A-LevelMathematicsDifferentiation9709/21 · May/June 2022 · Q47 Marks

A curve has equation x²y + 2y³ = 48. Find the equation of the normal to the curve at the point (4, 2), giving your answer in the form ax + by + c = 0 where a, b and c are integers.

(a)A curve has equation x²y + 2y³ = 48. Find the equation of the normal to the curve at the point (4, 2), giving your answer in the form ax + by + c = 0 where a, b and c are integers.[7]

Mark scheme

Marking points from the official mark scheme (May/June 2022). The mark or mark type is shown in brackets.

[1] Use product rule to differentiate x²y *M1 There must be evidence of implicit differentiation
[1] Obtain correct 2xy + x² dy/dx
[1] Obtain 2xy + x² dy/dx + 6y² dy/dx = 0 *B1
[1] Substitute x = 4, y = 2 to find value of dy/dx DM1 dependent on at least one term involving dy/dx
[1] Obtain -2/5 SOI, OE
[1] Attempt equation of normal passing through (4, 2) M1 with numerical gradient correctly obtained from the negative reciprocal of their derivative
[1] Obtain 5x-2y-16=0

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.

Topic: Differentiation, A-Level Mathematics (syllabus 9709). Structured question, 7 marks.
Source: A-Level Mathematics, May/June 2022 Paper 2 Variant 1, question 4.

Questions and mark schemes are from past examination papers and remain the copyright of the exam board. How Oracle Prep builds its content