Maths › Flashcards › Further Pure 2: lesson checks, part 1

Further Pure 2: lesson checks, part 1 flashcards

This deck has 7 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.

Further Maths · 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.

• Closure just means the answer lies somewhere sensible, in the universal set if nowhere else.Spot the error
• In the group of integers modulo 8 under addition, find the order of the element 6.Check
• A group of order 12 could have a subgroup of order 5, since 5 is smaller than 12.Spot the error
• A group has order 15. Explain why it cannot contain a subgroup of order 6.Check
• An integral of sin to the tenth power would take ten separate integrations by parts.Spot the error
• Given nI_n = (n − 1)I_n−2 with I₁ = 1, find I₃.Check
• The length of a curve between two points is found by integrating y with respect to x.Spot the error
• A curve is given parametrically by x = 5 cos t, y = 5 sin t. Write down the integrand for its arc length, and hence its total length for 0 ≤ t ≤ 2π.Check
• If both partial derivatives vanish at a point, the surface has a maximum or a minimum there, just as a curve would.Spot the error
• For f(x, y) = x³y − 4y², find f_x, f_y and the mixed derivative f_xy.Check
• Every real matrix has a real direction it leaves on its own line.Spot the error
• A 2 × 2 matrix has eigenvalues 3 and −4. Write down its trace and determinant.Check
• Every square matrix can be written as PDP⁻¹ with D diagonal.Spot the error
• A 2 × 2 matrix M has trace 6 and determinant 5. Write down the equation Cayley-Hamilton gives, and hence M⁻¹ in terms of M and I.Check

The lessons these cards come from

• Arc length and surface area
• Diagonalisation and the Cayley-Hamilton theorem
• Eigenvalues and eigenvectors
• Functions of two variables
• Groups and their axioms
• Reduction formulae
• Subgroups, Lagrange's theorem and isomorphism

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.