IB Mathematics: Applications and Interpretation question bank

$u_{30}=22+(30-1)\times 3$ (M1)

$=109$ (seats) A1

[2 marks]

$S_{30}=\frac{30}{2}(22+109)$ OR $S_{30}=\frac{30}{2}(2\times 22+29\times 3)$ (M1)

$=1965$ (seats) A1

Note: Follow through from their answer to part (a).

[2 marks]

$\frac{n}{2}(2\times 22+(n-1)\times 3)\ge 2500$ (or $=2500$) (M1)

$n=34.559\dots$ (A1)

OR

listing $S_{34}=2431$ and $S_{35}=2555$ (M1)(A1)

THEN

35 rows are needed, so $35-30=5$ rows must be added A1

Note: Award the final mark only for the number of rows added (5), not 35.

[3 marks]

$18+0.08\times (420-300)$ (M1)

$27.60$ (GBP) A1

Note: Accept $27.6$.

[2 marks]

$C=18+0.08(m-300)$ A1A1

OR

$C=0.08m-6$ A1A1

Note: Award A1 for $0.08(m-300)$ or $0.08m$, A1 for the constant consistent with their form.

[2 marks]

$18+0.08(m-300)=33.20$ (M1)

$m=490$ (minutes) A1

[2 marks]

$\sqrt{6^2+(-8{)}^2}$ (M1)

$10{\text{ km h}}^{-1}$ A1

[2 marks]

$t=1.5$ (M1)

$\mathit{r}=\left(\begin{array}{c}2\\ 5\end{array}\right)+1.5\left(\begin{array}{c}6\\ -8\end{array}\right)=\left(\begin{array}{c}11\\ -7\end{array}\right)$ A1

[2 marks]

${\tan }^{-1}\left(\frac{6}{8}\right)=36.869\dots \mathrm{°}$ (angle east of south) (M1)

$180\mathrm{°}-36.869\dots \mathrm{°}=143\mathrm{°}$ $(143.130\dots \mathrm{°})$ A1

Note: Accept any correct right-angled triangle method, for example $90\mathrm{°}+{\tan }^{-1}\left(\frac{8}{6}\right)$.

[2 marks]

number of punctures: discrete A1

distance cycled: continuous A1

time for the time trial: continuous A1

Note: Do not accept "discrete" for the time, even though it may be recorded to the nearest second or minute.

[3 marks]

population: all 340 members of the Ridgeway Cycling Club A1

sample: the 45 members who replied A1

[2 marks]

the members chose whether to reply (self-selected), so, for example, the most active or keenest cyclists may be more likely to reply R1

Note: Accept any reasonable answer referring to the context, e.g. members who rarely check email are under-represented. Do not accept "the sample is too small" alone.

[1 mark]

$f^{\mathrm{\prime }}(x)=6x^2-10x+1$ A1A1

Note: Award A1 for any two correct terms, A2 for all three correct terms and no extra terms. Award A1A0 if the constant term 4 is still present.

[2 marks]

$f(2)=2$ A1

[1 mark]

$f^{\mathrm{\prime }}(2)=6(2{)}^2-10(2)+1$ (M1)

$=5$ (A1)

$y-2=5(x-2)$

$y=5x-8$ A1

Note: Follow through from their $f^{\mathrm{\prime }}(x)$ in part (a) and their $f(2)$ in part (b). Award the final A1 only for an answer in the form $y=mx+c$.

[3 marks]