Mathematics (Core), 2008, WASSCE/WAEC MAY/JUNE, Exam, Paper 1 | Objectives

Paper Info

Year :

2008

Title :

Mathematics (Core)

Exam :

WASSCE/WAEC MAY/JUNE

Paper 1 | Objectives

41 - 45 of 45 Questions

#	Question	Ans
41.	If the perimeter of \(\bigtriangleup\)PQR in thr diagram is 24cm, what is the area of \(\bigtriangleup\)PRS? A. 19.5cm² B. 15.0cm² C. 13.0cm² D. 9.3cm² Show Content Detailed Solution Perimeter of \(\bigtriangleup\) PQR = PQ + QR + PR 24cm = 6cm + 8cm = PR 24 = 14 + PR PR = 24 - 14 = 10cm Area of \(\bigtriangleup\) PRS = \(\frac{1}{2} \times 10 \times 3cm^3\) = 15cm³	B
42.	In the diagram, PX is a tangent to the circle and RST is an equilateral triangle. Calculate < PTS A. 60^o B. 90^o C. 120^o D. 150^o Show Content Detailed Solution \(\bigtriangleup\) RST is equilateral triangle, hence < TRS = < RTS = < RSt = 60^o But < PTR = 60^o(Angle between a chord and a tangent at the point of contact = Angle in the alt. segment). From the diagram < PTS = < PTR + < RTS = 60^o + 60^o = 120^o	C
43.	In the diagram, < QPR = 60^o < PQR = 50^o < QRS = 2x^o < SRP = 3x^o < UQP = y^o and RS//TU calculate y A. 102^o B. 78^o C. 70^o D. 60^o Show Content Detailed Solution < RQT = < QRS = 2x (Alternate angles). But in \(\bigtriangleup\) PRQ 50 + 60 + (2x + 3x) = 180^o(Angles in a triangle) 110 + 5x = 180^o 5x = 180^o - 110 = 70^o x = \(\frac{70}{5}\) = 14^o Also y + 50 + 2(14) = 180^o y + 50 + 28 = 180^o y = 180 - 78	A
44.	In the diagram, find the size of the angle marked a° A. 60^o B. 80^o C. 120^o D. 160^o Show Content Detailed Solution 2 x s = 280°(Angle at centre = 2 x < at circum) S = \(\frac{280^o}{2}\) = 140° < O = 360 - 280 = 80° 60 + 80 + 140 + a = 360° (< in a quad); 280 + a = 360 a = 360 - 280 a = 80°	B
45.	Every staff in an office owns either a Mercedes and/or a Toyota car. 20 own Mercedes, 15 own Toyota and 5 own both. How many staff are there in the office? A. 25 B. 30 C. 35 D. 45 Show Content Detailed Solution M = Mercedez; T = Toyota Number of staff = 0 + (20 - 5) + (15 - 5) + 5 0 + 15 + 10 + 5 = 30	B

41.	If the perimeter of \(\bigtriangleup\)PQR in thr diagram is 24cm, what is the area of \(\bigtriangleup\)PRS? A. 19.5cm² B. 15.0cm² C. 13.0cm² D. 9.3cm² Show Content Detailed Solution Perimeter of \(\bigtriangleup\) PQR = PQ + QR + PR 24cm = 6cm + 8cm = PR 24 = 14 + PR PR = 24 - 14 = 10cm Area of \(\bigtriangleup\) PRS = \(\frac{1}{2} \times 10 \times 3cm^3\) = 15cm³	B
42.	In the diagram, PX is a tangent to the circle and RST is an equilateral triangle. Calculate < PTS A. 60^o B. 90^o C. 120^o D. 150^o Show Content Detailed Solution \(\bigtriangleup\) RST is equilateral triangle, hence < TRS = < RTS = < RSt = 60^o But < PTR = 60^o(Angle between a chord and a tangent at the point of contact = Angle in the alt. segment). From the diagram < PTS = < PTR + < RTS = 60^o + 60^o = 120^o	C
43.	In the diagram, < QPR = 60^o < PQR = 50^o < QRS = 2x^o < SRP = 3x^o < UQP = y^o and RS//TU calculate y A. 102^o B. 78^o C. 70^o D. 60^o Show Content Detailed Solution < RQT = < QRS = 2x (Alternate angles). But in \(\bigtriangleup\) PRQ 50 + 60 + (2x + 3x) = 180^o(Angles in a triangle) 110 + 5x = 180^o 5x = 180^o - 110 = 70^o x = \(\frac{70}{5}\) = 14^o Also y + 50 + 2(14) = 180^o y + 50 + 28 = 180^o y = 180 - 78	A

44.	In the diagram, find the size of the angle marked a° A. 60^o B. 80^o C. 120^o D. 160^o Show Content Detailed Solution 2 x s = 280°(Angle at centre = 2 x < at circum) S = \(\frac{280^o}{2}\) = 140° < O = 360 - 280 = 80° 60 + 80 + 140 + a = 360° (< in a quad); 280 + a = 360 a = 360 - 280 a = 80°	B
45.	Every staff in an office owns either a Mercedes and/or a Toyota car. 20 own Mercedes, 15 own Toyota and 5 own both. How many staff are there in the office? A. 25 B. 30 C. 35 D. 45 Show Content Detailed Solution M = Mercedez; T = Toyota Number of staff = 0 + (20 - 5) + (15 - 5) + 5 0 + 15 + 10 + 5 = 30	B