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Coordinate geometry and series: lesson checks flashcards

This deck has 8 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.

• Perpendicular gradients are negatives of each other.Spot the error
• Find the equation of the line through (−1, 4) perpendicular to the line 3x + y − 2 = 0, giving your answer in the form ax + by + c = 0.Check
• A line that meets a circle meets it twice.Spot the error
• Find the centre and radius of the circle x² + y² + 8x − 2y + 8 = 0, and state whether the point (−1, 1) lies on it.Check
• Eliminating the parameter changes nothing.Spot the error
• The curve C is given by x = 2 cos t, y = 2 sin t for 0 ≤ t ≤ π. Find the Cartesian equation of C, and state precisely which points of that Cartesian curve C consists of.Check
• The coefficient of x^r in (a + bx)ⁿ is nCr times b^r.Spot the error
• Find the first three terms, in ascending powers of x, of (2 − x)⁵, and use them to estimate 1.998⁵.Check
• The expansion of (1 + x)⁻¹ works for every x.Spot the error
• Expand (1 + 3x)⁻² in ascending powers up to x², state the validity, and use the expansion to estimate 1.03⁻².Check
• A decreasing sequence must eventually go below zero.Spot the error
• A sequence has u_n = 40 − 3n. Find u₁₀, determine when terms first go negative, and evaluate Σu_n for n from 1 to 4.Check
• The 10th term of an arithmetic sequence is a + 10d.Spot the error
• Prove that the sum of the first n natural numbers is n(n + 1)/2, and evaluate the sum of the first 100.Check
• For the series 5 + 4 + 3.2 + …, find the sum to infinity, and the sum of the first 10 terms to 4 significant figures.Check

The lessons these cards come from

• Arithmetic series
• Circles
• Geometric series
• Parametric equations
• Sequences and sigma notation
• Straight lines
• The binomial expansion
• The general binomial expansion

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