CSCA Physics Formulas: Equations, Units and Worked Examples

How should you use a Physics formula?

Start with the physical situation, not a memorized symbol. Draw a quick sketch; label what is known, what is asked, and the direction of motion or current. Choose a relationship whose conditions fit the question, convert quantities to consistent units, calculate, then ask whether the size and unit of the answer make sense. For example, constant-acceleration equations assume acceleration is constant; an ideal-gas ratio assumes the stated variables stay fixed. A formula can be algebraically correct yet misapplied. The published Physics paper has 48 single-choice questions in 60 minutes, according to the official CSCA exam introduction, so use these habits until they become quick.

• Write units beside each number. In gas-law questions, convert Celsius to kelvin before forming temperature ratios.
• Keep a chosen positive direction for velocity, force and momentum until the final step.
• Check assumptions such as constant acceleration, negligible friction, ideal gas and steady current.

Mechanics and waves: which equations matter?

Mechanics starts with movement and forces. Use displacement for a change in position, velocity for displacement per time, acceleration for change in velocity per time, and force for the cause of acceleration. The syllabus also includes momentum, work and energy, circular motion, gravitation, oscillations and waves. This is a revision selection, not a claim that every equation below appears on the exam.

• Constant acceleration: v = u + at and s = ut + ½at². Here u and v are initial and final velocity in m/s, a is acceleration in m/s², t is time in s, and s is displacement in m.
• Net force: ΣF = ma. A newton (N) equals kg·m/s². Subtract opposing forces before dividing by mass.
• Momentum and impulse: p = mv; impulse J = Δp = FΔt for a constant net force. Momentum and impulse have units kg·m/s or N·s. Preserve direction signs.
• Energy and work: kinetic energy Ek = ½mv²; near Earth, change in gravitational potential energy ΔEp = mgΔh; work W = Fs cosθ for a constant force. Energy and work use joules (J).
• Uniform circular motion: centripetal acceleration ac = v²/r, pointing toward the circle’s center. For waves, v = fλ and T = 1/f; speed is m/s, frequency f is hertz, wavelength λ is meters, and period T is seconds.

Worked example — displacement, not final speed. A cyclist starts at 3 m/s and accelerates steadily at 2 m/s² for 4 s. Use s = ut + ½at²: s = (3 × 4) + (½ × 2 × 4²) = 12 + 16 = 28 m. The final speed is v = 3 + (2 × 4) = 11 m/s, but 11 m/s is not the distance. Check the units: (m/s) × s and (m/s²) × s² both give meters. If acceleration varied, these constant-acceleration equations would not apply directly. For more original questions, see our Physics practice questions with worked answers.

Electricity and magnetism: how do the formulas connect?

The electromagnetism module moves from charges and electric fields to DC circuits, magnetic forces and induction. Decide whether the question asks about a point charge, a complete circuit, a current-carrying wire, or changing magnetic flux. These are different physical setups, even if they reuse the letters F, V and I.

• Electrostatic force: F = k|q₁q₂|/r² for point charges separated by distance r. Charge q is in coulombs (C); force is in newtons (N). Attraction or repulsion depends on charge signs.
• Electric field and potential: E = F/q for a small test charge and potential difference V = W/q. Electric field has units N/C; potential difference has units volts, or J/C.
• Ohm’s law: V = IR for an ohmic component under the applicable conditions. V is volts, I amperes, R ohms (Ω). Electrical power P = VI, measured in watts (W).
• Resistors: in series, Rtotal = R₁ + R₂ + … . In parallel, 1/Rtotal = 1/R₁ + 1/R₂ + … . The parallel total must be smaller than the smallest branch resistance.
• Magnetism and induction: the magnitude of force on a straight current-carrying wire is F = BIL sinθ in a uniform field; induced emf magnitude is |ε| = N|ΔΦ|/Δt for N turns and a specified flux change. State the geometry and units before substituting.

Worked example — parallel circuit. A 4 Ω resistor and a 12 Ω resistor are in parallel across a 12 V ideal source. The branches share the same voltage, so their currents are 12/4 = 3 A and 12/12 = 1 A. Total current is 4 A. Equivalently, 1/Rtotal = 1/4 + 1/12 = 1/3, hence Rtotal = 3 Ω and I = V/Rtotal = 4 A. Adding 4 Ω and 12 Ω would treat the circuit as series. Sketching the branches first prevents that mistake. You can then try free Physics practice.

Thermodynamics: why must temperature be in kelvin?

The ideal-gas relationship pV = nRT connects pressure p, volume V, amount n and absolute temperature T. Use pascals, cubic meters, moles and kelvin when using R = 8.314 J/(mol·K). In comparison questions where n and V stay fixed, p/T is constant; where n and p stay fixed, V/T is constant. The wording matters. The first law of thermodynamics can be written ΔU = Q − Wby, where Wby is work done by the gas. Some textbooks define work done on the gas instead and write a plus sign, so identify the sign convention before solving.

Worked example — constant volume. A sealed rigid container holds an ideal gas at 120 kPa and 280 K. It warms to 350 K without changing the amount of gas. Since V and n stay fixed, p₂/p₁ = T₂/T₁. Therefore p₂ = 120 × 350/280 = 150 kPa. The pressure rises by 25%, matching the temperature ratio 1.25. A Celsius temperature ratio would be invalid; kelvin measures temperature from absolute zero. If the container expanded, the same shortcut would no longer apply.

Optics: which light equations are useful?

Reflection and refraction are in the published optics scope, alongside interference and diffraction. For a plane reflecting surface, the angle of incidence equals the angle of reflection, both measured from the normal. For refraction across a boundary, n₁sinθ₁ = n₂sinθ₂. The refractive index n has no units, and the angles are measured from the normal, not from the surface. A thin-lens equation may appear in teaching materials, but revise the official syllabus before treating any extra formula as a guaranteed test requirement.

Worked example — refraction. A ray travels from air (n ≈ 1.00) into glass (n = 1.50) at 30° to the normal. Snell’s law gives sinθ₂ = (1.00/1.50) × sin30° = 1/3. Therefore θ₂ ≈ 19.5°. The smaller angle is physically sensible: the ray bends toward the normal in the higher-index medium. A common error is measuring 30° from the surface; that would be a different incident angle.

Modern physics: how do energy and frequency connect?

The modern-physics part of the syllabus includes the photoelectric effect and basic atomic and nuclear ideas. Photon energy is E = hf, where h is Planck’s constant and f is frequency. For the basic photoelectric model, the maximum kinetic energy of an emitted electron is Kmax = hf − φ, provided the photon energy reaches the work function φ. Frequency below the threshold f₀ = φ/h does not produce emission in that model. Energy can be expressed in joules or electronvolts, but do not mix them in one subtraction.

Worked example — threshold reasoning. A surface has work function 2.4 eV and receives photons of energy 2.0 eV. Since 2.0 eV is less than 2.4 eV, the basic photoelectric model predicts no emitted electron. A brighter beam means more photons, but does not change the energy of each photon at the same frequency. With 3.0 eV photons, Kmax would be 3.0 − 2.4 = 0.6 eV. This comparison tests the condition for emission before any arithmetic.

How should you revise formulas for the CSCA Physics paper?

Make a one-page sheet from memory, then compare it with your notes. For each equation, record the meaning and unit of every symbol, the conditions under which it applies, and one situation where it does not. Practice rearranging it before putting numbers in. Use a 60-minute mixed set only after single-topic errors are under control; the published 48-question format gives an average of 75 seconds per question, though some questions will need less time and others more. Mark wrong answers as concept, setup, algebra, unit, or reading errors. Redo them without notes the next day.

• Mechanics: explain why displacement is not the same as final speed, and why net force includes opposing forces.
• Circuits: identify series versus parallel before applying V = IR; check that parallel resistance is smaller than any branch.
• Thermal physics: state which gas variables are fixed and use kelvin for temperature ratios.
• Optics and modern physics: measure angles from the normal and test a photon against the work-function threshold.

Move from this guide to free Physics practice, then review the eight original worked Physics questions. When you are ready for mixed timing, use the mock-test study method. The free mini test and full mock access are different products; check the current access details on each page.

Frequently asked questions

• Is this an official CSCA formula sheet? No. It is an independently written revision guide. Check the official syllabus for the tested scope; do not assume a formula sheet will be supplied on exam day.
• Do I need to memorize every equation here? Treat this as a study selection, not a definitive requirement list. Prioritize the current syllabus and your target university’s subject and language requirements.
• Are the worked examples past-paper questions? No. They are original teaching examples. Do not confuse them with official samples or verified past papers.
• What should I study after memorizing formulas? Explain the conditions, solve unfamiliar questions, and review mistakes. Formula recall without physical reasoning is unreliable in multiple-choice problems.

Sources checked 26 October 2026: The official CSCA Physics Examination Syllabus (2025 edition) specifies five content modules, 48 single-answer questions, 60 minutes, language options and the 100-point score. Check the organizer’s syllabus page and exam introduction for updates before your session. The equations and worked examples here are independently written teaching material; the official syllabus does not supply this formula list or guarantee that each equation will be tested. CSCA.ai is an independent preparation platform. Confirm exam rules and your university’s requirements with the organizer and university.