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Date November 2010 Marks available 3 Reference code 10N.2.sl.TZ0.2
Level SL only Paper 2 Time zone TZ0
Command term Sketch Question number 2 Adapted from N/A

Question

The velocity v ms−1 of an object after t seconds is given by \(v(t) = 15\sqrt t  - 3t\) , for \(0 \le t \le 25\) .

On the grid below, sketch the graph of v , clearly indicating the maximum point.


[3]
a.

(i)     Write down an expression for d .

(ii)    Hence, write down the value of d .

[4]
b(i) and (ii).

Markscheme


     A1A1A1     N3

Note: Award A1 for approximately correct shape, A1 for right endpoint at \((25{\text{, }}0)\) and A1 for maximum point in circle.

[3 marks]

a.

(i) recognizing that d is the area under the curve     (M1)

e.g. \(\int {v(t)} \)

correct expression in terms of t, with correct limits     A2     N3

e.g. \(d = \int_0^9 {(15\sqrt t } - 3t){\rm{d}}t\) , \(d = \int_0^9 v {\rm{d}}t\)

(ii) \(d = 148.5\) (m) (accept 149 to 3 sf)     A1     N1

[4 marks]

b(i) and (ii).

Examiners report

The graph in part (a) was well done. It was pleasing to see many candidates considering the domain as they sketched their graph.

a.

Part (b) (i) asked for an expression which bewildered a great many candidates. However, few had difficulty obtaining the correct answer in (b) (ii).

b(i) and (ii).

Syllabus sections

Topic 6 - Calculus » 6.5 » Definite integrals, both analytically and using technology.
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