DP Mathematics: Applications and Interpretation Questionbank

the total number of seats in the concert hall.

the number of seats in the last row.

Find $h$, the height of the tank.

Show that the volume of the tank is $624 000 {\text{m}}^3$, correct to three significant figures.

Write down the common difference, $d$.

Find the amount of fuel pumped into the tank in the $\text{13th}$ hour.

Find the value of $n$ such that $u_n=0$.

Write down the number of hours that the pump was pumping fuel into the tank.

Find the total amount of fuel pumped into the tank in the first $8$ hours.

Show that the tank will never be completely filled using this pump.

Write down the value of $\underset{i=1}{\overset{9}{\text{Σ}}}{u}_i$.

Find the value of $u_1$.

A game is played in which the arrow attached to the centre of the disc is spun and the sector in which the arrow stops is noted. If the arrow stops in sector $1$ the player wins $10$ points, otherwise they lose $2$ points.

Let $X$ be the number of points won

Find $\text{E}\left(X\right)$.

Given the width of a pixel is approximately $0.025 \text{cm}$, find the number of squares in the final image.

Find an expression for the width of $U_n$ in centimetres.

Charlie ran on day $20$ of his fitness programme.

Daniella ran on day $20$ of her fitness programme.

Find an expression for $u_n$.

Calculate the total amount of acceptance fees paid to the university in the first $10$ years.

Calculate the percentage increase in applications from the first year to the second year.

Find $k$.

State whether, for all $n>k$, the university will have places available for all applicants. Justify your answer.

Write down the common ratio of the sequence.

Find the number of student applications the university expects to receive when $n=11$. Express your answer to the nearest integer.

Write down an expression for $v_n$ .

$a$.

$w_n$.

$b$.

$l_n$.

Show that Eddie needs $144$ tiles.

Find the value of $w_n$ for this path.

Find the total cost of buying 2 tickets in each of the first 16 rows.

Write down the value of the common difference, $d$

Calculate the price of a ticket in the 16th row.

fed to the dog per day.

remaining in the bag at the end of the first day.

Calculate the number of days that Scott can feed his dog with one bag of food.

Determine the amount that Scott expects to spend on dog food in $2025$. Round your answer to the nearest dollar.

find the value of $d$.

determine the value of $\sum _{r=1}^N{u}_r$.

the value of $d$;

the value of $r$;

Find the first term and the common difference of the sequence.

Calculate the number of positive terms in the sequence.

Show that there will be approximately 2645 fish in the lake at the start of 2020.

Find the approximate number of fish in the lake at the start of 2042.

Show that A is an arithmetic sequence, stating its common difference d in terms of r.

A particular geometric sequence has u₁ = 3 and a sum to infinity of 4.

Find the value of d.

Suppose that $u_1$ is the first term of a geometric series with common ratio $r$.

Prove, by mathematical induction, that the sum of the first $n$ terms, $s_n$ is given by

$s_n=\frac{u_1\left(1-r^n\right)}{1-r}$, where $n\in {\mathbb{Z}}^{+}$.

Write down the value of $u_1$.

Find the value of $u_6$.

Prove that $\{u_n\}$ is an arithmetic sequence, stating clearly its common difference.

Find an expression for $A_1$ and show that $A_2={1.004}^{2}x+1.004x$.

(i)     Write down a similar expression for $A_3$ and $A_4$.

(ii)     Hence show that the amount in Mary’s account the day before she turned 10 years old is given by $251({1.004}^{120}-1)x$.

Write down an expression for $A_n$ in terms of $x$ on the day before Mary turned 18 years old showing clearly the value of $n$.

Mary’s grandparents wished for the amount in her account to be at least $\mathrm{\$}20000$ the day before she was 18. Determine the minimum value of the monthly deposit $\mathrm{\$}x$ required to achieve this. Give your answer correct to the nearest dollar.

As soon as Mary was 18 she decided to invest $\mathrm{\$}15000$ of this money in an account of the same type earning 0.4% interest per month. She withdraws $\mathrm{\$}1000$ every year on her birthday to buy herself a present. Determine how long it will take until there is no money in the account.

In an arithmetic sequence, the sum of the 3rd and 8th terms is 1.

Given that the sum of the first seven terms is 35, determine the first term and the common difference.

Find the common difference.

Find the tenth term.

Find the sum of the first ten terms.

Given that x_{k + 1} = x_k + a, find a.

Hence find the value of n such that $\sum _{k=1}^n{x}_k=861$.

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

Find the value of $k$.

Find the exact value of $S_k$.

Show that $F=3240$.

An infinite geometric series is given as $S_{\mathrm{\infty }}=a+\frac{a}{\sqrt{2}}+\frac{a}{2}+\dots$, $a\in {\mathbb{Z}}^{+}$.

Find the largest value of $a$ such that .

Find u₈.

The sum of an infinite geometric sequence is 33.25. The second term of the sequence is 7.98. Find the possible values of $r$.

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 $p\in \mathbb{Q}$.

Write down the first three non-zero terms of $w_n$.

Find the value of $r$.

Find the value of $m$.

Write down the distance Rosa runs in the third training session;

Write down the distance Rosa runs in the $n$th training session.

Find the value of $k$.

Calculate the total distance, in kilometres, Rosa runs in the first 50 training sessions.

Find the distance Carlos runs in the fifth month of training.

Calculate the total distance Carlos runs in the first year.

For that day find how much weight was added after each lift.

For that day find the weight of Sergei’s first lift.

On that day, Sergei made 12 successive lifts. Find the total combined weight of these lifts.

Find the café’s profit during the 11th week.

Calculate the café’s total profit for the first 12 weeks.

Find the tea-shop’s profit during the 11th week.

Calculate the tea-shop’s total profit for the first 12 weeks.

In the mth week the tea-shop’s total profit exceeds the café’s total profit, for the first time since they both opened.

Find the value of m.

Diagram $n$ is formed with 52 sticks. Find the value of $n$.

Find the total number of sticks used by Tomás for all 24 diagrams.

Find the distance from the base of this ladder to the top rung.

The company also makes a ladder that is 1050 cm long.

Find the maximum number of rungs in this 1050 cm long ladder.

Calculate, in CAD, the total amount John pays for the bicycle.

Find the value of the bicycle during the 5th year. Give your answer to two decimal places.

Calculate, in years, when the bicycle value will be less than 50 USD.

Find the total amount John has paid to insure his bicycle for the first 5 years.

Write down an equation, in terms of $u_1$ and $d$, for the amount of the drug that she receives on the seventh day.

Write down an equation, in terms of $u_1$ and $d$, for the amount of the drug that she receives on the eleventh day.

Write down the value of $d$ and the value of $u_1$.

Calculate the total amount of the drug, in mg, that she receives.

Find the amount of antibiotic, in mg, that Ted receives on the fifth day.

The daily amount of antibiotic Ted receives will first be less than 0.06 mg on the $k$ th day. Find the value of $k$.

Hence find the total amount of antibiotic, in mg, that Ted receives during the first $k$ days.

Find the number of triangular panes in the $12\text{th}$ level.

Show that the total number of triangular panes, $S_n$, in the first $n$ levels is given by:

$S_n=n^2+4n$.

Hence, find the total number of panes in a glass face with $18$ levels.

Find the maximum number of complete levels that Maegan can build.

Each triangular pane has an area of $1.84 {\text{m}}^2$.

Find the total area of the decorative glass face, if the maximum number of complete levels were built. Express your area to the nearest ${\text{m}}^2$.