MY CAT. Binomial expansion

1. a) Using binomial expansion, determine the first five terms of the expansion: (2-1) (2mks) b) Use the expansion above to evaluate (1.75) (2mks) 2. (a) Expand and simplify the binomial expression (2 + x) upto the term in x". (2mks) (b) Use your expression to estimate (1.97)* correct to 4 s.f. (2mks) 3. (a) Expand [1 - 3x] (b) use your expansion to estimate the value of (0.997 ] Correct to 4 d.p. 4. (i) Expand 3 + upto the term in X" (ii) Use your expansion to estimate the value of correct to one decimal place 5. (a) Expand ( 3 + 2x)" up to the fourth term (b) Use your expansion to estimate:- (3 3)* 6 Two dice are thrown once and their sum noted. Find the probability that the sum is odd Find the length PR in a triangle POR having PQ =-12em, QR = 8.4cm angle QPR = 35" and angle PRQ = 75" leaving your answer correct to decimal places 8 (a) Use binomial expansion to evaluate (2+3) up to the fifth term (b) By expressing 9.5 in the form (2 + 3), use the expansion in (a) above to calculate (9.5) correct to 3 d.p 9. Use the expansion of (x - 0.2) to find the exact value of 9.85 10. Solve for x in the equation; log (x + 24) = 2 log 3 + log (9 - 2x). 11. Expand in ascending powers of x upto the fourth term. Use the four terms to evaluate |$/4| 90 4 decimal places. 12. (a) Expand and simplify the binominal expression ( 1 + 12 x)* (b) Use the expansion up to the fourth term to evaluate (1.05)" to 2 decimal places 13. Expand (3 + x)" in ascending powers of x. Use the first three terms of the expansion to evaluate (3.02)", correct to 3 decimal places