Mathematical, data, formula and circuit-symbol skills

Exam analysis

Most tested topics

Mathematical requirements

$(a×10ᵐ)(b×10ⁿ)=ab×10ᵐ⁺ⁿ (a×10ᵐ)/(b×10ⁿ)=(a/b)×10ᵐ⁻ⁿ normalise so 1≤|a|<10$

Convert prefixes before calculation: G=10⁹, M=10⁶, k=10³, m=10⁻³, μ=10⁻⁶, n=10⁻⁹. For squared/cubed quantities, apply the power to the conversion factor too.

Keep unrounded calculator values through intermediate steps. Round only the final answer, usually to the significant figures justified by the least precise measured input or by the question instruction.

Do an order-of-magnitude check: round inputs to one convenient significant figure, calculate the approximate power of ten, and compare sign, scale and unit with the calculator result.

Enter brackets explicitly for numerators, denominators, roots and powers; verify degree/radian mode before trigonometry. For a mean, add all values and divide by the number of values.

Significant figures describe justified precision, not the number of decimal places. A trailing zero after a decimal may be significant; leading zeros are not.

Write the model. 2. Rearrange for the target symbol. 3. Convert every quantity to consistent units. 4. Substitute with brackets. 5. Calculate. 6. Check dimensions, sign and physical scale.

Undo operations in reverse order and apply the same operation to both sides. For simultaneous equations eliminate one variable; for a quadratic use x=(−b±√(b²−4ac))/(2a), then reject branches that violate the physical conditions.

$[v]=L T⁻¹, [a]=L T⁻², [F]=M L T⁻² An equation can be valid only if every added term and both sides have identical dimensions.$

Keep unit factors with values and derive the result unit from the algebra. A dimensionally consistent equation may still have a wrong numerical constant or wrong physical model, so dimensional agreement is necessary but not sufficient.

$percentage change=((new−original)/original)×100% percentage difference=|A−B|/reference×100%$

Do not mix cm with m, μF with F or minutes with seconds inside one substitution. Rearranging symbolically first makes powers, roots and reciprocal relationships visible and reduces calculator errors.

Sketch the geometry, label lengths/angles and vector directions, choose positive perpendicular axes, then project each vector onto those axes before adding components.

$If θ is measured from the +x direction: Vₓ=V cosθ, Vᵧ=V sinθ Rₓ=ΣVₓ, Rᵧ=ΣVᵧ R=√(Rₓ²+Rᵧ²), tanφ=Rᵧ/Rₓ$

$a²+b²=c² sinθ=opposite/hypotenuse cosθ=adjacent/hypotenuse tanθ=opposite/adjacent$

Use similarity when corresponding side ratios are equal. Common geometry: circle area πr², sphere area 4πr², sphere volume 4πr³/3, cylinder volume πr²L. Convert all lengths before squaring or cubing.

A negative component means opposite to the chosen positive axis, not a negative magnitude. Use inverse trigonometry and the signs/quadrant of both components to state the final direction.

Cosine is not always horizontal and sine is not always vertical: cosine gives the component adjacent to the labelled angle. Add scalar magnitudes only when vectors are collinear in the same signed axis.

Identify x and y quantities with units, use most of both axes with simple scales, plot accurately, then choose a straight best-fit line or smooth curve that represents the trend rather than joining points dot-to-dot.

$gradient=Δy/Δx units=(y-axis unit)/(x-axis unit) Use two well-separated points on the best-fit line, not necessarily measured data points.$

For an instantaneous rate on a curve, draw a tangent at the required point and calculate its gradient using a large triangle. An intersection is where two plotted quantities satisfy both relationships; an intercept is the model value when the other axis variable is zero.

$area under y against x ≈ Σ y Δx units=(y-axis unit)(x-axis unit) It represents a physical quantity only when the governing relation makes that product meaningful.$

A straight line indicates y=mx+c; proportionality requires a straight line through the origin. Curvature may signal powers, reciprocals, exponentials, changing rate or a limited model—use physics and any requested transformation to distinguish them.

A visually straight trend is not automatically direct proportionality. Always test the intercept within uncertainty and attach compound units to gradient and area.

$θ(rad)=θ(°)π/180 s=rθ, arc length s for |θ|≪1 rad: sinθ≈tanθ≈θ and cosθ≈1−θ²/2$

$ln(ab)=ln a+ln b ln(a/b)=ln a−ln b ln(aⁿ)=n ln a ln(eˣ)=x$

$y=axⁿ ⇒ ln(y/y₀)=n ln(x/x₀)+constant plot ln(y/y₀) against ln(x/x₀): gradient=n$

$y=aeᵏˣ ⇒ ln(y/y₀)=kx+constant plot ln(y/y₀) against x: gradient=k$

The intercept determines the scale factor in the chosen reference-unit system. Gradient units are dimensionless for a log-log power plot and inverse x-units for ln(y/y₀) against x. Use natural or base-10 logs consistently with the model.

Small-angle approximations require radians. A logarithm must act on a dimensionless ratio such as y/y₀; writing ln(3 m) without a reference unit is not physically complete.

Key quantities, symbols and units

SI base quantities used in Physics: length metre (m), mass kilogram (kg), time second (s), electric current ampere (A), thermodynamic temperature kelvin (K), amount mole (mol), luminous intensity candela (cd).

$velocity: m s⁻¹ acceleration: m s⁻² force: N=kg m s⁻² energy: J=N m=kg m² s⁻² power: W=J s⁻¹$

$charge: C=A s potential difference: V=J C⁻¹ resistance: Ω=V A⁻¹ capacitance: F=C V⁻¹ magnetic flux: Wb=V s flux density: T=Wb m⁻²$

Other common coherent units follow their definitions: pressure Pa=N m⁻², frequency Hz=s⁻¹, field strength N C⁻¹ or V m⁻¹, activity Bq=s⁻¹, dose Gy=J kg⁻¹. Angular quantities use rad where clarity needs it.

When unsure, start from the defining equation, replace every quantity by its unit, then cancel and collect powers. For the ohm, R=V/I, so Ω=V A⁻¹.

A named derived unit is not a base unit. Quantity symbols are italic algebraic labels such as F or V; unit symbols such as N or V are upright and case-sensitive.

A complete measured quantity has numerical value × prefix scale × unit, with a named physical meaning. Write 3.71 N kg⁻¹, not just 3.71 or 'force'.

$1 km=10³ m; 1 ms=10⁻³ s; 1 μF=10⁻⁶ F (1 cm)²=10⁻⁴ m²; (1 cm)³=10⁻⁶ m³$

Use a space or centred dot for multiplication and negative powers or one solidus for division: m s⁻², N m, W m⁻². Preserve every denominator factor when rearranging or converting.

Read symbols from their local definition: V may denote potential difference or volume; I may denote current or intensity; E may denote energy, electric field or Young modulus. Subscripts distinguish related quantities, for example V₀ and Vout.

Unit symbols are case-sensitive, have no plural and normally no full stop: 5 kg, 20 N, 3.0 MHz. Leave a space between value and unit; keep °C for temperature differences/context but convert to K where an absolute thermodynamic temperature is required.

Before submitting, ask: does the unit match the requested quantity, are all prefixes converted, do exponents apply to units, and is the magnitude physically plausible? Equivalent units such as m s⁻² and N kg⁻¹ can describe different but dimensionally related meanings.

Supplied data and formulae

$g=9.81 m s⁻² near Earth G=6.67×10⁻¹¹ N m² kg⁻² u=1.66×10⁻²⁷ kg$

$e=1.60×10⁻¹⁹ C mₑ=9.11×10⁻³¹ kg mₚ≈mₙ≈1.67×10⁻²⁷ kg N_A=6.02×10²³ mol⁻¹$

$R=8.31 J K⁻¹ mol⁻¹ k=1.38×10⁻²³ J K⁻¹ R=N_A k$

$ε₀=8.85×10⁻¹² F m⁻¹ h=6.63×10⁻³⁴ J s c=3.00×10⁸ m s⁻¹ σ=5.67×10⁻⁸ W m⁻² K⁻⁴$

Use the value printed on the examination data page. Match the requested model first, copy the unit and exponent carefully, and keep the full supplied value until final rounding.

G is the universal gravitational constant; g is local gravitational field strength/acceleration. u is unified atomic mass, not the micro-prefix μ. e is the positive elementary-charge magnitude; an electron has charge −e.

$v=u+at; s=(u+v)t/2 s=ut+at²/2; v²=u²+2as Only for straight-line motion with constant acceleration; choose one positive direction.$

$Δp=ρgΔh for a static fluid of uniform density upthrust=ρ_fluid g V_displaced$

For the supplied moving-source sound formula, decide whether source motion makes wavefronts closer or farther apart before choosing the sign: approaching raises observed frequency; receding lowers it.

$I=Anvq for charge carriers Series: R=R₁+R₂+… Parallel: 1/R=1/R₁+1/R₂+…$

State what each symbol means in this situation, convert to SI, and test the result: series resistance exceeds every component; parallel resistance is below the smallest branch; upthrust uses displaced volume, not automatically total object volume.

Being printed on the sheet does not make an equation universally applicable. Reject SUVAT for changing acceleration and hydrostatic Δp=ρgΔh when density is not adequately constant.

$gravitational potential φ=−GM/r pV=NkT=nRT with T in K SHM: a=−ω²x; v²=ω²(x₀²−x²)$

$point-charge potential V=Q/(4πε₀r) capacitors: series 1/C=Σ1/Cᵢ; parallel C=ΣCᵢ Hall voltage V_H=BI/(ntq) for the stated slab geometry$

$sinusoidal: V_rms=V₀/√2, I_rms=I₀/√2 x=x₀e⁻ˡᵃᵐᵇᵈᵃᵗ; λ=ln2/t₁/₂$

$acoustic impedance Z=ρc Stefan luminosity L=4πr²σT⁴ for small redshift: Δλ/λ≈v/c$

Before substitution mark the convention: zero potential at infinity, absolute temperature, amplitude versus instantaneous displacement, peak versus rms, decay constant time unit, surface area and small-speed redshift limit.

Do not remove a negative potential because energy magnitude is positive, use °C in pV=NkT or Stefan's law, or mix peak voltage with rms current in average-power calculations.

Name the system/process. 2. List known and target quantities. 3. State assumptions/conditions. 4. Select a relation containing the target and usable knowns. 5. Rearrange symbolically. 6. convert SI and calculate. 7. check unit, sign, scale and interpretation.

When several models could give energy, identify the transfer mechanism: ΔEₖ=mv²/2 for speed change, ΔEₚ=mgΔh near Earth, W=Fs cosθ for a force through displacement, E=Pt for steady power. Compare like quantities only after calculating each under its conditions.

A formula given in the question may be unfamiliar. Treat it as a model: define each symbol from the stem, inspect powers/roots, rearrange for the requested quantity, and derive the unit from the expression.

Show the selected equation and numerical substitution so method marks remain visible. Keep more figures than the final answer and carry previous answers at full precision where possible.

Finish in physics language: direction from sign, larger/smaller from a ratio, valid/invalid from conditions, or agreement/disagreement within precision. A bare number is not an explanation.

Matching symbol letters is not model selection: the same letter can mean different quantities, and the right variables in a relation do not guarantee that its assumptions hold.

Circuit symbols

Source/control family: a cell is one long and one short parallel line; a battery repeats cells; a d.c. supply has marked polarity; switches show open/closed contacts; earth is the reference-potential connection.

Passive family: fixed/variable resistors, thermistor and LDR share resistive behaviour but have distinct modifier marks; a capacitor has two plates (one curved for a polarised form where specified); an inductor/transformer uses coil symbols.

A diode conducts in its forward direction and blocks reverse current. An LED is a diode with arrows pointing away (light emitted); a photodiode has arrows pointing toward it (light received). Preserve the diode bar/orientation when copying.

Meters are circles labelled A or V; an oscilloscope/CRO symbol marks waveform display. Output/transducer symbols include lamp, heater, motor, loudspeaker, microphone, relay and sensors—identify whether each converts electrical energy to another form or the reverse.

Recognition routine: name the family, identify the distinguishing mark, note polarity/direction, then state the component's circuit role. Use the exact official appendix form when drawing in an examination.

Similar outline is not enough: arrows away versus toward distinguish LED and photodiode, and a repeated-cell battery is not the same as a single cell. Exact symbol geometry must follow the official paper appendix.

A continuous conductor is one node at one potential. A filled junction dot joins branches; crossing lines without a junction mark are not automatically connected. Redraw complicated layouts by preserving nodes, not page position.

Connect an ammeter in series with the branch whose current is measured; connect a voltmeter in parallel across the two nodes of the component. Put the positive meter terminal at the higher-potential side for a positive reading.

$For two series resistors across V_in: V_out=V_in R_output/(R₁+R₂) Identify which resistor lies between the output node and reference/earth before substituting.$

For a diode/LED output, first predict which node is at higher potential, then orient the diode for forward current in the required state. Opposite-parallel LEDs can indicate positive versus negative output; label each only after tracing polarity.

A relay separates the low-power sensing/control coil from the switched load circuit. Connect the coil to the intended output and use the relay contact in the separate load supply; include required protective/directional components as shown by the task.

Diagram audit: source present, switch/control sensible, no unintended short circuit, meter topology correct, junctions unambiguous, polarised components oriented, output path complete. Explain function as input change → component change → voltage/current change → output response.

Mathematical, data, formula and circuit-symbol skills

Exam analysis

Most tested topics

Mathematical requirements

Keep powers of ten and precision under control from input to final answer

Rearrange symbols first, then substitute SI values and audit dimensions

Let the diagram and chosen axes decide the trigonometry and vector signs

Read every graph feature as a physical ratio, value or accumulated quantity

Use radians for angle physics and logarithms to expose model parameters

Key quantities, symbols and units

Build every derived unit from the equation that defines the quantity

Audit every final answer for quantity, scale, unit algebra and context

Supplied data and formulae

Identify each supplied constant by physical role, unit and scale

Attach the missing condition to every supplied AS formula

Preserve signs, temperature scales and rms conventions in A Level formulae

Choose the model before touching the calculator

Circuit symbols

Recognise circuit symbols by distinctive feature, direction and function

Build and read circuit diagrams by tracing nodes, polarity and component role