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 positioning device converts a control setting to an output Figure 1 shows its calibration curve. The rule is
on the branch shown. Both and are measured in device units.
Use Figure 1 to write down the range of
Find
State the domain of
Complete each statement, including the appropriate domain for
A local market sells honey in jars. Let be the quantity, in thousands of jars per week, and let be the price, in dollars per jar. Figure 1 shows the demand and supply models for this market.
Write down the quantity at which the demand curve intersects the quantity axis.
Using graphing technology, find the market equilibrium. Give the quantity and price, with their units.
Write down the price at which the supply curve intersects the price axis.
During an 8-hour monitoring period, the water depths in two tanks are modelled by
where is the depth in Tank A, is the depth in Tank B, and is the time in hours since monitoring began. Depths are in centimetres, and
Construct a function such that means Tank A is deeper than Tank B. Give in expanded form.
Use a GDC to graph then sketch the graph for in your answer booklet. Label both axes with units and indicate the -intercept, turning point, -intercept and value at
Use your sketch to state which tank has the greater depth at
A technician records the volume of water in a reservoir during a filling test.
| Time, (min) | 0 | 5 | 10 | 15 |
|---|---|---|---|---|
| Volume, (L) | 18 | 31 | 43 | 56 |
The technician proposes a linear model
State one feature of the measurements that supports the use of a linear model.
Using the measurements at and show that the fitted model is
Hence estimate the volume of water after 12 minutes.
State whether using the model to predict the volume after 24 minutes is interpolation or extrapolation.
A website records the number of visits per day during the first five days after its launch.
| number of days after launch | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| visits per day | 320 000 | 470 000 | 760 000 | 1 040 000 | 1 700 000 |
To work with more manageable values, let The manager considers an exponential model and a power model
For the exponential model, determine the fitted values of and and the Pearson’s product moment correlation coefficient for the linearized data. Give your answers to three significant figures.
For the power model, determine the fitted values of and and the Pearson’s product moment correlation coefficient for the linearized data. Give your answers to three significant figures.
State which model is better supported by these data, giving a reason based on the correlation coefficients.
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