Equations and maths skills for physics — Edexcel GCSE Physics revision

Rearranging and using equations

• Always identify which quantity you need to find, then rearrange the equation before substituting numbers, keeping units consistent (SI units: kg, m, s, J, N, W, Pa).
• Common triangle method: for equations like density = mass ÷ volume, cover the quantity you want to find to see how the other two combine.
• Standard form (e.g. 3.2 × 10⁻⁵) is useful for very large or very small numbers common in physics, such as wavelengths or astronomical distances.
• Significant figures should generally match the least precise piece of data given in the question, typically 2 or 3 s.f. unless told otherwise.

Graphs and gradients

• The gradient of a graph = change in y ÷ change in x; use a large triangle spanning much of the line for accuracy.
• A curved graph's gradient at a point is found by drawing a tangent to the curve at that point and calculating its gradient.
• The area under a graph can represent a physical quantity, e.g. area under a velocity-time graph gives distance travelled; area under a force-extension graph gives elastic potential energy stored.
• Directly proportional relationships give a straight line through the origin; check this by seeing if doubling x doubles y.

Key terms

SI units

The standard international units used in physics, e.g. kg, m, s, N, J.

Standard form

A way of writing numbers as a value between 1 and 10 multiplied by a power of 10.

Gradient

The steepness of a graph line, calculated as change in y ÷ change in x.

Tangent

A straight line touching a curve at one point, used to find the gradient there.

Scalar

A quantity with magnitude only, no direction.

Vector

A quantity with both magnitude and direction.

Common exam traps

• Forgetting to convert units (e.g. cm to m, g to kg) before substituting into equations.
• Confusing scalar and vector quantities, e.g. treating speed and velocity as identical.
• Reading the gradient from too small a triangle, reducing accuracy.

Practice questions with answers

1. 1. What are the correct base SI units for mass, length and time?

   • • g, cm, min
   • • kg, m, s
   • • lb, ft, hr
   • • kg, cm, s

   Answer: kg, m, s

   SI base units for mass, length and time are kilograms, metres and seconds.

2. 2. Convert 250 g to kg.

   Answer: 0.25 kg

   1000 g = 1 kg, so 250 g = 250 ÷ 1000 = 0.25 kg.

3. 3. Convert 3.5 km to m.

   Answer: 3500 m

   1 km = 1000 m, so 3.5 × 1000 = 3500 m.

4. 4. How do you find the gradient of a straight-line graph?

   • • Δx ÷ Δy
   • • Δy ÷ Δx
   • • Δy × Δx
   • • Δy + Δx

   Answer: Δy ÷ Δx

   Gradient = change in y ÷ change in x (rise ÷ run).

5. 5. A distance-time graph rises from 0 m to 40 m over 8 s in a straight line. Calculate the gradient (speed).

   Answer: 5 m/s

   Gradient = Δy ÷ Δx = 40 ÷ 8 = 5 m/s.

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