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Grade 12 Physical Science Data Sheet

CAPS / NSC · Paper 1 Physics & Paper 2 Chemistry · Grades 10–12

⚛ Paper 1 · Physical Constants

Quantity	Symbol	Value	Quantity	Symbol	Value
Acceleration due to gravity	$g$	$9{,}8\ \text{m·s}^{-2}$	Speed of light in a vacuum	$c$	$3{,}0 \times 10^{8}\ \text{m·s}^{-1}$
Universal gravitational constant	$G$	$6{,}67 \times 10^{-11}\ \text{N·m}^{2}\text{·kg}^{-2}$	Planck's constant	$h$	$6{,}63 \times 10^{-34}\ \text{J·s}$
Radius of the Earth	$R_E$	$6{,}38 \times 10^{6}\ \text{m}$	Coulomb's constant	$k$	$9{,}0 \times 10^{9}\ \text{N·m}^{2}\text{·C}^{-2}$
Mass of the Earth	$M_E$	$5{,}98 \times 10^{24}\ \text{kg}$	Charge on an electron	$e$	$-1{,}6 \times 10^{-19}\ \text{C}$
Electron mass	$m_e$	$9{,}11 \times 10^{-31}\ \text{kg}$	Avogadro's constant	$N_A$	$6{,}02 \times 10^{23}\ \text{mol}^{-1}$

These are given to you in the exam. Everything in the formula sections below is given too — what is not given is which one to reach for, which is the whole exam.

→ Motion in One Dimension

Velocity $v_f = v_i + a\Delta t$

Displacement $\Delta x = v_i \Delta t + \tfrac{1}{2}a\Delta t^{2}$

No time $v_f^{\,2} = v_i^{\,2} + 2a\Delta x$

No acceleration $\Delta x = \left(\dfrac{v_i + v_f}{2}\right)\Delta t$

Vertical motion: replace $\Delta x$ with $\Delta y$. Choose a positive direction first and keep it for the whole question — most lost marks here are sign errors, not method errors.

⇄ Force, Momentum & Gravitation

Newton's second law $F_{net} = ma$

Weight $w = mg$

Momentum $p = mv$

Impulse $F_{net}\,\Delta t = \Delta p = mv_f - mv_i$

Static friction $f_s^{\text{max}} = \mu_s N$

Kinetic friction $f_k = \mu_k N$

Newton's law of gravitation $F = \dfrac{Gm_1 m_2}{r^{2}}$

Gravitational field $g = \dfrac{GM}{r^{2}}$

$r$ is measured from the centre of the planet, so an object at height $h$ has $r = R_E + h$.

⚡ Work, Energy & Power

Work $W = F\Delta x \cos\theta$

Gravitational PE $U = mgh \quad (E_P = mgh)$

Kinetic energy $K = \tfrac{1}{2}mv^{2} \quad (E_K = \tfrac{1}{2}mv^{2})$

Work–energy theorem $W_{net} = \Delta K = K_f - K_i$

Non-conservative $W_{nc} = \Delta K + \Delta U$

Power $P = \dfrac{W}{\Delta t}$

Power at constant speed $P_{av} = F v_{av}$

$\theta$ is the angle between the force and the displacement. A force perpendicular to the motion does no work at all — that is why the normal force never appears in the energy sum.

〜 Waves, Sound & Light

Wave equation $v = f\lambda$

Period $T = \dfrac{1}{f}$

Doppler effect $f_L = \dfrac{v \pm v_L}{v \mp v_s}\, f_s$

Photon energy $E = hf = \dfrac{hc}{\lambda}$

Photoelectric effect $E = W_0 + E_{k(max)}$

Work function $W_0 = hf_0$

Max. kinetic energy $E_{k(max)} = \tfrac{1}{2}mv_{max}^{2}$

Doppler signs: choose the operator that makes the observed frequency rise when source and listener move towards each other. Substituting first and reasoning afterwards is how this question is lost.

± Electrostatics

Coulomb's law $F = \dfrac{kQ_1Q_2}{r^{2}}$

Field of a point charge $E = \dfrac{kQ}{r^{2}}$

Field strength $E = \dfrac{F}{q}$

Potential difference $V = \dfrac{W}{q}$

Number of electrons $n = \dfrac{Q}{e}$

Substitute charge magnitudes into Coulomb's law and get the direction from the diagram. Feeding signs into the formula gives the right number with the wrong direction about half the time.

⏚ Electric Circuits

Ohm's law $R = \dfrac{V}{I}$

Series $R_s = R_1 + R_2 + \dots$

Parallel $\dfrac{1}{R_p} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \dots$

Charge $q = I\Delta t$

EMF and internal resistance $\varepsilon = I(R + r)$

Electrical energy $W = Vq = VI\Delta t = I^{2}R\Delta t = \dfrac{V^{2}\Delta t}{R}$

Electrical power $P = \dfrac{W}{\Delta t} = VI = I^{2}R = \dfrac{V^{2}}{R}$

Pick the power formula whose quantities you already have, rather than the one you remember first — all four are the same statement.

∿ Alternating Current

RMS current $I_{rms} = \dfrac{I_{max}}{\sqrt{2}}$

RMS voltage $V_{rms} = \dfrac{V_{max}}{\sqrt{2}}$

Average power $P_{av} = V_{rms}\,I_{rms}$

$P_{av} = I_{rms}^{2}\,R$

$P_{av} = \dfrac{V_{rms}^{2}}{R}$

A quoted mains voltage is always the rms value. The peak is $\sqrt{2}$ times larger.

🜁 Paper 2 · Chemistry Constants

Quantity	Symbol	Value
Standard pressure	$p^{\theta}$	$1{,}013 \times 10^{5}\ \text{Pa}$
Molar gas volume at STP	$V_m$	$22{,}4\ \text{dm}^{3}\text{·mol}^{-1}$
Standard temperature	$T^{\theta}$	$273\ \text{K}$
Avogadro's constant	$N_A$	$6{,}02 \times 10^{23}\ \text{mol}^{-1}$
Charge on an electron	$e$	$-1{,}6 \times 10^{-19}\ \text{C}$

STP is $0\,^\circ\text{C}$ and $101{,}3\ \text{kPa}$ — not room temperature. A question that says "at STP" is telling you to use $22{,}4\ \text{dm}^{3}\text{·mol}^{-1}$.

⚗ Paper 2 · Chemistry Formulae

From mass $n = \dfrac{m}{M}$

From particles $n = \dfrac{N}{N_A}$

From gas volume (STP) $n = \dfrac{V}{V_m}$

Concentration $c = \dfrac{n}{V} = \dfrac{m}{MV}$

Titration $\dfrac{c_a V_a}{c_b V_b} = \dfrac{n_a}{n_b}$

pH $\text{pH} = -\log[\text{H}_3\text{O}^{+}]$

Ionisation of water $K_w = [\text{H}_3\text{O}^{+}][\text{OH}^{-}] = 1 \times 10^{-14}$

Cell potential $E^{\theta}_{cell} = E^{\theta}_{cathode} - E^{\theta}_{anode}$

equivalently $E^{\theta}_{cell} = E^{\theta}_{reduction} - E^{\theta}_{oxidation}$

or $E^{\theta}_{cell} = E^{\theta}_{\text{oxidising agent}} - E^{\theta}_{\text{reducing agent}}$

$c$ in $\text{mol·dm}^{-3}$ means $V$ must be in $\text{dm}^{3}$. Millilitres are cubic centimetres; divide by $1000$ before anything else. $K_w$ is quoted at $298\ \text{K}$.

◱ SI Units You Are Expected to Know

Quantity	Unit	Quantity	Unit	Quantity	Unit
Force	newton, N	Energy / work	joule, J	Power	watt, W
Momentum	$\text{kg·m·s}^{-1}$	Charge	coulomb, C	Potential difference	volt, V
Current	ampere, A	Resistance	ohm, Ω	Frequency	hertz, Hz
Electric field	$\text{N·C}^{-1}$	Concentration	$\text{mol·dm}^{-3}$	Gravitational field	$\text{N·kg}^{-1}$

Units are not decoration: a final answer without one loses the mark it was carrying, and a unit that does not match the formula is the fastest way to catch your own arithmetic error before the marker does.

The constants are given to you. Choosing the right equation is not.

Physics marks are lost on setup rather than arithmetic — the wrong equation, or the right one with a sign the wrong way round. I tutor Physical Science one-to-one in Gqeberha, at your own table, in English or Afrikaans. The first consultation is free.

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An independent revision aid aligned to the CAPS/NSC Physical Sciences syllabus. Not an official Department of Basic Education document — check the data sheet issued with your paper.