Syllabus Edition

First teaching 2014

Last exams 2024

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Uncertainties & Errors (DP IB Physics: SL)

Exam Questions

3 hours44 questions
1
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1 mark

Part of a thermometer is shown below.

1-2-q1-sl-easy-mcq-phy

What is the correct reading on the thermometer and the uncertainty in this reading?

 

reading / °C

uncertainty in reading / °C

A.

34

±0.5

B.

34

±0.1

C.

34.0

±1.0

D.

34.0

±0.5

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    2
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    1 mark

    A student carries out a series of determinations of the acceleration of free fall, g. The table shows the results.

    g1 / m s–2 g2 / m s–2 g3 / m s–2 g4 / m s–2 g5 / m s–2 g6 / m s–2

    4.91

    4.89

    4.88

    4.90

    4.93

    4.92

     

    What can be said about the results obtained in this experiment?

    • The results are accurate and precise

    • The results are accurate but not precise

    • The results are not accurate and not precise

    • The results are precise but not accurate

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    31 mark

    Four people participate in a shooting competition. Each person gets four shots. The diagram shows the target boards of each participant after their turn.

    Which target has a low precision and a high accuracy?

    q7_limitation-of-physical-measurements_aqa-as-mcq

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      41 mark

      An ammeter has a systematic error of –0.05 A. The ammeter is then connected to a circuit and shows a reading of 2.45 A.

      What should the real reading be?

      • 2.35 A

      • 2.40 A

      • 2.50 A

      • 2.55 A

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      51 mark

      What is the absolute uncertainty for the following measurements?  

      16.8 cm 16.6 cm 16.7 cm 16.4 cm 16.4 cm 16.6 cm

      • 0.012

      • 0.024

      • 0.2 cm

      • 0.4 cm

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      61 mark

      A micrometer is used to measure the diameters of two spheres.

      Diameter of first sphere 15.01 ± 0.01 mm
      Diameter of second sphere 17.38 ± 0.02 mm

      The difference in the diameters is calculated.

      What is the uncertainty in this difference?

      • ± 0.01 mm

      • ± 0.02 mm

      • ± 0.03 mm

      • ± 0.06 mm

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      71 mark

      A student carries out an experiment and reaches a result which is far from the true value. They carry out an evaluation of the experiment to identify potential sources of systematic and random errors.

      Which of the following would not eliminate any systematic errors?

      • Performing more trials with the same equipment and using the same techniques

      • Performing more trials with the same equipment but using different techniques

      • Performing more trials with different equipment but using the same techniques

      • Checking the calibration of the equipment

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      81 mark

      A fixed quantity x subscript 0 is measured many times in an experiment that has experimental uncertainty. A graph is plotted to show the number, n, of times that a particular value of x is obtained.

      Which graph could be obtained if the measurement of x subscript 0 has a high precision and a low accuracy?

       q6_limitation-of-physical-measurements_aqa-as-mcq

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        9
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        1 mark

        The diagram shows the stem of a Celsius thermometer marked to show initial and final temperature values.

        q10_limitation-of-physical-measurements_aqa-as-mcq

        What is the temperature change with its absolute uncertainty?

        • 20.5 ± 0.25 °C

        • 20.5 ± 0.5 °C

        • 21 ± 1 °C

        • 22.0 ± 0.5 °C

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        10
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        1 mark

        A student plots a graph of height, h, against time, t, to show the motion of an object in a fluid. They include the error bars on their plotted points and maximum and minimum lines with their associated equations.

        1-2-q10-sl-easy-mcq-phy

        Which of the following equations would correctly calculate the percentage uncertainty in the gradient of the graph?

        • fraction numerator 0.92 plus 0.78 over denominator 2 end fraction cross times 100 percent sign

        • fraction numerator 0.92 minus 0.78 over denominator 2 end fraction cross times 100 percent sign

        • fraction numerator 168 plus 162 over denominator 2 end fraction cross times 100 percent sign

        • fraction numerator 168 minus 162 over denominator 2 end fraction cross times 100 percent sign

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        1
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        1 mark

        Systematic and random errors can be compared.

        What are the properties that apply to random errors?

        1  The error is consistently too high or too low and by different amounts

        2  The error is constantly too high or low and by the same amount each time

        3  The error can be fully eliminated

        4  The error cannot be fully eliminated

        5  The error can be reduced by averaging repeated measurements

        6  The error cannot be reduced by averaging repeated measurements

        • 1, 3 and 6

        • 2, 4 and 6

        • 2, 3 and 6

        • 1, 4 and 5

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        2
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        1 mark

        The measurement of a physical quantity may be subject to random errors and systematic errors.

        Which statement is correct?

        • random errors can be reduced by taking the average of several measurements

        • random errors are always caused by the person taking the measurement

        • a systematic error cannot be reduced by adjusting the apparatus

        • a systematic error results in a different reading each time the measurement is taken

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        3
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        1 mark

        A stone falls from rest to the bottom of a water well of depth d. The time t taken to fall is 3.0 ± 0.3 s. The depth of the well is calculated to be 30 m using d = begin mathsize 14px style 1 half end styleat2. The uncertainty in a is negligible.

        What is the absolute uncertainty in d?

        • ± 0.6 m

        • ± 3 m

        • ± 24 m

        • ± 6 m

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        4
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        1 mark

        The diagram shows an experiment to measure the speed of a small ball falling at constant speed through a clear liquid in a glass tube.q14_uncertainties--errors_ib-sl-physics-mcq

        There are two marks on the tube. The top mark is positioned at 15 ± 1 mm on the adjacent rule and the lower mark at 285 ± 1 mm. The ball passes the top mark at 2.50 ± 0.02 s and passes the lower mark at 4.50 ± 0.02 s.

        The constant speed of the ball is calculated to be 135 mm s–1.

        Which expression calculates the fractional uncertainty in the value of this speed?

        • begin mathsize 16px style 2 over 270 plus fraction numerator 0.04 over denominator 2.00 end fraction end style

        • begin mathsize 16px style 1 over 270 plus fraction numerator 0.02 over denominator 2.00 end fraction end style

        • begin mathsize 16px style 1 over 15 plus fraction numerator 0.02 over denominator 2.50 end fraction end style

        • begin mathsize 16px style 1 over 285 plus fraction numerator 0.02 over denominator 4.50 end fraction end style

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        5
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        1 mark

        The strain energy W of a spring is determined from its spring constant k and extension x. The spring obeys Hooke’s law and the value of W is calculated using the equation shown.

                                                                         W = begin mathsize 16px style 1 half end stylekx2

        The spring constant k is 200 ± 1 N m–1 and the extension x is 0.040 ± 0.004 m.

        What is the percentage uncertainty in the calculated value of W?

        • 20%

        • 20.5%

        • 10%

        • 10.5%

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        6
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        1 mark

        In an experiment investigating the electrolysis of copper, a student sets out to find the electrochemical equivalent, Z.

        The electrochemical equivalent of a substance is the amount of substance deposited on a cathode per Coulomb of charge.

        This can be determined using the equation:

                                                     Zbegin mathsize 16px style fraction numerator m subscript 1 minus m subscript 2 over denominator I t end fraction end style

        Where:

        • Mass of cathode before passing current, m subscript 1= (54.39 ± 0.01) × 10–3 kg
        • Mass of cathode after passing current, m subscript 2= (52.06 ± 0.01) × 10–3 kg
        • Current, begin mathsize 16px style I end style= 3.00 ± 1 A
        • Time, t = 4800 ± 100 s

        What is the largest possible value of Z from these readings?

        • begin mathsize 16px style 233 over 940 end style × 10–6 kg C–1

        • begin mathsize 16px style 231 over 940 end style × 10–6 kg C–1

        • begin mathsize 16px style 235 over 940 end style × 10–6 kg C–1

        • begin mathsize 16px style 253 over 720 end style × 10–6 kg C–1

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        7
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        1 mark

        The sides of a square are measured to be 8.0 ± 0.2 cm.

        Which of the following gives the area of the square and its uncertainty?

        • 64.0 ± 0.2 cm2 

        • 64.0 ± 0.4 cm2 

        • 64.0 ± 3.2 cm2 

        • 64.0 ± 1.6 cm2 

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        8
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        1 mark

        In an experiment, a radio-controlled car takes 1.50 ± 0.05 s to travel 30.0 ± 0.1 m.

        What is the car’s average speed and the uncertainty in this value?

        • 20.0 ± 0.732 m s–1

        • 20.0 ± 0.0366 m s–1

        • 20.0 ± 0.066 m s–1

        • 20.0 ± 9.91 m s–1

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        9
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        1 mark

        The diagram shows a thermometer reading of a liquid's temperature, before and after heating. 

        sl-mcq-1-2-hard-q10

        What is the best estimate for the temperature increase of the liquid?

        • (54.0 ± 0.5) degrees

        • (54 ± 1.0) degrees

        • (54 ± 1) degrees

        • (54.0 ± 2.0) degrees

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        10
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        1 mark

        A student collects values of the time period, T, of a pendulum at different lengths of string, L. They want to investigate the relationship:

                                                                        T = 2π begin mathsize 16px style square root of L over g end root end style

        They plot the values on a graph along with the error bars associated with each point, as shown in the diagram.

        q20_uncertainties--errors_ib-sl-physics-mcq 

        What is the percentage uncertainty in the experimental value of g?

        • begin mathsize 16px style 43 over 32 end style%

        • begin mathsize 16px style 43 over 1600 end style%

        • begin mathsize 16px style 43 over 800 end style%

        • begin mathsize 16px style 215 over 8000 end style%

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        1
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        1 mark

        Analogue meters often have a mirrored or metallic strip behind the pointer. 

        1-2-sl-mcq-hard-q1-phy

        What is the main purpose of this strip? 

        • To magnify the reading indicated by the pointer

        • To enable the pointer to be seen from different angles

        • To minimise the risk of parallax error

        • To reflect as much light as possible on the reading indicated by the pointer

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        2
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        1 mark

        Two lengths, n and n – 2 have an uncertainty of increment n. The uncertainty increment n is much less than n

        In which of the following quantities is the percentage uncertainty the largest? 

        • n left parenthesis n minus 2 right parenthesis

        • fraction numerator n over denominator n minus 2 end fraction

        • n plus left parenthesis n minus 2 right parenthesis

        • n minus left parenthesis n minus 2 right parenthesis

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        3
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        1 mark

        In an experiment to determine the acceleration of free fall g, a student presents their calculated value as 9.7835 m s–2 and states their value is only accurate to ± 5%.

        Which of the following gives their calculated value to an appropriate number of significant figures? 

        • 10 m s–2

        • 9.8 m s–2

        • 9.78 m s–2

        • 9.785 m s–2

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        4
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        1 mark

        A small conker is attached to a string and whirled overhead in a horizontal circle. The tension in the string T is measured for a variety of different linear speeds v and the following graph is obtained.

        1-2-sl-mcq-hard-q4-phy 

        These experimental results suggest that there is...

        • a systematic error in v and small random error

        • a systematic error in T and small random error

        • a random error in v and small systematic error

        • a random error in T and small systematic error

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        5
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        1 mark

        Which of the following experimental techniques does not reduce the random error associated with the quantity being measured? 

        • Calibrating the Y-sensitivity of the oscilloscope before measuring a voltage

        • Timing a large number of oscillations to determine the periodic time

        • Using the gradient of a graph of current against voltage to determine the resistance of an ohmic conductor

        • Measuring the distance between a large number of nodes on a standing wave to determine the wavelength of the wave

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        6
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        1 mark

        The length and breadth of a rectangular card was found to be (5.0 ± 0.2) cm and (3.0 ± 0.2) cm respectively. The area of the card cannot be more than: 

        • 5 cm2

        • 8 cm2

        • 15 cm2

        • 18 cm2

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        7
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        1 mark

        An object dropped from the edge of a cliff is timed to take (10.0 ± 0.1) s to fall to the surface of the sea. If the acceleration due to free fall is (10.0 ± 0.2) m s–2, the calculated height of the cliff from which the object was released should be quoted as: 

        • (500 ± 2.0) m 

        • (500 ± 20.0) m 

        • (500 ± 2) m 

        • (50 ± 2) × 101

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        8
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        1 mark

        A certain rule can be read to the nearest millimetre. It is used to measure the length of a piece of string whose true length is 50 mm. Repeated measurements of the string give the following readings:

        Reading Length / mm
        1 52
        2 52
        3 51
        4 52
        5 51
        6 51

        Are the readings accurate and precise to within 1 mm? 

          Readings are accurate to within 1 mm Readings are precise to within 1 mm
        A. No No
        B. No Yes
        C. Yes No
        D. Yes Yes

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          9
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          1 mark

          A researcher plots a graph to investigate the variation of current and potential difference of a resistor.

          q19_uncertainties--errors_ib-sl-physics-mcq

          After realising they have read the manufacturers label of their electrical equipment incorrectly, they determine the size of the error bars shown should decrease.

          Which row correctly describes how this will affect the value of the maximum gradient Gmax, the minimum gradient Gmin, and the resistance of the resistor R?

           

          Gmax

          Gmin

          R

          A.

          increase

          increase

          increase

          B.

          decrease

          decrease

          decrease

          C.

          increase

          decrease

          no change

          D.

          decrease

          increase

          no change

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            10
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            1 mark

            A mass is dropped from rest and falls through a distance of 2.0 m in a vacuum. An observer records the time taken for the mass to fall through this distance using a manually operated stopwatch and repeats the measurements a further two times.

            The average result of these measured times, displayed in the table below, was used to determine a value for the acceleration of free fall. This was calculated to be 9.8 m s–2.

             

            first measurement

            second measurement

            third measurement

            average

            time/ s

            0.6

            0.73

            0.59

            0.64

            Which statement best describes the quality of the measurements taken for this experiment?

            • The measurements are precise and accurate with no evidence of random errors.

            • The measurements are not accurate and not always recorded to the degree of precision of the measuring device but the calculated experimental result is accurate.

            • The measurements are not always recorded to the degree of precision of the measuring device but are accurate. Systematic errors may be present.

            • The range of results shows that there were random errors made but the calculated value is correct so the experiment was successful.

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