Maths › Flashcards › Further vectors, hyperbolics and polars: lesson checks
Further vectors, hyperbolics and polars: lesson checks flashcards
This deck has 6 check-yourself questions and 4 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.
- A plane needs three separate equations to describe, one for each coordinate.Spot the error
- Does the point (7, −1, 5) lie on the line r = (1, 2, 3) + λ(2, −1, 1)?Check
- To find where a line meets a plane you must solve three simultaneous equations in three unknowns.Spot the error
- Find the acute angle between the planes x + 2y + 2z = 11 and x − z = −1, to one decimal place.Check
- Functions with names like sinh and cosh must be periodic like sine and cosine.Spot the error
- Using the definitions, find the exact values of cosh(ln 3) and sinh(ln 3), and verify the identity connecting them.Check
- Differentiate y = cosh 3x, and state the gradient at x = 0.Check
- Every point has exactly one pair of polar coordinates.Spot the error
- Convert the polar point (2, π/6) to cartesian coordinates, exactly.Check
- Find the area swept by r = 3 as θ runs from 0 to 2π/3.Check
The lessons these cards come from
- Areas with polar coordinates
- Calculus with hyperbolic functions
- Hyperbolic functions and identities
- Intersections, angles and distances
- Lines and planes in three dimensions
- Polar curves
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