A-LevelMathematicsDifferentiation9709/23 · Oct/Nov 2024 · Q67 Marks
A curve has parametric equations x = (e^(2t)-2) / (e^(2t)+1), y = e^(3t) + 1.
- (a)Find an expression for dy/dx in terms of t.[4]
- (b)Find the exact gradient of the curve at the point where the curve crosses the y-axis.[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2024). The mark or mark type is shown in brackets.
- [4] Differentiate x using quotient rule or correct equivalent *M1
- Obtain (e^(2t)+1)2e^(2t) - (e^(2t)-2)2e^(2t) / (e^(2t)+1)² or equivalent A1
- Attempt expression for dy/dt in terms of t DM1
- Obtain 3e^(3t) A1
- Obtain 6e^(3t) (e^(2t)+1)² / (6e^(2t)) or (unsimplified) equivalent A1 No fractions within fractions. Attempt to simplify (e^(2t)+1)2e^(2t) – (e^(2t) – 2)2e^(2t) must be seen.
- [3] Identify t = ½ln2 at point where curve crosses y-axis B1
- Substitute non-zero value of t in their expression for dy/dx and attempt simplification M1
- Obtain 2√2 or exact equivalent A1
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 →