Using the Equation Sheet and Formulae

Physics is the equation-heavy science, and J249 handles this with a mix that trips up the unprepared: some equations are printed on a sheet inside the exam, and some you must recall from memory. Students who assume "it's all on the sheet" walk into calculations they cannot start; students who over-prepare waste revision time memorising equations that are handed to them. Getting the balance right — and having a reliable method for using any equation once you have it — is worth a large fraction of the marks, because roughly 40% of the paper is maths and application.

By the end of this lesson you should understand which equations are given versus which must be recalled, know how to find and read data values, and have a dependable four-step method for rearranging and substituting into any physics equation.

---

Given vs Recalled — the Key Distinction

The J249 papers include an equation sheet listing many of the physics formulae. But a set of core equations are not on the sheet and must be recalled. The examiners expect these to be second nature.

Commonly RECALLED (learn these — not on the sheet):

Quantity	Equation	Symbols
Speed	$v = \dfrac{s}{t}$v=ts​	speed, distance, time
Acceleration	$a = \dfrac{\Delta v}{t}$a=tΔv​	acceleration, change in velocity, time
Force	$F = ma$F=ma	force, mass, acceleration
Weight	$W = mg$W=mg	weight, mass, gravitational field strength
Work done	$W = Fs$W=Fs	work, force, distance
Power	$P = \dfrac{E}{t}$P=tE​	power, energy, time
Kinetic energy	$E_k = \dfrac{1}{2}mv^2$Ek​=21​mv2	kinetic energy, mass, speed
Charge	$Q = It$Q=It	charge, current, time
Potential difference	$V = IR$V=IR	p.d., current, resistance
Electrical power	$P = IV$P=IV	power, current, p.d.
Wave speed	$v = f\lambda$v=fλ	speed, frequency, wavelength
Density	$\rho = \dfrac{m}{V}$ρ=Vm​	density, mass, volume

Commonly GIVEN on the sheet (available, but still recognise and use them):

Quantity	Equation
Gravitational PE	$E_p = mgh$Ep​=mgh
Energy to heat (specific heat capacity)	$E = mc\Delta\theta$E=mcΔθ
Force on a spring	$F = ke$F=ke
Pressure (from a column of liquid)	$p = h\rho g$p=hρg (Higher)
Final velocity (equation of motion)	$v^2 = u^2 + 2as$v2=u2+2as (Higher)

Exam Tip: The single most valuable revision list you can make is a "must-recall equations" card. If you cannot write the recalled equations from memory, you cannot even start those calculations in the exam — the sheet will not rescue you. Test yourself on them until they are automatic.

Do not treat the exact contents of the sheet as fixed in your head — always check the version at the front of your paper. But the habit to build is: know the core equations cold, and lean on the sheet only for the longer or less-common ones.

There is a subtle time-management benefit to knowing which equations are recalled versus given. If you have memorised the core equations, you can write them straight down without breaking your concentration to hunt through the sheet — the sheet is then a backup you consult only for the handful of longer formulae. A student who has memorised nothing, by contrast, must flip to the sheet for every calculation, which wastes time and, worse, invites the error of grabbing a similar-looking but wrong equation under pressure. The recalled equations should be so familiar that reproducing them feels automatic, freeing your working memory to think about the physics of the problem rather than the mechanics of finding a formula. Treat the "must-recall" list as non-negotiable core knowledge, and the equation sheet as a convenience for the rest.

Exam Tip: Knowing the core equations by heart is partly a speed advantage — you write them instantly instead of searching the sheet mid-calculation. Reserve the sheet for the longer, less-common formulae, and you keep both your time and your concentration for the physics itself.

---

Reading the Data and Equation Sheet

Alongside equations, the paper provides data values you will need. The most important is the gravitational field strength:

$g = 9.8\text{ N/kg (near the Earth's surface)}$g=9.8 N/kg (near the Earth’s surface)

Other values you may be given include the speed of light in a vacuum, the speed of sound in air, and specific heat capacities within a question. Two rules keep you safe:

1. Use the value the paper gives you. If the question or sheet states $g = 9.8\text{ N/kg}$g=9.8 N/kg, use $9.8$9.8, not a remembered $10$10. Using the wrong value can lose the accuracy mark.
2. Read values with their units. A specific heat capacity in J/kg°C tells you the mass must be in kg and the temperature change in °C for the arithmetic to work.

Exam Tip: Before a calculation, glance at the data sheet to confirm the value and unit you need. Substituting $g = 10$g=10 out of habit when the paper says $9.8$9.8 is a needless slip — the value is right there in front of you.

---

A Reliable Method for Any Calculation

Whether an equation is given or recalled, the process of using it is the same. Follow a disciplined four-step method and you pick up the method marks even if the final digit slips.

flowchart LR
    A[1. Write the equation] --> B[2. Convert units, list values]
    B --> C[3. Rearrange for the unknown]
    C --> D[4. Substitute and evaluate with unit]

Step 1 — Write the equation. Copy it out in full first (from memory or the sheet). This alone often earns a mark and stops you guessing.

Step 2 — List your values and fix the units. Write down what you know and convert to the right units now: mass in kg, distance in m, time in s. Millimetres, grams and minutes are the commonest unit traps.

Step 3 — Rearrange for the unknown. Do the algebra before you put numbers in — it is cleaner and less error-prone.

Step 4 — Substitute and evaluate. Put the numbers in, calculate, and write the unit on the answer. A number with no unit rarely gets full marks in physics.

Exam Tip: Rearrange before you substitute. Manipulating letters is far less error-prone than juggling numbers, and it keeps your working legible for the examiner to award method marks. Substitute only at the very end.

---

Rearranging — the Formula Triangle and Beyond

For any equation of the form $A = B \times C$A=B×C, a formula triangle makes rearranging foolproof. Cover the quantity you want; what's left tells you the operation.

For $V = IR$V=IR:

• Cover V → $V = I \times R$V=I×R
• Cover I → $I = \dfrac{V}{R}$I=RV​
• Cover R → $R = \dfrac{V}{I}$R=IV​

The triangle works for every "product of two things" equation — $F = ma$F=ma, $W = Fs$W=Fs, $Q = It$Q=It, $v = f\lambda$v=fλ, $\rho = \dfrac{m}{V}$ρ=Vm​ and more.

For equations with a square or a fraction — like $E_k = \dfrac{1}{2}mv^2$Ek​=21​mv2 — the triangle is not enough, and you must rearrange algebraically:

$E_k = \dfrac{1}{2}mv^2 \quad\Rightarrow\quad v^2 = \dfrac{2E_k}{m} \quad\Rightarrow\quad v = \sqrt{\dfrac{2E_k}{m}}$Ek​=21​mv2⇒v2=m2Ek​​⇒v=m2Ek​​​