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Date	May 2018	Marks available	1	Reference code	18M.1.SL.TZ1.1
Level	Standard level	Paper	Paper 1	Time zone	1
Command term		Question number	1	Adapted from	N/A

Question

A student measures the radius r of a sphere with an absolute uncertainty Δr. What is the fractional uncertainty in the volume of the sphere?

A. ${(\frac{Δ r}{r})}^{3}$ ${\left( {\frac{{\Delta r}}{r}} \right)^3}$

B. $3 \frac{Δ r}{r}$ $3\frac{{\Delta r}}{r}$

C. $4 π \frac{Δ r}{r}$ $4\pi \frac{{\Delta r}}{r}$

D. $4 π {(\frac{Δ r}{r})}^{3}$ $4\pi {\left( {\frac{{\Delta r}}{r}} \right)^3}$

Markscheme

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Syllabus sections

Core » Topic 1: Measurements and uncertainties » 1.2 – Uncertainties and errors

Show 56 related questions

19M.3.SL.TZ1.1b.i: There is an advantage and a disadvantage in using two masses that are almost equal. State...
19M.3.SL.TZ1.1b.ii:
There is an advantage and a disadvantage in using two masses that are almost equal.

State and explain the disadvantage with reference to your answer to (a)(ii).
18M.3.SL.TZ1.1a:
Draw on the graph the line of best fit for the data.
18M.3.SL.TZ1.1d:
State how the value of K can be obtained from the graph.
22M.1.SL.TZ2.2:
Two different experiments, P and Q, generate two sets of data to confirm the proportionality of variables $x$ $x$ and $y$ $y$ . The graphs for the data from P and Q are shown. The maximum and minimum gradient lines are shown for both sets of data.

What is true about the systematic error and the uncertainty of the gradient when P is compared to Q?
18M.3.SL.TZ1.1b.i:
Write down the time taken for one oscillation when B = 0.005 T with its absolute uncertainty.
19M.1.HL.TZ1.1:
A student is verifying the equation

$x = \frac{2 λ Y}{z}$ $x = \frac{{2\lambda Y}}{z}$

The percentage uncertainties are:

What is the percentage uncertainty in x?

A. 5 %

B. 15 %

C. 25 %

D. 30 %
22M.1.HL.TZ1.3:
The uncertainty in reading a laboratory thermometer is 0.5 °C. The temperature of a liquid falls from 20 °C to 10 °C as measured by the thermometer. What is the percentage uncertainty in the change in temperature?

A. 2.5 %

B. 5 %

C. 7.5 %

D. 10 %
18M.3.SL.TZ1.2c:
Outline how using a variable resistance could improve the accuracy of the value found for the internal resistance.
19M.3.SL.TZ2.3b: Explain how the student could use this apparatus to obtain a more reliable value for λ.
18M.3.SL.TZ1.2b:
It is noticed that the resistor gets warmer. Explain how this would affect the calculated value of the internal resistance.
17M.1.SL.TZ1.15: Two pulses are travelling towards each other. What is a possible pulse shape when the...
17N.1.SL.TZ0.30: The diagram shows an analogue meter with a mirror behind the pointer. What is the main...
18N.1.SL.TZ0.2: The length of the side of a cube is 2.0 cm ± 4 %. The mass of the cube is 24.0 g ± 8 %. What...
18N.3.SL.TZ0.1d: The numerical value of the constant c in SI units is 1.67. Determine g, using the graph.
18N.3.SL.TZ0.1c.i: Draw the line of best fit for these data.
18N.3.SL.TZ0.1b: A student records the time for 20 oscillations of the rod. Explain how this procedure leads...
18M.3.SL.TZ1.1b.iii:
State the unit of K.
19M.3.SL.TZ1.1a.i:
Calculate the percentage error in the measured value of g.
19N.3.SL.TZ0.1b:
Determine the fractional uncertainty in v when T = 2.115 s, correct to one significant figure.
19M.3.SL.TZ2.1a: The student has plotted error bars for the potential difference. Outline why no error bars...
19M.1.HL.TZ2.2: A proton has momentum 10-20 N s and the uncertainty in the position of the proton is 10-10 m....
18N.3.SL.TZ0.1c.ii:
Suggest whether the data are consistent with the theoretical prediction.
18M.3.SL.TZ2.2a:
This relationship can also be written as follows.

$\frac{1}{\sqrt{I}} = K x + K C$ $\frac{1}{{\sqrt I }} = Kx + KC$

Show that $K = 2 \sqrt{\frac{π}{P}}$ $K = 2\sqrt {\frac{\pi }{P}}$ .
17N.1.SL.TZ0.2: An object is positioned in a gravitational field. The measurement of gravitational force...
19M.3.SL.TZ1.1a.ii:
Deduce the value of g and its absolute uncertainty for this experiment.
19N.3.SL.TZ0.1d:
The lines of the minimum and maximum gradient are shown.

Estimate the absolute uncertainty in a.
18M.3.SL.TZ2.2b.ii:
Determine P, to the correct number of significant figures including its unit.
17M.3.SL.TZ2.1b.ii:
percentage uncertainty in d ².
17M.1.SL.TZ2.1:
A stone falls from rest to the bottom of a water well of depth d. The time t taken to fall is 2.0 ±0.2 s. The depth of the well is calculated to be 20 m using d = $\frac{1}{2}$ $\frac{1}{2}$ at ². The uncertainty in a is negligible.

What is the absolute uncertainty in d?

A. ± 0.2 m

B. ± 1 m

C. ± 2 m

D. ± 4 m
17M.3.SL.TZ2.2c.ii:
After taking measurements the student observes that the ammeter has a positive zero error. Explain what effect, if any, this zero error will have on the calculated value of the internal resistance in (b).
17M.3.SL.TZ2.2c.i:
State what is meant by a zero error.
18M.3.SL.TZ1.1c:
The student plots a graph to show how P² varies with $\frac{1}{B}$ $\frac{1}{B}$ for the data.

Sketch the shape of the expected line of best fit on the axes below assuming that the relationship $P = \frac{K}{\sqrt{B}}$ $P = \frac{K}{{\sqrt B }}$ is verified. You do not have to put numbers on the axes.
18M.3.SL.TZ2.1a:
Determine the distance fallen, in m, by the centre of mass of the sphere including an estimate of the absolute uncertainty in your answer.
18M.3.SL.TZ2.2b.i:
Estimate C.
16N.3.SL.TZ0.1a:
(i) Outline why OY has a greater percentage uncertainty than OX for each pair of data points.

(ii) The refractive index of the water is given by $\frac{O X}{O Y}$ $\frac{{{\rm{OX}}}}{{{\rm{OY}}}}$ when OX is small.

Calculate the fractional uncertainty in the value of the refractive index of water for OX = 1.8 cm.
18M.3.SL.TZ1.2a:
Draw a suitable circuit diagram that would enable the internal resistance to be determined.
20N.3.SL.TZ0.1b(iii):
In order to find the uncertainty for $γ$ $γ$ , a maximum gradient line would be drawn. On the graph, sketch the maximum gradient line for the data.
19M.1.SL.TZ2.1:
A student measures the radius R of a circular plate to determine its area. The absolute uncertainty in R is ΔR.

What is the fractional uncertainty in the area of the plate?

A. $\frac{2 Δ R}{R}$ $\frac{{2\Delta R}}{R}$

B. ${(\frac{Δ R}{R})}^{2}$ ${\left( {\frac{{\Delta R}}{R}} \right)^2}$

C. $\frac{2 π Δ R}{R}$ $\frac{{2\pi \Delta R}}{R}$

D. $π {(\frac{Δ R}{R})}^{2}$ $\pi {\left( {\frac{{\Delta R}}{R}} \right)^2}$
20N.3.SL.TZ0.1b(v):
The expected value of $γ$ $γ$ is $0.027$ $0.027$ . Comment on your result.
19M.1.SL.TZ1.1:
A student wants to determine the angular speed ω of a rotating object. The period T is 0.50 s ±5 %. The angular speed ω is

$ω = \frac{2 π}{T}$ $\omega = \frac{{2\pi }}{T}$

What is the percentage uncertainty of ω?

A. 0.2 %

B. 2.5 %

C. 5 %

D. 10 %
20N.3.SL.TZ0.1b(iv):
The percentage uncertainty for $γ$ $γ$ is $15 %$ $15 %$ . State $γ$ $γ$ , with its absolute uncertainty.
16N.3.SL.TZ0.1b:
A graph of the variation of OY with OX is plotted.

(i) Draw, on the graph, the error bars for OY when OX = 1.8 cm and when OY = 5.8 cm.

(ii) Determine, using the graph, the refractive index of the water in the container for values of OX less than 6.0 cm.

(iii) The refractive index for a material is also given by $\frac{sin i}{sin r}$ $\frac{{\sin i}}{{\sin r}}$ where i is the angle of incidence and r is the angle of refraction.

Outline why the graph deviates from a straight line for large values of OX.
18N.3.SL.TZ0.1a:
State the unit of c.
21M.1.SL.TZ1.2: Two sets of data, shown below with circles and squares, are obtained in two experiments. The...
18M.3.SL.TZ2.1b:
Using the following equation

$acceleration due to gravity = \frac{2 \times distance fallen by centre of mass of sphere}{{(measured time to fall)}^{2}}$ ${\text{acceleration due to gravity}} = \frac{{2 \times {\text{distance fallen by centre of mass of sphere}}}}{{{{{\text{(measured time to fall)}}}^{\text{2}}}}}$

calculate, for these data, the acceleration due to gravity including an estimate of the absolute uncertainty in your answer.
21M.1.SL.TZ2.1:
A student measures the length l and width w of a rectangular table top.

What is the absolute uncertainty of the perimeter of the table top?

A.   $0.3 cm$ $0.3 cm$

B.   $0.6 cm$ $0.6 cm$

C.   $1.2 cm$ $1.2 cm$

D.   $2.4 cm$ $2.4 cm$
20N.3.SL.TZ0.2c(i):
The measurements of $T$ $T$ were collected five times. Explain how repeated measurements of $T$ $T$ reduced the random error in the final experimental value of $m r$ $m r$ .
20N.3.SL.TZ0.2a:
State why the experiment is repeated with different values of $W$ $W$ .
19M.3.SL.TZ2.1b: Determine, using the graph, the emf of the cell including the uncertainty for this value....
17M.3.SL.TZ1.2a:
In a simple pendulum experiment, a student measures the period T of the pendulum many times and obtains an average value T = (2.540 ± 0.005) s. The length L of the pendulum is measured to be L = (1.60 ± 0.01) m.

Calculate, using $g = \frac{4 π^{2} L}{T^{2}}$ $g = \frac{{4{\pi ^2}L}}{{{T^2}}}$ , the value of the acceleration of free fall, including its uncertainty. State the value of the uncertainty to one significant figure.
17M.3.SL.TZ2.1b.i:
fractional uncertainty in d.
19M.3.SL.TZ2.3a:
When d = 0.200 mm, s = 0.9 mm and D = 280 mm, determine the percentage uncertainty in the wavelength.
21N.1.SL.TZ0.2:
A ball of mass (50 ± 1) g is moving with a speed of (25 ± 1) m s⁻¹. What is the fractional uncertainty in the momentum of the ball?

A. 0.02

B. 0.04

C. 0.06

D. 0.08
22M.1.SL.TZ1.3: A student measures the time for 20 oscillations of a pendulum. The experiment is repeated...
22M.1.SL.TZ2.1:
The radius of a circle is measured to be (10.0 ± 0.5) cm. What is the area of the circle?

A. (314.2 ± 0.3) cm²

B. (314 ± 1) cm²

C. (314 ± 15) cm²

D. (314 ± 31) cm²

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