# Binomial Expansion

1. Binominial expansion
 5

1. a) Using binomial expansion, determine the first five terms of the expansion:                                                                                                                                                       (2mks)
2. b) Use the expansion above to evaluate                                                 (2mks)
3. (a) Expand and simplify the binomial expression (2 + x)5 upto the term in x3. (2mks)

(b) Use your expression to estimate (1.97)5 correct to 4 s.f.                                                   (2mks)

 5
1. (a) Expand 1 – 3x

(b) use your expansion to estimate the value of     0.997        Correct to 4 d.p.

1. (i) Expand 5 + X     upto the term in X3

2

(ii) Use your expansion to estimate the value of                  correct to one decimal place

1. (a) Expand ( 3 + 2x)6 up to the fourth term

(b) Use your expansion to estimate:- (3   3 )6

6          Two dice are thrown once and their sum noted. Find the probability that the sum is odd

 5x    2  x   -3

1. Find the length PR in a triangle PQR having PQ = 12cm, QR = 8.4cm angle QPR = 35o

and angle PRQ = 75o leaving your answer correct to decimal places

1. (a) Use binomial expansion to evaluate (2+3)5 up to the fifth  term

x

(b) By expressing 9.5 in the form (2 + 3), use the expansion in (a) above to calculate (9.5)5

correct to 3 d.p                                x

1. Use the expansion of (x – 0.2)5 to find the exact value of 9.85

1. Solve for x in the equation;

log (x + 24) = 2 log 3 + log (9 – 2x).

1. Expand 1 + x       in ascending powers of x upto the fourth term.
 6

12

Use the four terms to evaluate   5/4  to 4 decimal places.

1. (a) Expand and simplify the binominal expression ( 1 + ½ x)8

(b) Use the expansion up to the fourth term to evaluate (1.05)8 to 2 decimal places

1. Expand (3 + x)4 in ascending powers of x. Use the first three terms of the expansion to

evaluate (3.02)4, correct to 3 decimal places