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.
The function is defined by
State the equations of the vertical and horizontal asymptotes of the graph of
Sketch the graph of showing and labelling its asymptotes and its intercepts with the axes.
Determine including its domain, and hence state whether is self-inverse.
The function is defined by
Determine the equations of the vertical and horizontal asymptotes of the graph of
Verify algebraically that for Hence state the line of symmetry of the graph of and describe how reflection in this line maps the asymptotes found in part (a).
A capacitor is discharged from an initial voltage of 10 V. Its voltage in volts, seconds after discharge is modelled by
where After 4 seconds, the voltage is 6.4 V.
Determine the value of correct to three significant figures.
Let give the time, in seconds, at which the voltage is Determine stating its domain.
Hence determine the time at which the model predicts the voltage is 2.5 V. State whether the model predicts that the voltage reaches 0 V at any finite time, and justify your answer.
Figure 1 shows the graph of for
The graph of is obtained from the graph of by reflecting it in the -axis, applying a vertical stretch with scale factor and then translating it unit upwards.
Write down
On the same axes as Figure 1, sketch the graph of Mark the image of the point on for which
Using Figure 1, determine all values of for which
For the point on determine its image ordinate if the translation upwards by unit is performed after the reflection but before the vertical stretch. Hence state whether this order of transformations gives the same graph as
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