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Vectors and numerical methods: lesson checks flashcards

This deck has 5 check-yourself questions and 3 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.

• A sign change between a and b means exactly one root between a and b.Spot the error
• Show that x³ + x − 5 = 0 has a root in (1, 2), and use x_n+1 = (5 − x_n)^1/3 with x₀ = 1.5 to find the root to 3 decimal places.Check
• Show that x = e^−x has a root between 0.5 and 0.6, and find it to 5 decimal places using Newton-Raphson on f(x) = x − e^−x with x₀ = 0.6.Check
• The trapezium rule always underestimates, because the chords cut the corners off the curve.Spot the error
• Use the trapezium rule with 3 strips to estimate ∫₀³ 1/(1 + x) dx, and state with a reason whether the estimate is above or below the true value.Check
• Given a = 5i − 12j, find |a|, the unit vector in the direction of a, and a vector of magnitude 39 parallel to a.Check
• Adding a third dimension needs a whole new toolkit.Spot the error
• P is (2, −1, 4) and Q is (4, 3, 8). Find |PQ|, the midpoint of PQ, and a unit vector parallel to PQ.Check

The lessons these cards come from

• Locating roots and iteration
• The Newton-Raphson method
• The trapezium rule
• Vectors in three dimensions
• Vectors in two dimensions

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