IB Physics HL S1.3 Mathematics Question Bank

Practise IB Physics HL S1.3 by applying algebra, trigonometry, logarithms, calculus and uncertainty to extended physics models.

Exam points

apply algebra, trigonometry and graph methods accurately when modelling physical relationships
select units, significant figures and uncertainty conventions that match the physical calculation
check a mathematical result against dimensions, limiting cases and the context of the experiment

Covered syllabus points

S1.3.1—General mathematics S1.3.2—Vectors and diagrams S1.3.3—Units and numerical values S1.3.4—Uncertainties S1.3.5—Graphing

[Maximum number: 1]

A girl rides a bicycle that is powered by an electric motor. A battery transfers energy to the electric motor. The emf of the battery is 16 V and it can deliver a charge of 43 kC when discharging completely from a full charge.

The maximum speed of the girl on a horizontal road is $7.0 \mathrm{~m} \mathrm{~s}^{-1}$ with energy from the battery alone. The maximum distance that the girl can travel under these conditions is 20 km .

Show that the time taken for the battery to discharge is about $3 \times 10^{3} \mathrm{~s}$ .

time taken $\frac{2.0 \times 10^{4}}{7} \boldsymbol{<} \boldsymbol{=} \mathbf{2 8 6 0} \boldsymbol{\mathrm { s }} \boldsymbol{>} \boldsymbol{>} \boldsymbol{=} \mathbf{2 9 0 0} \boldsymbol{<} \boldsymbol{\mathrm { s }} \boldsymbol{>} \boldsymbol{>} \boldsymbol{}$

Must see at least two s.f.

[Maximum number: 1]

Two forces, F and G, act on a system.

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

F is reversed in direction and G is halved.
Which vector correctly represents the new resultant force?

Figure for Question S1.3 Mathematics question 2 — IB Physics HL — Option A

Figure for Question S1.3 Mathematics question 2 — IB Physics HL — Option B

Figure for Question S1.3 Mathematics question 2 — IB Physics HL — Option C

Figure for Question S1.3 Mathematics question 2 — IB Physics HL — Option D

[Maximum number: 1]

A rod, R , lies perpendicular to a uniform magnetic field B of strength 0.50 T directed into the plane of the page. R is connected to a circuit and the electric current $I_{\mathrm{R}}$ is 2.0 A .

$\quad B$ is removed and a wire Z, carrying a current $I_{Z}$ , is placed parallel to R.

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

Derive the units of $\mu_{0}$ in SI fundamental units.

$\mathrm{kg} \mathrm{m} \mathrm{s}^{-2} \mathrm{~A}^{-2}$

Marking guidance:

Allow fractional answers such as:
$\frac{k g m}{s^{2} A^{2}}$

All question bank results loaded

Covered syllabus points

S1.3 Mathematics question 1

S1.3 Mathematics question 2

S1.3 Mathematics question 3