Flashcards and recall.

Try this with Specialist Mathematics

1. Write one prompt per card. Use definitions, explanations or examples from your current topic.
2. Answer aloud before turning the card. Split a card if it asks for several unrelated facts.
3. Set aside missed cards and revisit them in a later session.

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Recall topics

• What is P(n) in an induction proof of 1+3+⋯+(2n−1)=n²?
• Error check: can a proof of P(n) for all n≥1 begin only at n=2?
• In an induction step, exactly what may be assumed about k?
• Application: if S_k=k² for the first k odd numbers, compute S_(k+1).
• Which sentence completes a proof after base and successor cases?
• Application: if 7^k−1 is divisible by6, rewrite 7^(k+1)−1.
• Error check: proving a series formula at k, which term is added for n=k+1?
• How does induction handle a product ∏_(r=1)^n a_r?
• Application: if h^(k)(x)=e^x(x+k), find h^(k+1)(x).
• Application: advance (cis θ)^k=cis(kθ) by one power.
• What is the key step for the extended triangle inequality by induction?
• Scope check: should an induction drill introduce unrelated recursion or advanced inequalities?
• Application: multiply (2+i)(1−3i).
• For z=−3+4i, identify Re z and Im z.
• Application: convert −1+i√3 to modulus-argument form.
• How do modulus and argument behave in a nonzero product zw?
• What geometric action does multiplication by 2cis(π/3) perform?
• Application: divide 6cis(5π/6) by 2cis(π/3).
• Application: compute [cis(π/7)]^7.
• Error check: is z^(1/2)=r^(1/2)cis(θ/2) the only square root?
• How does cis α cis β encode the cosine compound-angle rule?
• Application: add (2−i)+(−3+4i) as Argand vectors.
• Application: where does i(−2+5i) lie?
• Application: find the distance between z=1+2i and a=4−2i.
• What Cartesian equation represents |z−(2−i)|=3?
• Application: find the bisector |z−1|=|z−5|.
• What does arg(z−(1+i))=π/2 describe?
• Application: describe |z|≤2 and Im z≥0 together.
• Error check: may |z+w| be replaced by |z|+|w| always?
• Application: is z=3+i inside |z−(1+i)|<3?
• Application: what are centre and radius of |z−(n+i)|=n for n>0?
• What does complex conjugation do to an Argand point?
• Application: solve z³=8 in cis form.
• What are the fourth roots of unity?
• Application: sum all fifth roots of unity.
• What regular polygon is formed by the roots of z⁶=64?
• Application: area of the triangle formed by cube roots of 27.
• Error check: why list root arguments in a specified interval?
• Application: divide x³−1 by x−1.
• Application: determine A,B from 3x+1=A(x+1)+Bx.