DP Mathematics: Analysis and Approaches Questionbank

Find the value of $a$.

The $x$-intercept of the graph of $f$ is $\left(5, 0\right)$.

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

Find the value of $K$.

In the context of the model, state what the horizontal asymptote represents.

Find Jean-Pierre’s vertical speed after $10$ seconds. Give your answer in $\text{km} {\text{h}}^{-1}$ .

Show that $T_0=100$.

Show that $k=\frac{1}{10}\ln \frac{10}{7}$.

Find the temperature of the water when $t=15$.

Solve $f\left(x\right)>0$ for $x>0$.

Show that $A_0=100$.

Find the exact value of $a$.

Find, correct to the nearest $10$ years, the time taken after the plant’s death for $25\%$ of the carbon-14 to decay.

Show that $k=\frac{\ln 2}{5730}$.

Show that $a=8$.

Write down an expression for $f^{-1}\left(x\right)$.

Find the value of $f^{-1}\left(\sqrt{32}\right)$.

Find the value of $p$ and the value of $q$.

Show that $27, p, q$ and $125$ are four consecutive terms in a geometric sequence.

Solve the equation ${\log }_3 \sqrt{x}=\frac{1}{2 {\log }_2 3}+{\log }_3\left(4x^3\right)$, where $x>0$.

Find the values of $x$ for which $f\left(x\right)=0$.

Sketch the graph of $f$ on the following grid.