Mathematics (Core), 1995, WASSCE/WAEC MAY/JUNE, Exam, Paper 1 | Objectives

Paper Info

Year :

1995

Title :

Mathematics (Core)

Exam :

WASSCE/WAEC MAY/JUNE

Paper 1 | Objectives

21 - 30 of 48 Questions

#	Question	Ans
21.	The diagonals AC and BD of a rhombus ABCD are 16cm and 12cm long respectively. Calculate the area of the rhombus. A. 24cm² B. 36cm² C. 48cm² D. 60cm² E. 96cm² Show Content Detailed Solution Area of rhombus = \(\frac{pq}{2}\) where p and q are the diagonals of the rhombus. \(\therefore A = \frac{16 \times 12}{2}\) = 96 cm\(^2\)	E
22.	A water tank of height \(\frac{1}{2}\) m has a square base of side \(1\frac{1}{2}\) m. lf it is filled with water from a water tanker holding 1500 litres, how many litres of water are left in the water tanker? [1000 litres = 1m\(^3\)] A. 37.5litres B. 375 litres C. 3750 litres D. 37500 litres E. 375000 litres Show Content Detailed Solution Volume of water taken by the tank = \(\frac{3}{2} \times \frac{3}{2} \times \frac{1}{2}\) = \(\frac{9}{8} m^3\) = \(\frac{9}{8} \times 1000\) = 1125 litres \(\therefore\) Water left = (1500 - 1125) litres = 375 litres.	B
23.	A cylindrical container, closed at both ends, has a radius of 7cm and height 5cm [Take π = 22/7]Find the total surface area of the container A. 35cm³ B. 154cm³ C. 220cm² D. 528cm² E. 770cm² Show Content Detailed Solution T.S.A of a cylinder = \(2\pi r^2 + 2\pi rh\) = \(2\pi r(r + h)\) = \(2 \times \frac{22}{7} \times 7 \times (7 + 5)\) = \(44 \times 12\) = \(528 cm^2\)	D
24.	A cylindrical container, closed at both ends, has a radius of 7cm and height 5cm [Take π = 22/7]What is the volume of the container? A. 35cm³ B. 154cm³ C. 220cm³ D. 528cm³ E. 770cm³ Show Content Detailed Solution \(V = \pi r^2 h\) \(V = \frac{22}{7} \times 7 \times 7 \times 5\) = 770 cm\(^3\)	E
25.	Find the total surface area of solid circular cone with base radius 3cm and slant height 4cm. [Take π = 22/7] A. 37 5/7cm² B. 66cm² C. 75 3/7cm² D. 78 2/7cm² E. 88cm² Show Content Detailed Solution T.S.A of a cone = \(\pi r^2 + \pi rl\) = \(\frac{22}{7} \times 3^2 + \frac{22}{7} \times 3 \times 4\) = \(\frac{198}{7} + \frac{264}{7}\) = \(\frac{462}{7}\) = 66 cm\(^2\)	B
26.	A hollow sphere has a volume of kcm3 and a surface area of kcm2. Calculate the diameter of the sphere. A. 3cm B. 6cm C. 9cm D. 12cm E. More information is needed Show Content Detailed Solution \(Volume = \frac{4}{3} \pi r^3 = k\) ...(i) \(S.A = 4\pi r^2 = k\) ... (ii) Divide (i) by (ii), \(\frac{4}{3} \pi r^3 \div 4\pi r^2 = \frac{k}{k}\) \(\frac{r}{3} = 1 \implies r = 3cm\) Diameter = 2 x 3cm = 6cm	B
27.	The diagram above shows a cone with the dimensions of its frustrum indicated. Calculate the height of the cone. A. 12cm B. 15cm C. 18cm D. 24cm E. 30cm Show Content Detailed Solution Considering the smaller and larger triangle, these two are similar triangles. Hence, If the height of the smaller triangle = h, \(\therefore \frac{h}{6} = \frac{h + 12}{12}\) \(12h = 6h + 72 \implies 6h = 72\) \(h = 12 cm\) \(\therefore\) The height of the cone = 12 + 12 = 24 cm	D
28.	The positions of two countries P and Q are (15°N, 12°E) and (65°N, 12°E) respectively. What is the difference in latitude? A. 104^o B. 100^o C. 80^o D. 50^o E. 24^o Show Content Detailed Solution Latitudinal difference = 65° - 15° = 50°	D
29.	A 120° sector of a circle of radius 21cm is bent to form a cone. What is the base radius of the cone? A. 3¹/₂cm B. 7cm C. 1O¹/₂cm D. 14cm E. 21cm Show Content Detailed Solution The length of the arc subtended by the sector of angle 120° = circumference of the base of the cone. \(\frac{120}{360} \times 2 \times \frac{22}{7} \times 21 = 2\pi r\) \(44 = 2\pi r\) \(r = 22 \div \pi\) \(r = 22 \times \frac{7}{22}\) r = 7 cm	B
30.	The angle of a sector of a circle is 108°. If the radius of the circle is 31/2cm, find the perimeter of the sector A. 6 3/5cm B. 6 4/5cm C. 7 1/10cm D. 10 2/5cm E. 13 3/5cm, Show Content Detailed Solution Perimeter of sector = \(\frac{\theta}{360°} \times 2\pi r + 2r\) = \(\frac{108}{360} \times 2 \times \frac{22}{7} \times \frac{7}{2} + 2(\frac{7}{2})\) = \(6 \frac{3}{5} + 7\) = \(13 \frac{3}{5} cm\)	E

21.	The diagonals AC and BD of a rhombus ABCD are 16cm and 12cm long respectively. Calculate the area of the rhombus. A. 24cm² B. 36cm² C. 48cm² D. 60cm² E. 96cm² Show Content Detailed Solution Area of rhombus = \(\frac{pq}{2}\) where p and q are the diagonals of the rhombus. \(\therefore A = \frac{16 \times 12}{2}\) = 96 cm\(^2\)	E
22.	A water tank of height \(\frac{1}{2}\) m has a square base of side \(1\frac{1}{2}\) m. lf it is filled with water from a water tanker holding 1500 litres, how many litres of water are left in the water tanker? [1000 litres = 1m\(^3\)] A. 37.5litres B. 375 litres C. 3750 litres D. 37500 litres E. 375000 litres Show Content Detailed Solution Volume of water taken by the tank = \(\frac{3}{2} \times \frac{3}{2} \times \frac{1}{2}\) = \(\frac{9}{8} m^3\) = \(\frac{9}{8} \times 1000\) = 1125 litres \(\therefore\) Water left = (1500 - 1125) litres = 375 litres.	B
23.	A cylindrical container, closed at both ends, has a radius of 7cm and height 5cm [Take π = 22/7]Find the total surface area of the container A. 35cm³ B. 154cm³ C. 220cm² D. 528cm² E. 770cm² Show Content Detailed Solution T.S.A of a cylinder = \(2\pi r^2 + 2\pi rh\) = \(2\pi r(r + h)\) = \(2 \times \frac{22}{7} \times 7 \times (7 + 5)\) = \(44 \times 12\) = \(528 cm^2\)	D
24.	A cylindrical container, closed at both ends, has a radius of 7cm and height 5cm [Take π = 22/7]What is the volume of the container? A. 35cm³ B. 154cm³ C. 220cm³ D. 528cm³ E. 770cm³ Show Content Detailed Solution \(V = \pi r^2 h\) \(V = \frac{22}{7} \times 7 \times 7 \times 5\) = 770 cm\(^3\)	E
25.	Find the total surface area of solid circular cone with base radius 3cm and slant height 4cm. [Take π = 22/7] A. 37 5/7cm² B. 66cm² C. 75 3/7cm² D. 78 2/7cm² E. 88cm² Show Content Detailed Solution T.S.A of a cone = \(\pi r^2 + \pi rl\) = \(\frac{22}{7} \times 3^2 + \frac{22}{7} \times 3 \times 4\) = \(\frac{198}{7} + \frac{264}{7}\) = \(\frac{462}{7}\) = 66 cm\(^2\)	B

26.	A hollow sphere has a volume of kcm3 and a surface area of kcm2. Calculate the diameter of the sphere. A. 3cm B. 6cm C. 9cm D. 12cm E. More information is needed Show Content Detailed Solution \(Volume = \frac{4}{3} \pi r^3 = k\) ...(i) \(S.A = 4\pi r^2 = k\) ... (ii) Divide (i) by (ii), \(\frac{4}{3} \pi r^3 \div 4\pi r^2 = \frac{k}{k}\) \(\frac{r}{3} = 1 \implies r = 3cm\) Diameter = 2 x 3cm = 6cm	B
27.	The diagram above shows a cone with the dimensions of its frustrum indicated. Calculate the height of the cone. A. 12cm B. 15cm C. 18cm D. 24cm E. 30cm Show Content Detailed Solution Considering the smaller and larger triangle, these two are similar triangles. Hence, If the height of the smaller triangle = h, \(\therefore \frac{h}{6} = \frac{h + 12}{12}\) \(12h = 6h + 72 \implies 6h = 72\) \(h = 12 cm\) \(\therefore\) The height of the cone = 12 + 12 = 24 cm	D
28.	The positions of two countries P and Q are (15°N, 12°E) and (65°N, 12°E) respectively. What is the difference in latitude? A. 104^o B. 100^o C. 80^o D. 50^o E. 24^o Show Content Detailed Solution Latitudinal difference = 65° - 15° = 50°	D
29.	A 120° sector of a circle of radius 21cm is bent to form a cone. What is the base radius of the cone? A. 3¹/₂cm B. 7cm C. 1O¹/₂cm D. 14cm E. 21cm Show Content Detailed Solution The length of the arc subtended by the sector of angle 120° = circumference of the base of the cone. \(\frac{120}{360} \times 2 \times \frac{22}{7} \times 21 = 2\pi r\) \(44 = 2\pi r\) \(r = 22 \div \pi\) \(r = 22 \times \frac{7}{22}\) r = 7 cm	B
30.	The angle of a sector of a circle is 108°. If the radius of the circle is 31/2cm, find the perimeter of the sector A. 6 3/5cm B. 6 4/5cm C. 7 1/10cm D. 10 2/5cm E. 13 3/5cm, Show Content Detailed Solution Perimeter of sector = \(\frac{\theta}{360°} \times 2\pi r + 2r\) = \(\frac{108}{360} \times 2 \times \frac{22}{7} \times \frac{7}{2} + 2(\frac{7}{2})\) = \(6 \frac{3}{5} + 7\) = \(13 \frac{3}{5} cm\)	E