Physics Paper II punishes one particular kind of student: the one who understood the topic in class but cannot produce the right relationship under exam pressure. The topics feel familiar. The formula is gone. And in a paper built on calculations, a missing formula costs the whole question, not just a line of working. Prepare better with the IJMB past questions and answers app.
What follows is a working set of ten formula groups that carry most of the calculation load in IJMB Physics — mechanics, properties of matter, waves, optics, electricity and modern physics. Nobody can honestly rank formulae by how often they appear without counting through real papers, so treat this as the set you should be able to write from memory, then check the pattern against genuine past questions.
Why these ten and not others
Each group below either turns up across several topics or sits at the centre of a topic that keeps producing calculation questions. Learn the expression, but learn the condition attached to it: constant acceleration, ideal gas, a solid expanding in one dimension. Marks are usually lost because a correct formula was applied in a situation it does not describe.
The ten formula groups
Mechanics
- 1. Equations of uniform acceleration. v = u + at, s = ut + ½at², v² = u² + 2as. They hold only while acceleration stays constant. Projectile questions split motion into vertical and horizontal parts and apply these to each part separately.
- 2. Newton's second law and impulse. F = ma, and Ft = mv − mu. If the mass is changing, work with force as the rate of change of momentum instead.
- 3. Work, energy and power. W = Fs cos θ, KE = ½mv², PE = mgh, and P = W/t = Fv. Most energy questions collapse into "what was lost here was gained there".
Properties of matter and heat
- 4. Expansivity. e = l₀αΔθ for length, A = A₀βΔθ for area, V = V₀γΔθ for volume, with γ = 3α for a solid. Only the change in temperature matters, so Δθ can be in kelvin or Celsius.
- 5. Heat energy. Q = mcΔθ for a temperature change, Q = mL for a change of state, and heat lost = heat gained for mixtures. The classic error is reaching for mcΔθ while the substance is still melting.
- 6. Gas laws. PV = nRT, and P₁V₁/T₁ = P₂V₂/T₂. Convert to kelvin before you substitute anything, every single time.
Waves and optics
- 7. The wave equation. v = fλ, with v = √(T/μ) for a stretched string and v = 2f(l₂ − l₁) for a resonance tube. Read what each symbol means in the question; v is not always the speed of light.
- 8. Refraction and lenses. n = sin i / sin r, 1/f = 1/u + 1/v, magnification m = v/u, and power of a lens P = 1/f in dioptres, with f in metres. Sign conventions decide the answer, so state them before substituting.
Electricity and modern physics
- 9. Circuits and capacitors. V = IR, P = IV = I²R = V²/R, the series and parallel rules for resistors, Q = CV, C = C₁ + C₂ in parallel, 1/C = 1/C₁ + 1/C₂ in series, and E = ½CV².
- 10. Modern physics. E = hf, hf = W + KE(max) for the photoelectric effect, A = λN for activity, and the half-life relation that follows from it. Short formulae, heavy unit demands.
Two worked examples
Start with the capacitors. Two 3.5 μF capacitors in parallel across 24 V. In parallel, capacitances simply add: C = 3.5 + 3.5 = 7.0 μF. Then Q = CV = 7.0 × 10⁻⁶ × 24 = 1.68 × 10⁻⁴ C. Give the answer in coulombs unless the question specifically asks for microcoulombs.
Now expansivity. A wire 10 m long has linear expansivity 1.0 × 10⁻⁴ K⁻¹. If its temperature rises by 20 K, the extension is e = l₀αΔθ = 10 × 1.0 × 10⁻⁴ × 20 = 0.02 m. The whole question is one line — and it stays one line only because the formula was already in your head before you read it.
Mistakes that quietly cost marks
- Mixing units mid-calculation. Microfarads, centimetres and grams must be converted before substitution, not after.
- Celsius in a gas law. Volume and pressure ratios only behave properly with absolute temperature.
- Ignoring the condition. The equations of motion fail when acceleration is not constant; mcΔθ fails during a phase change.
- Rounding too early. Carry the extra figures through and round at the final answer.
- Writing the formula and then nothing. Show the substitution with the values in place. Even when the arithmetic goes wrong, the method is visible.
A drilling routine that actually sticks
- Take a blank sheet and write all ten groups from memory. No notes, no textbook.
- Compare with this list and mark what you missed. Those are your weak spots for the week.
- For each weak formula, solve five numeric problems — numbers, not symbols. Recognising a formula is not the same as using one.
- Write the unit beside every quantity as you go, and cancel them. If the final unit is wrong, the working is wrong.
- Once a week, sit a timed section from real past questions and mark it honestly against the answers.
Repeat the blank-sheet test the evening before the paper. It takes ten minutes and it tells you exactly where you stand.
Where past questions fit in
The formulae get you started; past questions tell you how IJMB actually phrases things, how many marks each step carries, and how much time you have per question. If you do not yet have genuine papers, FreshNote's guide to getting IJMB and JUPEB past questions explains where to look and how to check a file before trusting it. Work through papers topic by topic first, then switch to full timed papers once the formulae stop slowing you down.
Questions students ask
Will IJMB give me a formula sheet in Paper II?
Do not build your revision around that assumption. Check the instructions printed on the paper and the current IJMB syllabus for your session. The safe position is to know every formula on this list cold, so the question cannot ambush you.
Do these formulae also work for JUPEB and JAMB?
The physics is the same, so the formulae themselves carry over. The syllabi are not identical, though, so confirm with the current JUPEB or JAMB syllabus which topics are examinable and how the questions are usually framed.
What this page does and does not do
This page lists formulae and shows how to use them. It does not supply IJMB past questions, and any file advertised as "leaked" questions should be treated with suspicion. For anything about the examination itself — structure, timing, rules, syllabus — confirm directly with IJMB, Interim Joint Matriculation Board, Ahmadu Bello University, Zaria.
Ten formula groups, one blank sheet, five problems each. That is a manageable week of work, and it is the difference between recognising a formula on the page and producing it when the invigilator says to start.