A-LevelMathematicsSeries9709/12 · May/June 2012 · Q35 Marks
The coefficient of x³ in the expansion of (a + x)⁵ + (2 – x)⁶ is 90. Find the value of the positive constant a.
- The coefficient of x³ in the expansion of (a + x)⁵ + (2 – x)⁶ is 90. Find the value of the positive constant a.[5]
Mark scheme
Marking points from the official mark scheme (May/June 2012). The mark or mark type is shown in brackets.
- [B1 B1] Coeff of x³ in (a+x)⁵ = ¹⁰C₂ a² = 10a² (or ¹⁰C₃ a²x³); co co (for 10 and a²).
- [B1] Coeff of x³ in (2−x)⁶ = ⁶C₃ (2)³ (-x)³ = -160; co
- [M1] Sum of coefficients = 10a² - 160 = 90; forms an equation from 2 terms.
- [A1] → a = 5; co
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