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.

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1 comments:

Anonymous said...

Where is admin?!
By the way, anybody home?!

December 10, 2010 at 11:27 AM  

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