OCR MEI C2 — Question 2 5 marks

Exam BoardOCR MEI
ModuleC2 (Core Mathematics 2)
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicTangents, normals and gradients
TypeFind normal line equation at given point
DifficultyModerate -0.3 This is a straightforward differentiation and normal line question requiring standard techniques: find dy/dx, evaluate at the given point, find the normal gradient (negative reciprocal), then use point-slope form. It's slightly easier than average because it involves routine calculus procedures with no conceptual challenges, though the arithmetic with fractions requires some care.
Spec1.07i Differentiate x^n: for rational n and sums1.07m Tangents and normals: gradient and equations

Find the equation of the normal to the curve \(y = 8x^4 + 4\) at the point where \(x = \frac{1}{2}\). [5]

Question 2:
AnswerMarks
2dy
[ = ] 32x3 c.a.o.
dx
dy
substitution of x = ½ in their
dx
−1
grad normal =
their4
when x = ½, y = 4 ½ o.e.
y−41 =−1(x−1)i.s.w
AnswerMarks
2 4 2M1
M1
M1
B1
AnswerMarks
A1[= 4]
y =−1 x+45 o.e.
AnswerMarks
4 8must see kx3
their 4 must be obtained by calculus
Question 2:
2 | dy
[ = ] 32x3 c.a.o.
dx
dy
substitution of x = ½ in their
dx
−1
grad normal =
their4
when x = ½, y = 4 ½ o.e.
y−41 =−1(x−1)i.s.w
2 4 2 | M1
M1
M1
B1
A1 | [= 4]
y =−1 x+45 o.e.
4 8 | must see kx3
their 4 must be obtained by calculus
Find the equation of the normal to the curve $y = 8x^4 + 4$ at the point where $x = \frac{1}{2}$. [5]

\hfill \mbox{\textit{OCR MEI C2  Q2 [5]}}