A-LevelMathematicsIntegration9709/12 · May/June 2014 · Q88 Marks
The equation of a curve is such that d²y/dx² = 2x – 1. Given that the curve has a minimum point at (3, –10), find the coordinates of the maximum point.
- The equation of a curve is such that d²y/dx² = 2x – 1. Given that the curve has a minimum point at (3, –10), find the coordinates of the maximum point.[8]
Mark scheme
Marking points from the official mark scheme (May/June 2014). The mark or mark type is shown in brackets.
- [B1] dy/dx = x² – x + c Correct integration (ignore +c)
- [M1 A1] = 0 when x = 3 → c = –6 Uses a constant of integration. co
- [A1] x² – x – 6 = 0 when x = –2 (or 3) Puts dy/dx to 0
- [B1/B1] y = ¹/₃x³ – ¹/₂x² – 6x (+k) √ first 2 terms, √ for cx.
- [M1] = –10 when x = 3 Correct method for k
- [A1] → k = 3.5 → y = 10.8 Co – r 10.8
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 →