1,141 prompts matching "IGCSE Additional Maths Y10: A cubic with a repeated factor — IGCSE Exam Practice"
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Practice: Rationalising a denominator of the form root a
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Explain Back: Rationalising a denominator of the form a plus root b using the conjugate
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Show All Working: Expressing a number in the form a root b
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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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Practice: Converting between index form and logarithm form
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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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Practice: The condition for a quadratic equation to have equal roots
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Explain Back: The range of values of k for which the roots are real
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Show All Working: Solving a quadratic by completing the square
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Common Mistakes: Proving that a quadratic expression is positive for every real x
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Worked Example: Finding one over alpha plus one over beta
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Practice: Finding alpha minus beta from the sum and the product
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Explain Back: Finding alpha squared beta plus alpha beta squared
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Show All Working: Finding a coefficient given a stated relation between the roots
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Worked Example: Evaluating a polynomial by substitution
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Common Mistakes: Adding, subtracting and multiplying two polynomials
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