Exam-style questions in the shape of Paper 1 and Paper 2, with full markschemes. Read the markscheme, or type, photograph or draw your answer and get it marked.
A circular inspection window has a radius recorded as correct to the nearest
For this question, percentage error is
Write down the lower and upper bounds for the radius.
Calculate the estimated area of the window, giving your answer to three significant figures.
Determine the greatest possible percentage error in this estimated area. Use unrounded values in your calculations and give your answer to three significant figures.
A comet lander collects dust during a -minute sampling pulse. Figure 1 shows the rate at which particles enter the collection chamber. Assume that varies linearly between consecutive readings. The mean mass of a particle is
Determine the total mass of dust collected during the pulse. Give your answer in scientific notation to 2 significant figures.
A return canister has a maximum dust payload of Is it sufficient for the dust collected during the full pulse? Justify your answer with a numerical comparison.
Two accounts each receive a deposit of $10 000. The principal is returned in full by either account, so only interest and fees are compared.
Account A pays simple interest at per year and has no fees.
The annual interest payments observed for account B are shown below.
| Year | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| Interest payment ($) | 246 | 267 | 284 | 306 |
For a projection, an adviser models account B’s annual interest payments as an arithmetic sequence. The first term is the payment in year 1, and the common difference is the mean of the three consecutive changes shown in the table. Assume this model continues for years. Account B has a one-time opening fee of $200.
State the first term and common difference of the arithmetic model for account B.
Let be the total interest paid by account B during the first years. Show that
Hence determine the first whole number of years for which account B’s cumulative interest, after its opening fee, exceeds account A’s cumulative interest. Justify that this is the first such year.
A theatre records the total revenue from three group ticket sales. Let and be the prices, in dollars, of one adult, student and child ticket, respectively. The records are shown in Figure 1.
For a later performance, the regular adult ticket price is dollars. If the discount is dollars, the estimated number of discounted adult tickets sold is The revenue from these tickets is modelled by
where
Use your GDC to determine the values of and
Using your answer to (a), use your GDC to find all values of for which Give your answers to the nearest cent.
Unlock every question in this topic, then type, photograph or draw your answer and have it marked against the markscheme. Find out where you are dropping marks.