Showing posts with label icse board. Show all posts
Showing posts with label icse board. Show all posts

ICSE board maths solved paper free online

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.
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.
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)

3:18 AM | Labels: | 3 Comments  

ICSE Board mathematics 2008 solved exam paper free download

1.
Question: (a) Show that 2x + 7 is a factor of 2x3 + 5x2 − 11x − 14. Hence, factorise the given expression completely, using the factor theorem.
Answer:
Explanation: f(x) = 2x3 + 5x2 − 11x − 14
Divisor = (2x + 7)
∴ x = − 7
2
f ( − 7
2		 ) = 2 ( − 343
8
) + 5 ( 49
4
) − 11 ( − 7
2 		) − 14 (½) = − 343
4
+ 245
4
+ 77
2
− 14 = − 399 + 399
4
= 0 (1)
∴ (2x + 7) is a factor of f(x).
Hence proved.
Synthetic division:
−7
2
2 5 −11 −14
−7 7 14
2 −2 −4 0

f(x) = (2x + 7)(2x2 − 2x − 4) (½) = (2x + 7) (x2 − x − 2) = (2x + 7) (x2 + x − 2x − 2) = (2x + 7) (x + 1) (x − 2) (1)
2.
Question: (b) The median of the following observations 11, 12, 14, 18, (x + 4), 30, 32, 35, 41 arranged in ascending order is 24. Find x.
Answer: 20
Explanation:
Median = (
n + 1
2
) th observation [n is odd] (½)

24 =
(
9 + 1
2

) th observation (½) = 5th observation (½) = x + 4 (½)


x = 20 (1)

n = Number of observations.
Note that if n is even, Median = [( n
2		 ) th observation + ( n
2 		+ 1 ) th observation ] / 2
3.
Question: (c)

In the above figure, ∠BAD = 65°, ∠ABD = 70° and ∠BDC = 45°.
Find :-
(i) ∠BCD
(ii) ∠ADB
Hence show that AC is a diameter.
(Type in the answers separated by commas. Leave no spaces around the commas.)
Answer: 115,45
Explanation: (i) ∠BAD + ∠BCD = 180° [Sum of the opposite angles of cyclic quadrilateral ABCD = 180°]
∠BCD = 180° − ∠BAD (½)
∠BCD = 180° − 65° = 115° (1)

(ii) ∠BAD + ∠ABD + ∠ADB = 180° [Sum of the angles of ΔABD = 180°]
∠ADB = 180° − ∠BAD − ∠ABD (½)
∠ADB = 180° − 65° − 70° = 45° (1)

∠ADC = ∠ADB + ∠BDC
∠ADC = 45° + 45° = 90° (1)
AC is a diameter. [Converse of angle in a semicircle property] (½)
Hence proved.

3:16 AM | Labels: | 1 Comments  

ICSE board exam free solved papers maths

1.
Question: (a) Kiran purchases an article for Rs. 5,400 which includes 10% rebate on the marked price and 20% sales tax on the remaining price. Find the marked price of the article.
Answer: 5000.00
Explanation: Let the marked price of the article = Rs. x
Price after rebate =
90
100 		× x = Rs. ( 9x
10 		) (½)
Price after sales tax = 120
100 		× 9x
10 		= Rs. ( 27x
25
) (½)

By the given condition,
27x
25
= 5400 (1)

x = 5000
∴ The marked price of the article = Rs. 5000.00 (1)

2.
Question:
(b) If
 3x + 5y
3x − 5y 		= 7
3 		, find x : y.

(Leave no spaces around the : (colon) symbol.)
Answer: 25:6
Explanation:
3x + 5y
3x − 5y 		= 7
3

By Componendo and Dividendo, (½)
3x + 5y + 3x − 5y
3x + 5y − 3x + 5y 		= 7 + 3
7 − 3		 (1)
6x
10y 		= 10
4
(½)
x
y 		= 25
6

∴ x : y = 25 : 6 (1)

Alternative method:
9x + 15y = 21x − 35y (1)
−12x = −50y (½)
6x = 25y (½)
x
y 		= 25
6
∴ x : y = 25 : 6 (1)

3.
Question: (c) A person invests Rs. 10,000 for two years at a certain rate of interest compounded annually. At the end of one year this sum amounts to Rs. 11,200. Calculate :-
(i) the rate of interest per annum.
(ii) the amount at the end of the second year.
(Type in the answers separated by commas. Leave no spaces around the commas.)
Answer: 12,12544.00
Explanation: (i) I = A − P = 11200 − 10000 = Rs. 1200
I = PRT
100
⇒ R = 100I
PT
(½) = 100 × 1200
10000 × 1
(½) = 12% (1)

(ii) A = P ( 1 +
r
100 		) n (½) = 10000 ( 1 +
12
100		 ) 2 = 10000 × 28
25		 × 28
25		 (½) = Rs. 12544.00 (1)
Formula for simple interest: I = PRT
100
, where I = Simple interest, P = Principal, R = Rate and T = Time.
Formula for compound interest: A = P ( 1 +
r
100 		) n , where A = Amount, P = Principal, r = Rate and n = Time.

3:11 AM | Labels: | 1 Comments  

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