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St. Xavier’s College, Mumbai
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LILAVATIBAI LILAVATIBAI PODAR HIGH SCHOOL ISC STD X / SA2/ MATHS/2014-2015 WORKSHEET NO 1 STD X REMAINDER FACTOR THEOREM, BANKING, REFLECTION, SYMMETRY 1. Using the factor and remainder theorem factorize completely a. 6x3 7x2 11x + 12 b. 2x3 + 19x2 + 38x + 21 2. Find the value of a if (x - a) is a factor of x3 ax2 + x + 2 3. If the expression of x3 2x2 + ax + b has a factor (x + 2) and leaves a remainder 9 when divided by ( x + 1) find the values of a and b and factorize the given polynomial. 4. If x4 2x3 + 3x2 ax + b is divided by (x - 1) and ( x + 1) leaves the remainders 5 and 19 respectively. Find the values of a and b. Hence find the remainder when the given polynomial is divided by ( x 2) 5. Using factor theorem show that ( x 3) is a factor of x3 7x2 + 15x 9. Hence factorize the given expression completely. 6. Amar has a cumulative time deposits account in Grindley s bank for 4 years at 7.5% p.a. , simple interest. Find the monthly instalment. 7. Saloni deposited Rs.150 per month in a bank for 8 months under the recurring deposit scheme. What will be the maturity value of her deposits if the rate of interest is 8%p.a. 8. Mr. Ashok has an account in the Central Bank of India . The following entries are from his passbook. Date Particulars Withdrawals Deposits Balance 01-01-05 B/F 1200.00 07-01-05 By Cash 500.00 1700.00 17-01-05 To cheque 400.00 1300.00 10-02-05 By cash 800.00 2100.00 25-02-05 To cheque 500.00 1600.00 20-09-05 By cash 700.00 2300.00 21-11-05 To cheque 600.00 1700.00 05-12-05 By cash 300.00 2000.00 If Mr Ashok gets Rs. 83.75 as interest at the end of the year where the interest is compounded annually, calculate the rate of interest paid by the bank in his account on 31st December, 2005. 9. Use graph paper for this question. Take 1cm = 1 unit on both axis. i. Plot the points A(4, 5) B (2,6) and C (2,-3) ii. Write the co-ordinates of A1 the reflection of A in the line x = 0, A2 the reflection of A in origin. iii. Write co-ordinates of A3, the reflecting of A in the line y = 0 iv. Assign the special name to the figure ABCA3 Hence find its area. 1

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