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Date May 2014 Marks available 3 Reference code 14M.1.sl.TZ1.10
Level SL only Paper 1 Time zone TZ1
Command term Find Question number 10 Adapted from N/A

Question

Let f(x)=x4.

Write down f(x).

[1]
a.

Point P(2,6) lies on the graph of f.

Find the gradient of the tangent to the graph of y=f(x) at P.

[2]
b.

Point P(2,16) lies on the graph of f.

Find the equation of the normal to the graph at P. Give your answer in the form ax+by+d=0, where a, b and d are integers.

[3]
c.

Markscheme

(f(x)=)   4x3     (A1)     (C1)

 

[1 mark]

a.

4×23     (M1)

 

Note: Award (M1) for substituting 2 into their derivative.

 

=32     (A1)(ft)     (C2)

 

Note: Follow through from their part (a).

 

[2 marks]

b.

y16=132(x2)   or   y=132x+25716     (M1)(M1)

 

Note: Award (M1) for their gradient of the normal seen, (M1) for point substituted into equation of a straight line in only x and y (with any constant ‘c’ eliminated).

 

x+32y514=0 or any integer multiple     (A1)(ft)     (C3)

 

Note: Follow through from their part (b).

 

[3 marks]

c.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.

Syllabus sections

Topic 5 - Geometry and trigonometry » 5.1 » Equation of a line in two dimensions: the forms y=mx+c and ax+by+d=0 .
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