| 1. | | Question: | (a) Mohan deposits Rs. 80 per month in a cumulative deposit account for six years. Find the amount payable to him on maturity, if the rate of interest is 6% per annum. | | Answer: | 6811.20 | | Explanation: | Equivalent P for 1 month = MI × [n(n + 1) / 2] = 80 × (72 × 73 / 2) = Rs. 210240 (1)
I = PRT / 100 = (210240 × 6 × 1) / (100 × 12) = Rs. 1051.20 (1)
MV = MI × n + I = 80 × 72 + 1051.2 = Rs. 6811.20 (1)
Formula for principal: Equivalent P for 1 month = MI × [n(n + 1) / 2], where P = Principal, MI = Monthly installment and n = Number of months.
Formula for simple interest: I = PRT / 100, where I = Interest, P = Principal, R = Rate and T = Time = 1/12.
Formula for maturity value: MV = MI × n + I, where MV = Maturity value, MI = Monthly installment, n = Number of months and I = Interest. |
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| 2. | | Question: | (b) A rectangular playground has two semicircles added to its outside with its smaller sides as diameters. If the sides of the rectangle are 120 m and 21 m, find the area of the playground.
(π = 22/7)
| | Answer: | 2866.5 | | Explanation: |
 (½)
Area of the playground = Area of the semicircle + Area of the rectangle + Area of the semicircle
= Area of the rectangle + Area of the circle (½)
= lb + π r2 (½) = 120 × 21 + 22/7 × (21/2)2= 2520 + 346.5 (½) = 2866.5 m2 (1)
Formula for area of a rectangle: A = lb, where A = Area, l = Length and b = Breadth / width.
Formula for area of a circle: A = π r2, where A = Area, π = 22/7 and r = Radius. |
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| 3. | | Question: | (c) Use graph paper for this question.
The points A (2, 3), B (4, 5) and C (7, 2) are the vertices of ΔABC.
(i) Write down the coordinates of A', B', C' if triangle ΔA'B'C' is the image of ΔABC, when reflected in the origin.
(ii) Write down the coordinates of A", B", C" if triangle ΔA"B"C" is the image of ΔABC, when reflected in the x-axis.
(iii) Mention the special name of the quadrilateral BCC"B" and find its area.
(Type in the answers separated by commas. Leave no spaces around the commas.) | | Answer: | (−2,−3),(−4,−5),(−7,−2),(2,−3),(4,−5),(7,−2),isosceles trapezium,21 | | Explanation: |
(i) The image of the point (x, y) in the origin is the point (−x, −y).
The coordinates of A', B', C' are (−2, −3), (−4, −5), (−7, −2) respectively. (½ + ½ for graph)
(ii) The image of the point (x, y) in the X-axis is the point (x, −y).
The coordinates of A", B", C" are (2, −3), (4, −5), (7, −2) respectively. (½ + ½ for graph)
(iii) The special name of the quadrilateral BCC"B" is isosceles trapezium. (½ + ½ for graph)
Area of the trapezium = ½ × (Sum of the parallel sides) × Height (½) = 1/2 × (10 + 4) × 3 = 21 square units (½)
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