IB Physics SL Mathematics

Review IB Physics mathematics through SI units, dimensional checks, graph gradients and areas, uncertainty propagation and significant-figure decisions.

Syllabus
First assessment 2025
Topic
S1.3
Level
SL

Exam points

  • derive SI units and check dimensional consistency for constants, fields and equations
  • use graph gradients, intercepts, areas or tangents to extract physical quantities
  • propagate absolute, fractional and percentage uncertainties to suitable significant figures

Covered syllabus points

S1.3.1—General mathematicsS1.3.2—Vectors and diagramsS1.3.3—Units and numerical valuesS1.3.4—UncertaintiesS1.3.5—Graphing

S1.3 Mathematics question 1

[Maximum number: 4]

A group of students is investigating refraction in a semi-circular glass block.

Light from a ray box enters the curved side of the block. The light passes through the block and leaves, refracted, at P .

Question (a)

(a)

The students vary the position of the ray box to obtain data to determine the refractive index of the glass. They use a protractor to collect values for the angles of incidence θi\theta_{i} and refraction θr\theta_{r} at P and record them on a table.

Figure for Question (a) — IB Physics SL
[ 1 ]

Question (i)

(i)

Complete the table.

Table for Question (i) — IB Physics SL
[ 1 ]

Question (b)

(b)

They plot a graph of the variation with the sine of θi\theta_{i} of the sine of θr\theta_{r}.
They add uncertainty bars for sin⁡θr\sin \theta_{r} for the first and last data point and draw the best-fit line.

Figure for Question (b) — IB Physics SL
[ 3 ]

Question (i)

(i)

Determine the gradient of the students' best-fit line.

[ 2 ]

Question (ii)

(ii)

Draw on the students' graph the line of maximum gradient.

[ 1 ]

S1.3 Mathematics question 2

[Maximum number: 3]

A glider is an aircraft with no engine. To be launched, a glider is uniformly accelerated from rest by a cable pulled by a motor that exerts a horizontal force on the glider throughout the launch.

Figure for Question S1.3 Mathematics question 2 — IB Physics SL

At a particular instant in the flight the glider is losing 1.00 m of vertical height for every 6.00 m that it goes forward horizontally. At this instant, the horizontal speed of the glider is 12.5 m s−112.5 \mathrm{~m} \mathrm{~s}^{-1}. Calculate the velocity of the glider. Give your answer to an appropriate number of significant figures.

S1.3 Mathematics question 3

[Maximum number: 6]

A group of students uses pressurized air to move a piston that forces a nail into a block of wood. A gauge is used to measure the pressure P of compressed air above atmospheric pressure. The nail enters the wood perpendicular to its surface.

Figure for Question S1.3 Mathematics question 3 — IB Physics SL

The students use a ruler to measure the length of the nail which remains above the surface of the wood as shown. The depth of the nail inside the wood is d. All necessary length measurements are recorded using a ruler with uncertainty ±1 mm\pm 1 \mathrm{~mm}.

Figure for Question S1.3 Mathematics question 3 — IB Physics SL

Question (a)

(a)

The students systematically increase the pressure and calculate d.

Table for Question (a) — IB Physics SL
[ 1 ]

Question (i)

(i)

State the absolute uncertainty of d.

[ 1 ]

Question (b)

(b)

The students suggest the following relationship between d and P :

d=kPd=k \sqrt{P}

where k is a constant.
To verify the relationship, the variation of d with P\sqrt{P} is plotted.
One data point is missing.

Figure for Question (b) — IB Physics SL
[ 5 ]

Question (i)

(i)

The percentage uncertainty in P is ±8%\pm 8 \%. Determine the uncertainty for P\sqrt{P} when d=33 mmd=33 \mathrm{~mm} and draw the uncertainty bar for this data point on the graph.

[ 3 ]

Question (ii)

(ii)

The SI units of k can be expressed as kg−12 mx sy\mathrm{kg}^{-\frac{1}{2}} \mathrm{~m}^{x} \mathrm{~s}^{y}. Determine the values of x and y.

[ 2 ]
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