Maths Skills in Physics

Approximately 30% of marks in the Edexcel GCSE Physics (1PH0) exam require mathematical skills. This lesson covers the key maths skills you need, with physics-specific examples and exam tips.

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Rearranging Equations

This is the single most important maths skill in physics. You must be able to take any equation and rearrange it to make any variable the subject.

The Golden Rule

Whatever you do to one side of the equation, you must do to the other side.

Common Rearrangements

Original	To Find	Rearranged
v = fλ	f	f = v / λ
v = fλ	λ	λ = v / f
V = IR	I	I = V / R
V = IR	R	R = V / I
P = IV	I	I = P / V
KE = ½mv²	v	v = √(2KE / m)
GPE = mgh	h	h = GPE / (mg)
F = ma	m	m = F / a

Exam Tip: Practise rearranging every equation you know. In the exam, the question will often give you the values for the "other" variables, forcing you to rearrange. If you cannot rearrange, you cannot answer the question.

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Substituting Values

After identifying the correct equation and rearranging if necessary, you must substitute the given values correctly.

Checklist Before Substituting

1. Are all values in the correct units? (Convert if needed.)
2. Have you rearranged the equation to make the required variable the subject?
3. Are you substituting into the correct places?

Worked Example

A wave has a speed of 340 m/s and a frequency of 256 Hz. Calculate the wavelength.

Step 1: Identify the equation: v = fλ

Step 2: Rearrange: λ = v / f

Step 3: Substitute: λ = 340 / 256

Step 4: Calculate: λ = 1.33 m (to 3 s.f.)

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Unit Conversions

Many exam questions give values in non-standard units. You MUST convert them before substituting.

Quick Reference Table

Conversion	Method
km → m	× 1000
cm → m	÷ 100
mm → m	÷ 1000
g → kg	÷ 1000
mg → kg	÷ 1,000,000
km/h → m/s	÷ 3.6
kW → W	× 1000
kJ → J	× 1000
MJ → J	× 1,000,000
minutes → seconds	× 60
hours → seconds	× 3600
kWh → J	× 3,600,000

Exam Tip: A very common trap is giving speed in km/h when the equation needs m/s. Always check units before you start calculating.

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Significant Figures

When You Must Round

• When the question says "give your answer to X significant figures".
• When the question says "give your answer to an appropriate number of significant figures" — match the data given.
• At the end of a multi-step calculation (never round intermediate values).

How to Count Significant Figures

Number	Significant Figures	Explanation
456	3	All non-zero digits count
4.56	3	Decimal point doesn't affect the count
0.00456	3	Leading zeros don't count
4060	3 (or 4)	Trailing zeros are ambiguous without a decimal point
4.060	4	Trailing zeros after a decimal point count
4000	1 (unless specified)	Use standard form to be clear: 4.00 × 10³ = 3 s.f.

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Standard Form

Writing Numbers in Standard Form

A × 10ⁿ where 1 ≤ A < 10.

Number	Standard Form
150,000	1.5 × 10⁵
0.0034	3.4 × 10⁻³
300,000,000	3 × 10⁸
0.00000000016	1.6 × 10⁻¹⁰

Calculating with Standard Form

Multiplication: Multiply the numbers, add the indices.

(3 × 10⁴) × (2 × 10³) = 6 × 10⁷

Division: Divide the numbers, subtract the indices.

(8 × 10⁶) ÷ (4 × 10²) = 2 × 10⁴

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Interpreting Graphs

Graphs are a major part of GCSE physics. You need to be able to extract information from them in several ways.

Reading the Gradient

The gradient (slope) of a graph represents the rate of change of y with respect to x.

How to calculate the gradient:

1. Choose two points on the line that are far apart (for accuracy).
2. Draw a large triangle.
3. Calculate: gradient = Δy / Δx = (y₂ − y₁) / (x₂ − x₁)

Physical meaning of gradients:

Graph	Gradient Represents
Distance–time	Speed
Velocity–time	Acceleration
Force–extension	Spring constant (k)
V–I graph	Resistance
Charge–time (capacitor)	Current

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Area Under the Graph

The area under a graph often represents a physical quantity.

Graph	Area Under Represents
Velocity–time	Distance travelled
Force–extension	Work done (energy stored)
Force–time	Change in momentum (impulse)
Power–time	Energy transferred

How to calculate the area:

• For rectangular sections: area = base × height.
• For triangular sections: area = ½ × base × height.
• For irregular shapes: count squares on the grid, or split into rectangles and triangles.

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The Y-Intercept

The point where the line crosses the y-axis. This often has a physical meaning:

• On a distance–time graph: the starting position.
• On a cooling curve: the starting temperature.
• On a force–extension graph: if the y-intercept is not zero, there may be a systematic error or the spring was already stretched.

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Drawing Lines of Best Fit

1. Plot all points carefully.
2. Draw a straight line or smooth curve that passes through or close to as many points as possible.
3. There should be roughly equal numbers of points above and below the line.
4. Ignore anomalous results when drawing the line.
5. The line does NOT have to pass through the origin unless the data requires it.

Exam Tip: Use a sharp pencil and a ruler for straight lines of best fit. For curves, draw a single smooth line — do not connect the dots. An examiner can tell the difference between a genuine curve and a series of joined straight segments.

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Percentage Change

Percentage change = (change / original value) × 100%

Worked Example

A spring has an original length of 10 cm and stretches to 14 cm. Calculate the percentage change in length.

Change = 14 − 10 = 4 cm

Percentage change = (4 / 10) × 100 = 40%

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Ratios and Proportions