[discia] GCSE Maths › Algebra › Trigonometric and Exponential Graphs

Trigonometric and Exponential Graphs

discia.org 10 questions · 25 marks
Name Date
  1. Either paper 2 marks

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

    xy90180270360-6-5-4-3-2-1120
    (a)

    Write down the amplitude of the curve.

    (b)

    Write down the period of the curve, in degrees.

    Show answer
    (a) \(3\)
    (b) \(360\) degrees
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  2. Either paper 5 marks

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

    xy90180270360-6-5-4-3-2-1120
    (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 \(x = 180\).

    Show answer
    (a) \((90, 1)\)
    (b) \((270, -5)\)
    (c) \(-2\)
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  3. Either paper 3 marks

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

    xy-2-11236121824303642480
    (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 \(y = 24\).

    Show answer
    (a) \((0, 6)\)
    (b) \(12\)
    (c) \(2\)
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  4. Either paper 3 marks

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

    t (weeks)y12310203040506070800
    (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 \(t = 3\).

    Show answer
    (a) growth
    (b) \(10\)
    (c) \(80\)
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  5. Either paper 1 mark

    \(y\) is an angle between 180° and 270°.

    Which statement is true? Tick one box.

    A \(\square\) \(\mathrm{ cos }\,y < 0\) and \(\mathrm{ tan }\,y > 0\)

    B \(\square\) \(\mathrm{ cos }\,y > 0\) and \(\mathrm{ tan }\,y > 0\)

    C \(\square\) \(\mathrm{ cos }\,y < 0\) and \(\mathrm{ tan }\,y < 0\)

    D \(\square\) \(\mathrm{ cos }\,y > 0\) and \(\mathrm{ tan }\,y < 0\)

    Show answer
    A: \(\mathrm{ cos }\,y < 0\) and \(\mathrm{ tan }\,y > 0\)
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  6. Either paper 1 mark

    The solution of \(2^x = 48\) lies between two consecutive integers.

    Work out the two integers.

    Show answer
    \(5\) and \(6\)
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  7. Either paper 3 marks

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

    xy90180270360-4-3-2-11234560
    (a)

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

    (b)

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

    Show answer
    (a) \(x = 30\) and \(x = 150\)
    (b) \(390\)
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  8. Either paper 4 marks

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

    xy90180270360-6-5-4-3-2-1120
    (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 \(x = 180\).

    Show answer
    (a) \(x = 90\) and \(x = 270\)
    (b) \(180\) degrees
    (c) \(-2\)
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  9. Either paper 1 mark

    Joel sketches the graph of \(y = 0.5^x\) for \(x \geq 0\).

    xy123-1123456780Diagram NOT accurately drawn

    Make one criticism of his sketch.

    Show answer
    The graph should be a curve, not a straight line.
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  10. Either paper 2 marks

    The curve \(y = 2^x\) is drawn on the axes below.

    xy-3-2-1123-11234567890

    Sketch the curve \(y = 3^x\) on the same axes.

    Show answer
    A curve through \((0, 1)\), \((1, 3)\) and \((-1, \frac{ 1 }{ 3 })\). For \(x > 0\) it is above the given curve (steeper); for \(x < 0\) it is below the given curve, closer to the \(x\)-axis.
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discia.org Trigonometric and Exponential Graphs · sheet 1
Answers Trigonometric and Exponential Graphs · sheet 1
  1. (a) \(3\)
    (b) \(360\) degrees
  2. (a) \((90, 1)\)
    (b) \((270, -5)\)
    (c) \(-2\)
  3. (a) \((0, 6)\)
    (b) \(12\)
    (c) \(2\)
  4. (a) growth
    (b) \(10\)
    (c) \(80\)
  5. A: \(\mathrm{ cos }\,y < 0\) and \(\mathrm{ tan }\,y > 0\)
  6. \(5\) and \(6\)
  7. (a) \(x = 30\) and \(x = 150\)
    (b) \(390\)
  8. (a) \(x = 90\) and \(x = 270\)
    (b) \(180\) degrees
    (c) \(-2\)
  9. The graph should be a curve, not a straight line.
  10. A curve through \((0, 1)\), \((1, 3)\) and \((-1, \frac{ 1 }{ 3 })\). For \(x > 0\) it is above the given curve (steeper); for \(x < 0\) it is below the given curve, closer to the \(x\)-axis.
discia.org Trigonometric and Exponential Graphs · sheet 1