Trigonometric and Exponential Graphs worksheet

10 GCSE practice questions with answers, free to print. Every sheet is generated, so you can make a fresh one whenever you need it.

1. 2 marks

   The diagram shows the graph of \(y = f(x)\) for \(0 \le x \le 360\), where \(x\) is measured in degrees.

   (a)

   Write down the amplitude of the curve.

   (b)

   Write down the period of the curve, in degrees.

2. 5 marks

   Here is the graph of \(y = 3\sin x - 2\) for \(0 \le x \le 360\), where \(x\) is measured in degrees.

   (a)

   Write down the coordinates of the maximum point of the curve.

   (b)

   Write down the coordinates of the minimum point of the curve.

   (c)

   State the value of \(y\) when \(x = 180\).

3. 3 marks

   The diagram shows the graph of \(y = 6 \times 2^x\).

   (a)

   State the coordinates of the point where the curve crosses the \(y\)-axis.

   (b)

   Use the graph to find the value of \(y\) when \(x = 1\).

   (c)

   Use the graph to find the value of \(x\) when \(y = 24\).

4. 3 marks

   The graph shows the number of duckweed plants in a tank after \(t\) weeks.

   (a)

   Does the graph show exponential growth or exponential decay?

   (b)

   State the value shown when \(t = 0\).

   (c)

   Use the graph to find the value shown when \(t = 3\).

5. 3 marks

   Here is the graph of \(y = 4\cos x - 1\) and the line \(y = -3\), for \(0 \le x \le 360\).

   (a)

   Use the graphs to solve \(4\cos x - 1 = -3\) for \(0 \le x \le 360\).

   (b)

   Write down one solution of the same equation that is larger than \(360\).

6. 4 marks

   Here is part of the graph of \(y = 3\tan 2x - 1\) for \(0 \le x \le 180\), where \(x\) is measured in degrees.

   (a)

   Write down the two values of \(x\) in this range for which the graph has no value.

   (b)

   State the period of the curve, in degrees.

   (c)

   State the value of \(y\) when \(x = 90\).

7. 2 marks

   Here is the graph of \(y = f(x)\) for \(0 \le x \le 360\), where \(x\) is measured in degrees.

   (a)

   Write down the amplitude of the curve.

   (b)

   Write down the period of the curve, in degrees.

8. 5 marks

   Here is the graph of \(y = 3\sin x + 1\) for \(0 \le x \le 360\), where \(x\) is measured in degrees.

   (a)

   Write down the coordinates of the maximum point of the curve.

   (b)

   Write down the coordinates of the minimum point of the curve.

   (c)

   Write down the value of \(y\) when \(x = 180\).

9. 3 marks

   The diagram shows the graph of \(y = 3 \times 3^x\).

   (a)

   Write down the coordinates of the point where the curve crosses the \(y\)-axis.

   (b)

   Use the graph to find the value of \(y\) when \(x = 1\).

   (c)

   Use the graph to find the value of \(x\) when \(y = 27\).

10. 3 marks

    The graph shows the number of water lilies on a pond after \(t\) weeks.

    (a)

    Does the graph show exponential growth or exponential decay?

    (b)

    State the value shown when \(t = 0\).

    (c)

    Use the graph to find the value shown when \(t = 2\).

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