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Date May 2009 Marks available 1 Reference code 09M.1.sl.TZ1.15
Level SL only Paper 1 Time zone TZ1
Command term Write down Question number 15 Adapted from N/A

Question

The straight line, L, has equation \(2y - 27x - 9 = 0\).

Find the gradient of L.

[2]
a.

Sarah wishes to draw the tangent to \(f (x) = x^4\) parallel to L.

Write down \(f ′(x)\).

[1]
b.

Find the x coordinate of the point at which the tangent must be drawn.

[2]
c, i.

Write down the value of \(f (x)\) at this point.

[1]
c, ii.

Markscheme

y = 13.5x + 4.5     (M1)


Note: Award (M1) for 13.5x seen.


gradient = 13.5     (A1)     (C2)

[2 marks]

a.

4x3     (A1)     (C1)

[1 mark]

b.

4x3 = 13.5     (M1)

Note: Award (M1) for equating their answers to (a) and (b).


x = 1.5     (A1)(ft)

[2 marks]

c, i.

\(\frac{{81}}{{16}}\)   (5.0625, 5.06)     (A1)(ft)     (C3)

Note: Award (A1)(ft) for substitution of their (c)(i) into x4 with working seen.

[1 mark]

c, ii.

Examiners report

The structure of this question was not well understood by the majority; the links between parts not being made. Again, this question was included to discriminate at the grade 6/7 level.

Most were successful in this part.

a.

The structure of this question was not well understood by the majority; the links between parts not being made. Again, this question was included to discriminate at the grade 6/7 level.

This part was usually well attempted.

b.

The structure of this question was not well understood by the majority; the links between parts not being made. Again, this question was included to discriminate at the grade 6/7 level.

Only the best candidates succeeded in this part.

c, i.

The structure of this question was not well understood by the majority; the links between parts not being made. Again, this question was included to discriminate at the grade 6/7 level.

Only the best candidates succeeded in this part.

c, ii.

Syllabus sections

Topic 6 - Mathematical models » 6.5 » Models using functions of the form \(f\left( x \right) = a{x^m} + b{x^n} + \ldots \); \(m,n \in \mathbb{Z}\) .
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