1,206 prompts matching "Explaining why sum to infinity only works for |r| < 1"
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Worked Example: Finding one over alpha plus one over beta
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Spot My Mistake: Forming an equation whose roots are alpha squared and beta squared
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Worked Example: Evaluating a polynomial by substitution
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Practice: Factorising a cubic completely once one factor is known
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Spot My Mistake: The relations between roots and coefficients for a quartic
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Worked Example: Solving a quadratic inequality by sketching the parabola
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Practice: Solving an inequality with the unknown in the denominator
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Learn: The meaning of n factorial, and how to evaluate it
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Worked Example: The number of arrangements of n different objects in a row
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Learn: The meaning of n choose r, and how to evaluate it
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Worked Example: The difference between a permutation and a combination
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Practice: The compound angle formula for cosine of A minus B
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Spot My Mistake: The double angle formula for sine
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Worked Example: Solving cos x equals a negative value, and finding both solutions
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Practice: Solving an equation of the form sin of 2x equals a given value
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Worked Example: The shape, period and range of the cosine curve
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Spot My Mistake: The general form ax plus by plus c equals nought
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Worked Example: The equation of a circle with a given centre and radius
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Spot My Mistake: The equation of the tangent to a circle at a point on it
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Practice: The ellipse in standard form, and its two axes
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