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 neighbourhood repair fund plans to increase its annual contribution by the same amount each year. Figure 1 shows the planned contributions for the first three years.
The planned contributions form an arithmetic sequence.
Write down the first term and the common difference of the sequence.
Find the planned contribution for year 8.
Calculate the total planned contributions for the first eight years.
A laboratory compares the hydrogen ion concentrations of two aqueous solutions. Figure 1 shows the measured concentrations. For these solutions, the one with the greater hydrogen ion concentration is more acidic.
For the pH calculations, use
where is the numerical value of the hydrogen ion concentration in
Write down the hydrogen ion concentration of solution B in standard form, including its unit.
Calculate the pH of solution A, giving your answer to 2 decimal places.
Determine the ratio of the hydrogen ion concentration of solution A to that of solution B, giving your answer in standard form.
Hence state which solution is more acidic.
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.
A point on an Argand diagram is represented by
Write down the real part and the imaginary part of
Write down the complex conjugate of
Determine the distance of from the origin, in units.
Use your GDC to calculate giving your answer in Cartesian form.
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