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Date November 2020 Marks available 2 Reference code 20N.1.SL.TZ0.T_13
Level Standard Level Paper Paper 1 (with calculator from previous syllabus) Time zone Time zone 0
Command term Find Question number T_13 Adapted from N/A

Question

Consider the graph of the function fx=x2-kx.

The equation of the tangent to the graph of y=fx at x=-2 is 2y=4-5x.

Write down f(x).

[3]
a.

Write down the gradient of this tangent.

[1]
b.

Find the value of k.

[2]
c.

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure. It appeared in a paper that permitted the use of a calculator, and so might not be suitable for all forms of practice.

2x+kx2     (A1)(A1)(A1)    (C3)


Note: Award (A1) for 2x, (A1) for +k, and (A1) for x-2 or 1x2.
Award at most (A1)(A1)(A0) if additional terms are seen.

 

[3 marks]

a.

-2.5  -52     (A1)    (C1)

[1 mark]

b.

-2.5=2×-2+k-22       (M1)


Note:
Award (M1) for equating their gradient from part (b) to their substituted derivative from part (a).


k= 6      (A1)(ft)    (C2)


Note:
Follow through from parts (a) and (b).


[2 marks]

c.

Examiners report

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

Syllabus sections

Topic 5 —Calculus » SL 5.3—Differentiating polynomials, n E Z
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Topic 5 —Calculus » SL 5.4—Tangents and normal
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