ICSE Guess Paper 2010

Mathematics

Class - X

SECTION I (40 Marks)
Attempt all questions from this Section

(a) The simple interest on a sum of money for 2 years at 4% per annum is Rs.340. Find

i. the sum of money

ii. the compound interest on this sum for one year payable half yearly at the same rate.

(b)Solve x² - 6x + 2 = 0 by completing the square. (Ans: x = 5.646 or 0.354)

(c) Find the fourth proportional to 2xy, x², y².

2. (a) Solve using the Quadratic Formula: 2 x² +8x +4 =0 (Ans: 0.586 , 3.414)

(b) Find the value of p and q, if (x + 3) and (x – 4) are the factors of x³ – px² – qx + 24.

(c) Solve 4x² – 0.2125x + .00125 = 0 for values upto 4 decimal places. (Ans: 0.0464 and 0.0067)

3. (a) Prove that sec⁴ -tan⁴ = 1 +2 tan² .

(b) Bharti has a recurring deposit account in a bank for 5 years at 9% per annum simple interest. If she gets Rs.51607.50 at the time of maturity, find the monthly installment.

(c) A man invests Rs 20020 in buying shares of nominal value Rs 26 at 10 % premium. The dividend on the shares is 15 % per annum. Calculate

i. The number of shares he buys.

ii. The dividend he receives annually.

iii. The rate of interest he gets on his money.

4. (a) Find the value of n such that the equation (2n + 3) x² + 2 (n + 3) x + (n + 5) = 0 has equal roots. (Ans: n = –1, n = –6).

(b) If the equation (1 + m²) x² + 2mcx + c² −a² = 0 has equal roots, prove that c² = a² (1 + m²).

(c) Prove that the roots of the equation (a – b) x² + 2 (a–b) x + (a–b–c) = 0 are real.

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