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Date May 2008 Marks available 2 Reference code 08M.1.sl.TZ2.12
Level SL only Paper 1 Time zone TZ2
Command term Find Question number 12 Adapted from N/A

Question

Consider the function f(x)=12x32x2+3.

Find f(x).

[2]
a.

Find f(x).

[2]
b.

Find the equation of the tangent to the curve of f at the point (11.5).

[2]
c.

Markscheme

3x224x     (A1)(A1)     (C2)

Note: Award (A1) for each correct term and no extra terms; award (A1)(A0) for both terms correct and extra terms; (A0) otherwise.

[2 marks]

a.

3x4     (A1)(ft)(A1)(ft)     (C2)

Note: accept 3x140

[2 marks]

b.

y=2.5x+4 or equivalent     (A1)(ft)(A1)     (C2)

Note: Award (A1)(ft) on their (a) for 2.5x (must have x), (A1) for 4 or equivalent correct answer only.
Accept y1.5=2.5(x1)

[2 marks]

c.

Examiners report

The final part of this question was not well answered. Most candidates could gain 4 marks in this question as most knew how to differentiate and they were required to do it twice. However, few realized that they could find the gradient of the tangent from their answer to part (a). This part was badly answered by most candidates.

a.

The final part of this question was not well answered. Most candidates could gain 4 marks in this question as most knew how to differentiate and they were required to do it twice. However, few realized that they could find the gradient of the tangent from their answer to part (a). This part was badly answered by most candidates.

b.

The final part of this question was not well answered. Most candidates could gain 4 marks in this question as most knew how to differentiate and they were required to do it twice. However, few realized that they could find the gradient of the tangent from their answer to part (a). This part was badly answered by most candidates.

c.

Syllabus sections

Topic 7 - Introduction to differential calculus » 7.3 » Equation of the tangent at a given point.
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