DP Mathematics: Applications and Interpretation Questionbank

Find the equation of the regression line for $\ln k$ on $\frac{1}{T}$.

(i)   the gradient of this line in terms of $c$;

(ii)  the $y$-intercept of this line in terms of $A$.

Show that $\text{lo}{\text{g}}_{r^2}x=\frac{1}{2}\text{lo}{\text{g}}_{r}x$ where $r,x\in {\mathbb{R}}^{+}$.

Express $y$ in terms of $x$. Give your answer in the form $y=p{x}^q$, where p , q are constants.

The region R, is bounded by the graph of the function found in part (b), the x-axis, and the lines $x=1$ and $x=\alpha$ where $\alpha >1$. The area of R is $\sqrt{2}$.

Find the value of $\alpha$.

Solve .

Solve the equation $4^x+2^{x+2}=3$.

Show that $abc=8$.

Solve the equation ${\log }_2(x+3)+{\log }_2(x-3)=4$.

Find the value of a and of b.

Use the regression equation to estimate the value of y when x = 3.57.

The relationship between x and y can be modelled using the formula y = kxⁿ, where k ≠ 0 , n ≠ 0 , n ≠ 1.

By expressing ln y in terms of ln x, find the value of n and of k.

Let $p=c^2$ and $q=c^3$. Find the value of $\sum _{n=1}^{20}{u}_n$.

Find the common ratio.

Find $r$.

Show that the sum of the infinite sequence is $4{\log }_{2}x$.

Find $d$, giving your answer as an integer.

Show that $S_{12}=12{\log }_{2}x-66$.

Given that $S_{12}$ is equal to half the sum of the infinite geometric sequence, find $x$, giving your answer in the form $2^p$, where $p\in \mathbb{Q}$.