A-LevelMathematicsDifferentiation9709/22 · Feb/Mar 2023 · Q68 Marks
The diagram shows the curve with equation y = (4e^(2x) + 9)/(e^x + 2). The curve has a minimum point M and crosses the y-axis at the point P. [Figure X.X]
- (a)Find the exact value of the gradient of the curve at P.[4]
- (b)Find the exact coordinates of M.[4]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (Feb/Mar 2023). The mark or mark type is shown in brackets.
- [M1] (a) Differentiate using quotient rule OE
- [A1] (a) Obtain (eˣ + 2) 8e²ˣ – (4e²ˣ + 9) eˣ / (eˣ + 2)² OE
- [M1] (a) Substitute x=0 in first derivative and attempt evaluation
- [A1] (a) Obtain 9/8
- [M1] (b) Equate first derivative to zero and attempt factorisation or equivalent
- [M1] (b) Solve a three-term quadratic equation in eˣ to obtain eˣ =... (2eˣ + 9)(2eˣ - 1) = 0 .
- [A1] (b) Obtain x-coordinate ln½ or -ln2
- [A1] (b) Obtain y-coordinate 4
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 →