A-LevelMathematicsAlgebra9709/12 · Feb/Mar 2023 · Q66 Marks
In the expansion of (x/a + a/x²)⁷ , it is given that (the coefficient of x⁴) / (the coefficient of x) = 3. Find the possible values of the constant a.
- (a)Find the possible values of the constant a.[6]
Mark scheme
Marking points from the official mark scheme (Feb/Mar 2023). The mark or mark type is shown in brackets.
- [B1 B1] ⁷C₁ (x/a)⁶ (a/x²)¹ or ⁷C₆ (x/a)¹ (a/x²)⁶ ; ⁷C₅ (x/a)² (a/x²)⁵ or ⁷C₂ (x/a)⁵ (a/x²)² Coefficients x⁴ & x. Can be seen in an expansion.
- [M1] (7/a⁵) / (21/a³) = 3 OE. Allow extraneous x⁴ and x at this stage; numerator and denominator must be functions of a. Allow errors in evaluation of the combinations.
- [A1] Completely correct. 7/a⁵ / 21/a³ = 3.
- [A1] a² = 1/9 SOI (implied by a = 1/3).
- [A1] a = ±1/3 Allow ± 0.333.
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