) = \(\frac{m - y}{m + 1}\) k\(^2\)m + k\(^2\) = m - y k\(^2\) + y = m - k\(^2\)m \(\frac{k^2 + y}{1 - k^2}\) = m\(\frac{(1 - k^2)}{1 - k^2}\) m = \(\frac{y + k^2}{1 - k^2}\)	B
14.	Find the quadratic equation whose roots are \(\frac{1}{2}\) and -\(\frac{1}{3}\) A. 3x\(^2\) + x + 1 = 0 B. 6x\(^2\) + x - 1 = 0 C. 3x\(^2\) + x - 1 = 0 D. 6x\(^2\) - x - 1 = 0 Show Content Detailed Solution x = \(\frac{1}{2}\) and x = \(\frac{-1}{3}\) (2x - 1) = 0 and (3x + 1) = 0 (2x - 1) (3x + 1) = 0 6x\(^2\) - x - 1 = 0	D
15.	Given that x is directly proportional to y and inversely proportional to Z, x = 15 when y = 10 and Z = 4, find the equation connecting x, y and z A. x = \(\frac{6y}{z}\) B. x = \(\frac{12y}{z}\) C. x = \(\frac{3y}{z}\) D. x = \(\frac{3y}{2z}\) Show Content Detailed Solution \(x\) x \(\frac{y}{z}\) x = \(\frac{ky}{z}\) 15 = \(\frac{10k}{4}\) \(\frac{60}{10}\) = k = 6 Therefore; x = \(\frac{6y}{z}\)	A
16.	Two buses start from the same station at 9.00am and travel in opposite directions along the same straight road. The first bus travel at a speed of 72 km/h and the second at 48 km/h. At what time will they be 240km apart? A. 1:00 pm B. 12:00 noon C. 11:00 am D. 10:00 am Show Content Detailed Solution Let x be the time Then 72x + 48x = 240 \(\frac{120}{120} \times \frac{240}{120}\) x = 2hrs 9:00 + 2hrs = 11:00 am	C
17.	A solid cuboid has a length of 7 cm, a width of 5 cm, and a height of 4 cm. Calculate its total surface area. A. 280 cm\(^2\) B. 166 cm\(^2\) C. 140 cm\(^2\) D. 83 cm\(^2\) Show Content Detailed Solution Total = 2(LB + BH + LH) Surface area = 2(7 x 5 + 5 x 4 + 7 x 4) = 2(35 + 20 + 28) = 2(83) = 166cm\(^2\)	B
18.	In the diagram, PQ // SR. Find the value of x A. 34 B. 46 C. 57 D. 68 Show Content Detailed Solution x + 68\(^o\) + 246\(^o\) = 360\(^o\) x + 314\(^o\) = 360\(^o\) x = 360\(^o\) - 314\(^o\) x = 46\(^o\)	B
19.	Find the equation of the line parallel to 2y = 3(x - 2) and passes through the point (2, 3) A. y = \(\frac{2}{3} x - 3\) B. y = \(\frac{2}{3} x - 2\) C. y = \(\frac{2}{3} x\) D. y = \(\frac{-2}{3} x\) Show Content Detailed Solution 2y = 3(x - 2) \(\frac{2y}{2} = \frac{3x}{2} - \frac{6}{2}\) y = \(\frac{3}{2}x - 3\) m = \(\frac{3}{2}\) \(\frac{y - y_1}{x - x_1}\) = m \(\frac{y - 3}{x - 2} = \frac{3}{2}\) 2y - 6 = 3x - 6 \(\frac{2y}{2} = \frac{3x}{2}\) y = \(\frac{3}{2}\)x	C
20.	The expression \(\frac{5x + 3}{6x (x + 1)}\) will be undefined when x equals A. {0, 1} B. {0, -1} C. {-3, -11} D. {-3, 0} Show Content Detailed Solution 6x(x + 1) = 0 When 6x = 0 and x + 1 = 0 x = 0 and x = -1 (0, -1)	B

11.	The first term of a geometric progression (G.P) is 3 and the 5th term is 48. Find the common ratio. A. 2 B. 4 C. 8 D. 16 Show Content Detailed Solution T\(_5\) = ar\(^4\) \(\frac{48}{3} = \frac{3r^4}{3}\) 16 = r\(^4\) r = \(4\sqrt{16}\) = 2	A
12.	Solve \(\frac{1}{3}\)(5 - 3x) < \(\frac{2}{5}\)(3 - 7x) A. x > \(\frac{7}{22}\) B. x < \(\frac{7}{22}\) C. x > \(\frac{-7}{27}\) D. x < \(\frac{-7}{27}\) Show Content Detailed Solution \(\frac{1}{3}\)(5 - 3x) < \(\frac{2}{5}\)(3 - 7x) 5(5 - 3x) < 6(3 - 7x) 25 - 15x < 18 - 42x - 15x + 42x < 18 - 25 \(\frac{27x}{27}\) < \(\frac{-7}{27}\) x < \(\frac{-7}{27}\)	C
13.	Make m the subject of the relation k = \(\frac{m - y}{m + 1}\) A. m = \(\frac{y + k^2}{k^2 + 1}\) B. m = \(\frac{y + k^2}{1 - k^2}\) C. m = \(\frac{y - k^2}{k^2 + 1}\) D. m = \(\frac{y - k^2}{1 - k^2}\) Show Content Detailed Solution k = \(\frac{m - y}{m + 1}\) k\(^2\) = \(\frac{m - y}{m + 1}\) k\(^2\)m + k\(^2\) = m - y k\(^2\) + y = m - k\(^2\)m \(\frac{k^2 + y}{1 - k^2}\) = m\(\frac{(1 - k^2)}{1 - k^2}\) m = \(\frac{y + k^2}{1 - k^2}\)	B
14.	Find the quadratic equation whose roots are \(\frac{1}{2}\) and -\(\frac{1}{3}\) A. 3x\(^2\) + x + 1 = 0 B. 6x\(^2\) + x - 1 = 0 C. 3x\(^2\) + x - 1 = 0 D. 6x\(^2\) - x - 1 = 0 Show Content Detailed Solution x = \(\frac{1}{2}\) and x = \(\frac{-1}{3}\) (2x - 1) = 0 and (3x + 1) = 0 (2x - 1) (3x + 1) = 0 6x\(^2\) - x - 1 = 0	D
15.	Given that x is directly proportional to y and inversely proportional to Z, x = 15 when y = 10 and Z = 4, find the equation connecting x, y and z A. x = \(\frac{6y}{z}\) B. x = \(\frac{12y}{z}\) C. x = \(\frac{3y}{z}\) D. x = \(\frac{3y}{2z}\) Show Content Detailed Solution \(x\) x \(\frac{y}{z}\) x = \(\frac{ky}{z}\) 15 = \(\frac{10k}{4}\) \(\frac{60}{10}\) = k = 6 Therefore; x = \(\frac{6y}{z}\)	A

16.	Two buses start from the same station at 9.00am and travel in opposite directions along the same straight road. The first bus travel at a speed of 72 km/h and the second at 48 km/h. At what time will they be 240km apart? A. 1:00 pm B. 12:00 noon C. 11:00 am D. 10:00 am Show Content Detailed Solution Let x be the time Then 72x + 48x = 240 \(\frac{120}{120} \times \frac{240}{120}\) x = 2hrs 9:00 + 2hrs = 11:00 am	C
17.	A solid cuboid has a length of 7 cm, a width of 5 cm, and a height of 4 cm. Calculate its total surface area. A. 280 cm\(^2\) B. 166 cm\(^2\) C. 140 cm\(^2\) D. 83 cm\(^2\) Show Content Detailed Solution Total = 2(LB + BH + LH) Surface area = 2(7 x 5 + 5 x 4 + 7 x 4) = 2(35 + 20 + 28) = 2(83) = 166cm\(^2\)	B
18.	In the diagram, PQ // SR. Find the value of x A. 34 B. 46 C. 57 D. 68 Show Content Detailed Solution x + 68\(^o\) + 246\(^o\) = 360\(^o\) x + 314\(^o\) = 360\(^o\) x = 360\(^o\) - 314\(^o\) x = 46\(^o\)	B
19.	Find the equation of the line parallel to 2y = 3(x - 2) and passes through the point (2, 3) A. y = \(\frac{2}{3} x - 3\) B. y = \(\frac{2}{3} x - 2\) C. y = \(\frac{2}{3} x\) D. y = \(\frac{-2}{3} x\) Show Content Detailed Solution 2y = 3(x - 2) \(\frac{2y}{2} = \frac{3x}{2} - \frac{6}{2}\) y = \(\frac{3}{2}x - 3\) m = \(\frac{3}{2}\) \(\frac{y - y_1}{x - x_1}\) = m \(\frac{y - 3}{x - 2} = \frac{3}{2}\) 2y - 6 = 3x - 6 \(\frac{2y}{2} = \frac{3x}{2}\) y = \(\frac{3}{2}\)x	C
20.	The expression \(\frac{5x + 3}{6x (x + 1)}\) will be undefined when x equals A. {0, 1} B. {0, -1} C. {-3, -11} D. {-3, 0} Show Content Detailed Solution 6x(x + 1) = 0 When 6x = 0 and x + 1 = 0 x = 0 and x = -1 (0, -1)	B