O-LevelAdditional MathematicsSeries4037/21 · May/June 2023 · Q107 Marks
In the expansion of (ax + b/x²)⁹ where a and b are constants with a > 0, the term independent of x is -145152 and the coefficient of x⁶ is –6912. Show that a²b = -12 and find the value of a and the value of b.
- In the expansion of (ax + b/x²)⁹ where a and b are constants with a > 0, the term independent of x is -145152 and the coefficient of x⁶ is –6912. Show that a²b = -12 and find the value of a and the value of b.[7]
Mark scheme
Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.
- [B1] [Term independent of x:] ⁹C₃ × (ax)⁶ × (b/x²)³ or 84 × a⁶ × b³
- [M1] a⁶b³ = -145152 / 84
- [A1] (a²b)³ = −1728 leading to a²b=-12 or a²b = ³√-1728 = -12
- [B1] ⁹C₁ × (ax)⁸ × (b/x²)¹ or 9 × a⁸ × b
- [M1] Correctly solves correct equations simultaneously 9 × a⁸ × b = -6912 and a²b = -12
- [B2] a = 2, b = -3 and no other values nfww
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 →