IB Mathematics AA SL 1.1 Number and Algebra Question Bank

$$3\times10^4$$
or $30000\,\mathrm{km}$. Accept $3\bullet10^4$.

A1

Use the volume of a sphere with radius $3\times10^4$:
$$\frac43\pi(3\times10^4)^3=36\pi\times10^{12}=\pi(3.6\times10^{13}).$$$$a=3.6,\qquad k=13$$
A1, A1, A1

Sorin's future value after n years $=120000\left(1+\frac{4}{100 \times 12}\right)^{12 n}$

Sorin's total $=120000\left(1+\frac{4}{100 \times 12}\right)^{6}(=122420.09)$

Daniela's total $=\frac{2000\left(1-1.06^{6}\right)}{1-1.06}(=13950.64)$
total value =($) 136370.73

EITHER (finding number of months, m )
$120000\left(1+\frac{4}{100 \times 12}\right)^{m}+\frac{2000\left(1-1.06^{m}\right)}{1-1.06}(\geq 250000)$$m \geq 26.0905 \ldots$ OR $(m=26 \Rightarrow) 249157 \ldots$ AND $(m=27 \Rightarrow) 258692 \ldots$

Note: Condone use of an equation or strict inequality.
OR (finding number of years, n )
$120000\left(1+\frac{4}{100 \times 12}\right)^{12 \times n}+\frac{2000\left(1-1.06^{12 \times n}\right)}{1-1.06}(\geq 250000)$$n \geq 2.17421 \ldots$ (years)

Note: Condone use of an equation or strict inequality.

THEN
m=27 (months)

EITHER
N=24
OR
N=6
$\mathrm{PV}=\mp 40000$$\mathrm{PV}=\mp 40000$
PMT=0
PMT=0
$\mathrm{FV}= \pm 53000$$\mathrm{FV}= \pm 53000$
P / Y=4
P / Y=1
C / Y=4
C / Y=4
(M1)(A1)
Note: Award (M1) for an attempt to use a financial app in their technology with at least two entries seen, and award (A1) for all entries correct. PV and FV must have opposite signs.

OR
$40000\left(1+\frac{r}{100 \times 4}\right)^{6 \times 4}=53000$
(M1)(A1)

Note: Award (M1) for attempting to substitute into compound interest formula, award (A1) for correct equation.

THEN
$4.71781 \ldots$
( r= ) 4.72 (\%)