1,320 prompts matching "Finding the identity element from a rule such as a*b = a + b - 3"
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Common Mistakes: Solving an equation in which the unknown sits under a root
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Learn: The multiplication and division laws of indices used together
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Explain Back: The laws of logarithms for a product and for a quotient
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Spot My Mistake: The power law of logarithms
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Show All Working: Solving a logarithmic equation and rejecting the invalid root
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Final Revision: Sketching the graph of a logarithmic function
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Explain Back: The range of values of k for which the roots are real
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Spot My Mistake: Forming a new equation whose roots are the reciprocals of the original
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WAEC Prep: Forming an equation whose roots are each two more than the original
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Show All Working: Solving a quadratic by completing the square
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Common Mistakes: Symmetric functions when the three roots of a cubic are involved
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Final Revision: Checking a symmetric-function answer by solving the equation outright
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Learn: The degree of a polynomial and its leading coefficient
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Spot My Mistake: The factor theorem for a divisor of the form ax minus b
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Final Revision: The zeros of a polynomial and where its graph cuts the x-axis
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Worked Example: The sum of the products of the roots of a cubic taken two at a time
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Spot My Mistake: The relations between roots and coefficients for a quartic
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Final Revision: Checking that the roots found satisfy the original equation
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Learn: Solving a linear inequality, and reversing the sign on dividing by a negative
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Worked Example: Solving a quadratic inequality by sketching the parabola
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