O-LevelAdditional MathematicsSeries4037/21 · May/June 2016 · Q87 Marks
Use the Binomial Theorem to expand (a + b)⁴, giving each term in its simplest form.
- (a)(i)Use the Binomial Theorem to expand (a + b)⁴, giving each term in its simplest form.[2]
- (a)(ii)Hence find the term independent of x in the expansion of (2x + 1/(5x))⁴.[2]
- (b)The coefficient of x³ in the expansion of (1 + x/2)^n equals 5n/12. Find the value of the positive integer n.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2016). The mark or mark type is shown in brackets.
- [B2,1,0] a⁴ + 4a³b + 6a²b² + 4ab³ + b⁴ final answer -1 each error/omission
- [M1] 6(2x)² (1/(5x))² soi Could be in full expansion
- [A1] 24/25 or 0.96 isw Must be explicitly identified
- [M1] 1/8 n(n-1)(n-2) = 5n/12 soi leading to a cubic or quadratic (n² -3n-18 = 0 ) Must attempt to expand and remove fractions
- [M1] Solves their quadratic [(n – 6)(n + 3)] must have come from a valid attempt
- [A1] [n =] 6 only, not from wrong working Must be n if labelled
Write your answer and get it marked
On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.
Sign up free →