1,334 prompts matching "Test me under exam conditions on complex numbers"
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Common Mistakes: Proving that a quadratic expression is positive for every real x
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Spot My Mistake: Forming an equation whose roots are alpha squared and beta squared
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Practice: Factorising a cubic completely once one factor is known
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Common Mistakes: Adding, subtracting and multiplying two polynomials
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Spot My Mistake: The relations between roots and coefficients for a quartic
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Learn: Solving a linear inequality, and reversing the sign on dividing by a negative
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Common Mistakes: The range of values of x for which an expression stays positive
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Learn: The meaning of n factorial, and how to evaluate it
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Practice: Arrangements when some of the objects are identical
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Spot My Mistake: Arrangements in which two particular objects must be kept apart
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Learn: The meaning of n choose r, and how to evaluate it
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Practice: Choosing a committee that must contain one particular person
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Common Mistakes: Selections in which at least one of a kind must appear
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Learn: The Pythagorean identity, sin squared plus cos squared equals one
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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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Practice: Solving an equation of the form sin of 2x equals a given value
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Spot My Mistake: Solving an equation by first applying a Pythagorean identity
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Practice: The equation of a line through a point with a given gradient
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Common Mistakes: The angle between two lines found from their gradients
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Learn: The equation of a circle with its centre at the origin
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