O-LevelAdditional MathematicsSeries4037/21 · May/June 2017 · Q55 Marks

Given that a is a constant, expand (2 + ax)⁴, in ascending powers of x, simplifying each term of your expansion.

(i)Given that a is a constant, expand (2 + ax)⁴, in ascending powers of x, simplifying each term of your expansion.[2]
(ii)Given also that the coefficient of x² is equal to the coefficient of x³, show that a = 3,[1]
(iii)use your expansion to show that the value of 1.97⁴ is 15.1 to 1 decimal place.[2]

Mark scheme

Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.

[B2] 16 + 32ax + 24a²x² + 8a³x³ + a⁴x⁴ B1 for at most 2 terms incorrect or missing or for correct but unsimplified form SC1 for 16 + 32ax + 24ax² + 8ax³ + ax⁴ or all terms correct listed
[B1] 24a² = 8a³ and solves to given answer or verifies that a = 3 leads to coeff of 216 for both terms must be from correct terms in (i)
[M1] x = -0.01 or ax = -0.03 soi
[A1] 16 + 32(3)(-0.01) + 24(9)(-0.01)² leading to 16 - 0.96 + 0.0216 or 15.06...isw Must show clear substitution into their expansion for A1 and reach a value which rounds to 15.1

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