IB Math Analysis & Approaches Questionbank-Topic: SL 3.7 Real-life contexts SL Paper 1

Question

Let $$f(x) = 3\sin \left( {\frac{\pi }{2}x} \right)$$, for $$0 \leqslant x \leqslant 4$$.

(i) Â  Â  Write down the amplitude of $$f$$.

(ii) Â  Â  Find the period of $$f$$.

[3]
a.

On the following grid sketch the graph of $$f$$.

[4]
b.

Markscheme

(i) Â  Â  3 Â  Â  A1 Â  Â  N1

(ii) Â  Â  valid attempt to find the period Â  Â  (M1)

eg$$\,\,\,\,\,$$$$\frac{{2\pi }}{b},{\text{ }}\frac{{2\pi }}{{\frac{\pi }{2}}}$$

period $$= 4$$Â Â  Â  A1 Â  Â  N2

[3 marks]

a.

Â  Â  Â A1A1A1A1 Â  Â  N4

[4 marks]

b.

Examiners report

Almost all candidates correctly stated the amplitude but then had difficulty finding the correct period. Few students faced problems in sketching the graph of the given function, even if they had found the wrong period, thus indicating a lack of understanding of the term â€˜periodâ€™ in part a(ii). Most sketches were good although care should be taken to observe the given domain and to draw a neat curve.

a.

Almost all candidates correctly stated the amplitude but then had difficulty finding the correct period. Few students faced problems in sketching the graph of the given function, even if they had found the wrong period, thus indicating a lack of understanding of the term â€˜periodâ€™ in part a(ii). Most sketches were good although care should be taken to observe the given domain and to draw a neat curve.

b.