Mathematics (Core), 2018, WASSCE/WAEC MAY/JUNE, Exam, Paper 1 | Objectives

Paper Info

Year :

2018

Title :

Mathematics (Core)

Exam :

WASSCE/WAEC MAY/JUNE

Paper 1 | Objectives

31 - 40 of 50 Questions

#	Question	Ans
31.	In the diagram, which of the following ratios is equal to \(\frac{\|PN\|}{\|PQ\|}\)? A. \(\frac{\|PN\|}{\|PR\|}\) B. \(\frac{\|PM\|}{\|PQ\|}\) C. \(\frac{\|PM\|}{\|PR\|}\) D. \(\frac{\|PR\|}{\|PQ\|}\) Show Content Detailed Solution \(\frac{\|PN\|}{\|PQ\|}\) = \(\frac{\|PM\|}{\|PR\|}\)	C
32.	If P and Q are two statements, under what condition would p\|q be false? A. If p is true and q is true B. If p is true and q is false C. If p is false and q is false D. If p is false and q is true Show Content Detailed Solution From the truth table above, p \(\to\) q would be false if p is true and q is false	B
33.	Find the median of 2, 1, 0, 3, 1, 1, 4, 0, 1 and 2 A. 0.0 B. 0.5 C. 1.0 D. 1.5 Show Content Detailed Solution First arrange the numbers in ascending order of magnitude; 0, 0, 1, 1, 1, 1, 2, 2, 3, 4 Counting from the right, the fifth number is 1 Counting from the left, the fifth number is 1 Hence, median = \(frac{1 + 1}{2}\) = \(\frac{2}{2}\) = 1	C
34.	Find the mean deviation of 20, 30, 25, 40, 35, 50, 45, 40, 20 and 45 A. 8 B. 9 C. 10 D. 12 Show Content Detailed Solution Mean = \(\frac{\sum f x}{\sum f}\) = \(\frac{350}{10}\) = 35 = \(\frac{\sum f \|d\|}{\sum f}\) = \(\frac{90}{10}\) = 9	B
35.	Find the value of t in the diagram A. 63\(^o\) B. 117\(^o\) C. 126\(^o\) D. 234\(^o\) Show Content Detailed Solution In the diagram, \(\alpha\) = 180\(^o\) - 177\(^o\) (angles on a straight line) \(\alpha\) = 63\(^o\) t = 2 x 63\(^o\) (angle at centre = 2 x angle at circum) = 126\(^o\)	C
36.	In the diagram, PR is a tangent to the circle at Q, QT//RS, A. 40\(^o\) B. 65\(^o\) C. 85\(^o\) D. 95\(^o\) Show Content Detailed Solution In the diagram, a = 50\(^o\) (alternate angles) b\(_1\) + a 35\(^o\) = 180\(^o\) (sum of angles on a straight line) i.e; b\(_1\) + 50\(^o\) + 35\(^o\) = 180v b\(_1\) + 180\(^o\) - 85\(^o\) = 90\(^o\) But b\(_2\) = \(b_1\) = 95\(^o\) (angles in alternate segement) <QST = b\(_2\) = 95\(^o\)	D
37.	In the diagram, WXYZ is a rectangle with dimension 8cm by 6cm. P, Q, R and S are the midpoints of the sides of the rectangle as shown. Using this information, what type of quadrilateral is the shaded region? A. Trapezium B. Prism C. Rectangle D. Rhombus	D
38.	In the diagram, PS and RS are tangents to the circle centre O, A. 110\(^o\) B. 135\(^o\) C. 165\(^o\) D. 225\(^o\)
39.	In the diagram, WXYZ is a rectangle with diamension 8cm by 6cm. P, Q, R and S are the midpoints of the rectangle as shown. Using this information calculate the area of the part of the rectangle that is not shaded A. 25cm\(^2\) B. 24cm\(^2\) C. 16cm\(^2\) D. 12cm\(^2\)
40.	The solution of x + 2 \(\geq\) 2x + 1 is illustrated A. i B. ii C. iii D. iv Show Content Detailed Solution x + 2 \(\geq\) 2x + 1 x - 2x \(\geq\) 1 - 2 -x \(\geq\) -1 \(\frac{-x}{-1}\) \(\geq\) \(\frac{-1}{-1}\) x \(\leq\) 1	A

31.	In the diagram, which of the following ratios is equal to \(\frac{\|PN\|}{\|PQ\|}\)? A. \(\frac{\|PN\|}{\|PR\|}\) B. \(\frac{\|PM\|}{\|PQ\|}\) C. \(\frac{\|PM\|}{\|PR\|}\) D. \(\frac{\|PR\|}{\|PQ\|}\) Show Content Detailed Solution \(\frac{\|PN\|}{\|PQ\|}\) = \(\frac{\|PM\|}{\|PR\|}\)	C
32.	If P and Q are two statements, under what condition would p\|q be false? A. If p is true and q is true B. If p is true and q is false C. If p is false and q is false D. If p is false and q is true Show Content Detailed Solution From the truth table above, p \(\to\) q would be false if p is true and q is false	B
33.	Find the median of 2, 1, 0, 3, 1, 1, 4, 0, 1 and 2 A. 0.0 B. 0.5 C. 1.0 D. 1.5 Show Content Detailed Solution First arrange the numbers in ascending order of magnitude; 0, 0, 1, 1, 1, 1, 2, 2, 3, 4 Counting from the right, the fifth number is 1 Counting from the left, the fifth number is 1 Hence, median = \(frac{1 + 1}{2}\) = \(\frac{2}{2}\) = 1	C
34.	Find the mean deviation of 20, 30, 25, 40, 35, 50, 45, 40, 20 and 45 A. 8 B. 9 C. 10 D. 12 Show Content Detailed Solution Mean = \(\frac{\sum f x}{\sum f}\) = \(\frac{350}{10}\) = 35 = \(\frac{\sum f \|d\|}{\sum f}\) = \(\frac{90}{10}\) = 9	B
35.	Find the value of t in the diagram A. 63\(^o\) B. 117\(^o\) C. 126\(^o\) D. 234\(^o\) Show Content Detailed Solution In the diagram, \(\alpha\) = 180\(^o\) - 177\(^o\) (angles on a straight line) \(\alpha\) = 63\(^o\) t = 2 x 63\(^o\) (angle at centre = 2 x angle at circum) = 126\(^o\)	C

36.	In the diagram, PR is a tangent to the circle at Q, QT//RS, A. 40\(^o\) B. 65\(^o\) C. 85\(^o\) D. 95\(^o\) Show Content Detailed Solution In the diagram, a = 50\(^o\) (alternate angles) b\(_1\) + a 35\(^o\) = 180\(^o\) (sum of angles on a straight line) i.e; b\(_1\) + 50\(^o\) + 35\(^o\) = 180v b\(_1\) + 180\(^o\) - 85\(^o\) = 90\(^o\) But b\(_2\) = \(b_1\) = 95\(^o\) (angles in alternate segement) <QST = b\(_2\) = 95\(^o\)	D
37.	In the diagram, WXYZ is a rectangle with dimension 8cm by 6cm. P, Q, R and S are the midpoints of the sides of the rectangle as shown. Using this information, what type of quadrilateral is the shaded region? A. Trapezium B. Prism C. Rectangle D. Rhombus	D
38.	In the diagram, PS and RS are tangents to the circle centre O, A. 110\(^o\) B. 135\(^o\) C. 165\(^o\) D. 225\(^o\)
39.	In the diagram, WXYZ is a rectangle with diamension 8cm by 6cm. P, Q, R and S are the midpoints of the rectangle as shown. Using this information calculate the area of the part of the rectangle that is not shaded A. 25cm\(^2\) B. 24cm\(^2\) C. 16cm\(^2\) D. 12cm\(^2\)
40.	The solution of x + 2 \(\geq\) 2x + 1 is illustrated A. i B. ii C. iii D. iv Show Content Detailed Solution x + 2 \(\geq\) 2x + 1 x - 2x \(\geq\) 1 - 2 -x \(\geq\) -1 \(\frac{-x}{-1}\) \(\geq\) \(\frac{-1}{-1}\) x \(\leq\) 1	A