1,238 prompts matching "a GP with first term 100 and common ratio 0.5, find the sum to infinity"
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Explain Back: Rationalising a denominator of the form a plus root b using the conjugate
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Common Mistakes: Solving an equation in which the unknown sits under a root
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Worked Example: Simplifying an expression carrying both a negative and a fractional index
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Explain Back: The laws of logarithms for a product and for a quotient
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Show All Working: Solving a logarithmic equation and rejecting the invalid root
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Common Mistakes: Solving an exponential equation using logarithms
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Worked Example: The discriminant, and what each of its three cases means
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Common Mistakes: Proving that a quadratic expression is positive for every real x
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Common Mistakes: Symmetric functions when the three roots of a cubic are involved
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Common Mistakes: Three roots in geometric progression in a cubic
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Common Mistakes: The range of values of x for which an expression stays positive
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Worked Example: The difference between a permutation and a combination
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Explain Back: Choosing a committee with a stated number from each of two groups
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Show All Working: Counting the handshakes, or the lines joining n points
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Common Mistakes: Selections in which at least one of a kind must appear
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Worked Example: The identities for one plus tan squared and one plus cot squared
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Show All Working: The half angle formulae and the t-substitution
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Common Mistakes: Expressing a cos x plus b sin x in the form R cos of x minus alpha
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Worked Example: Solving cos x equals a negative value, and finding both solutions
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Common Mistakes: Giving the general solution of a trigonometric equation
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