A-Level Mathematics · Proof · A1

Structure of mathematical proof.

Understand how mathematicians construct rigorous proofs using assumptions, logical deductions and conclusions.

A1 Proof12 MinutesAnimated lesson

WATCH THE IDEA MOVE

Animated
explanation.

Pause, replay and follow every logical step at your own pace.

01 / KEY IDEA

A proof demonstrates that a statement is true for every possible case, not just one example.

02 / LEARNING OUTCOMES
  • Understand assumptions
  • Identify logical deductions
  • Recognise valid mathematical conclusions

WORKED EXAMPLE

Follow every
reason.

Prove that if n is even, then n² is even.

01

Write every even integer as n = 2k, where k is an integer.

02

Then n² = (2k)² = 4k² = 2(2k²).

03

Since 2k² is an integer, n² is divisible by 2. Therefore n² is even.

QUICK CHECK

Test the
logic.

Choose the statement that describes a valid mathematical proof.

What makes a mathematical proof valid?