Maths › Flashcards › Proof and algebra: lesson checks

Proof and algebra: lesson checks flashcards

This deck has 10 check-yourself questions and 7 spot-the-error cards. The misconception each lesson corrects, and its check-yourself question with the worked answer. Rate each answer, and the card comes back sooner or later depending on how you rated it.

Years 12–13 · all 584 maths cards

How the five kinds differ

Standard results ask you to recall a formula or a value. Definitions ask you to state a mathematical term precisely. Recall prompts ask for a rule, condition or method. Check yourself cards are a short question with its answer. Spot the error cards ask you to correct a statement that is wrong.

Every card in this deck

Choose any card to try it in the player above. Each card links to the lesson that teaches it.

• Checking a statement for the first few numbers proves it.Spot the error
• Prove that n³ − n is divisible by 6 for every integer n.Check
• To disprove a claim you must show it fails every time.Spot the error
• Prove by contradiction that there are no positive integers a and b with 21a + 14b = 1.Check
• √(a + b) = √a + √b.Spot the error
• Evaluate 32^3/5 without a calculator, and express 6/(√7 − 1) in the form a + √b.Check
• Express 3x² + 6x − 2 in the form a(x + p)² + q, state the minimum point, and use the discriminant to say how many real roots 3x² + 6x − 2 = 0 has.Check
• You can always multiply both sides of an inequality by x.Spot the error
• Find the set of values of x for which x² + 3x − 10 ≥ 0, giving the answer in set notation.Check
• Show that (x + 1) is a factor of f(x) = x³ − 7x − 6, and hence factorise f(x) completely.Check
• Replacing x by (x + a) moves the graph a units to the right.Spot the error
• The curve y = 3/x is transformed to y = 3/x − 2. State the equations of the asymptotes of the new curve, and find where it crosses the x-axis.Check
• With f(x) = 3x − 2 on all of ℝ, find f⁻¹(x), and solve |3x − 2| = 4.Check
• A squared bracket in the denominator needs just one fraction.Spot the error
• Express (7x − 1)/((x − 1)(x + 3)) in partial fractions.Check
• The best model is the one that fits the data most closely.Spot the error
• The value of a machine is modelled by V = 500 + 7500e^−0.25t pounds after t years. State the initial value, the long-term value, and what the 500 represents.Check

The lessons these cards come from

• Disproof and proof by contradiction
• Functions in modelling
• Functions, inverses and the modulus
• Graphs, proportion and transformations
• Indices and surds
• Partial fractions
• Polynomials and the factor theorem
• Quadratic functions
• Simultaneous equations and inequalities
• The structure of proof: deduction and exhaustion

Your progress is saved in this browser unless you sign in, as it is for the revision checklist. For offline revision, the Anki decks and printable packs have the same cards.