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 laboratory receives microscopic particles in sealed deliveries. Figure 1 shows the mass of one particle and the numbers of particles and cartridges in a cartridge and a delivery, respectively. The diagram is not to scale.
(a) Calculate the mass of particles in one cartridge. Give your answer in standard form, correct to 2 significant figures. [2]
(b) Calculate the total mass of particles in one delivery. Give your answer in standard form, correct to 2 significant figures. [2]
(c) A laboratory requires at least of particles. Find the minimum whole number of deliveries required. [2]
Calculate the mass of particles in one cartridge. Give your answer in standard form, correct to 2 significant figures.
Calculate the total mass of particles in one delivery. Give your answer in standard form, correct to 2 significant figures.
A laboratory requires at least of particles. Find the minimum whole number of deliveries required.
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 town records the annual grants it gives to a park. The recorded grants are not exactly arithmetic, so an arithmetic model is to be used for estimating future grants. Use the values for years 1 and 5 to estimate the common difference.
Write down the first term of the arithmetic model.
Estimate the common difference and hence write an expression for the estimated grant, in year
Write, in sigma notation, an expression for the total estimated grants in years 1 to 6, and calculate this total.
Using the model, determine the first year in which the estimated grant exceeds $7000.
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 fountain jet is modelled, for by
where is the horizontal distance from the nozzle, in metres, and is the height above the ground, in metres. The model passes through the points shown.
| 0 | 3 | 6 | |
|---|---|---|---|
| 1.20 | 4.80 | 5.10 |
Use technology to determine the values of and giving each to at least three significant figures.
Hence determine the horizontal distance(s), in the interval at which the model gives Give your answer to the nearest m.
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.
The equation has roots and where
Find in Cartesian form.
Let
Find in Cartesian form.
Find the modulus and principal argument of Give the argument in radians, correct to three significant figures, in the range
A shop records the weekly sales of two products. The sales are shown in Figure 1. The selling prices remain constant: product A costs $4.80 per unit and product B costs $6.25 per unit.
Write down the matrix of weekly sales, with rows corresponding to products A and B, in that order, and columns corresponding to Weeks 1, 2 and 3, in that order.
Let the row matrix of prices in dollars per unit.
Using your matrix from part (a), show that the revenue in Weeks 1, 2 and 3 is given by
Hence, state the week with the greatest revenue.
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