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YEAR 12 · SPECIALIST MATHEMATICS

Mathematical induction.

Construct and evaluate rigorous proofs of explicit identities and integer divisibility by mathematical induction.

6 lessons6 practice tests

Work through the topic

Learn the method, follow the examples, then try the worksheet.

01
Base case and induction hypothesis
Identify the first allowed case and state a precise induction hypothesis.
20 min · Worked examples & worksheet
02
Constructing the induction step
Connect the successor expression to the old case using a justified algebraic bridge.
20 min · Worked examples & worksheet
03
Proofs of summation formulas
Prove summation formulas by isolating the new term.
20 min · Worked examples & worksheet
04
Divisibility proofs
Exhibit an integer multiplier to prove divisibility.
20 min · Worked examples & worksheet
05
Identities involving powers and integers
Handle explicit powers, products and weighted sums.
20 min · Worked examples & worksheet
06
Recognising incomplete or invalid induction arguments
Find a missing base, a wrong next term or a circular implication.
20 min · Worked examples & worksheet

AFTER THE LESSONS

Topic review

Revisit the key ideas, then choose a practice paper.

6 practice tests · Separate worked marking guides