cardType":"basic","front":"Why is $x^3-2x+5$ a polynomial?","back":"Its powers of $x$ are non-negative integers.","points":1,"mcqOptions":null},{"id":"0fc088bb-d7e6-4451-9da7-fcdfd3966834","cardType":"cloze","front":"A rational function has the form $\\text{[...]}$, where $P(x)$ and $Q(x)$ are polynomials and $Q(x)\\neq 0$.","back":"A rational function has the form $\\boxed{\\frac{P(x)}{Q(x)}}$, where $P(x)$ and $Q(x)$ are polynomials and $Q(x)\\neq 0$.","points":null,"mcqOptions":null},{"id":"e8196233-8e44-4baa-b29d-31063038d781","cardType":"basic","front":"Which values must be excluded from $\\frac{3x+1}{(x-2)(x+4)}$?","back":"$x\\neq2$ and $x\\neq-4$.","points":1,"mcqOptions":null},{"id":"3d2c2d4a-0dd6-4d37-bc35-f96d3501136c","cardType":"cloze","front":"A rational function is proper when the numerator's degree is [ ].","back":"A rational function is proper when the numerator's degree is less than the denominator's degree.","points":null,"mcqOptions":null},{"id":"a1f81f9e-4468-4139-b722-efff9641797d","cardType":"basic","front":"Why is $\\frac{2x+3}{x^2-x-6}$ proper?","back":"The numerator has degree 1, below the denominator's degree 2.","points":2,"mcqOptions":null},{"id":"86a4a486-bcf2-45c0-a9da-8d5afa364bbe","cardType":"basic","front":"What must be done before decomposing an improper rational function?","back":"Use polynomial division to produce a proper remainder fraction.","points":1,"mcqOptions":null},{"id":"311344b0-3148-4f31-8f69-cfc9d6bd0dcd","cardType":"cloze","front":"Above a linear denominator, the partial-fraction numerator must be a [ ].","back":"Above a linear denominator, the partial-fraction numerator must be a constant.","points":null,"mcqOptions":null},{"id":"239066b1-0d65-4656-a6e1-1cfdb8df40be","cardType":"basic","front":"What partial-fraction form corresponds to denominator $(x-a)(x-b)$, where the factors are distinct?","back":"$\\frac{A}{x-a}+\\frac{B}{x-b}$","points":1,"mcqOptions":null},{"id":"be0aeb3f-f3de-4820-a61a-d88e35075dca","cardType":"basic","front":"What partial-fraction form is required for denominator $(x-a)^2$?","back":"$\\frac{A}{x-a}+\\frac{B}{(x-a)^2}$","points":1,"mcqOptions":null},{"id":"e641c7c9-0328-4ae0-a777-7dfff3cd7881","cardType":"cloze","front":"A repeated factor $(x-a)^3$ requires terms with denominators [ ].","back":"A repeated factor $(x-a)^3$ requires terms with denominators $x-a$, $(x-a)^2$ and $(x-a)^3$.","points":null,"mcqOptions":null},{"id":"7d0d7564-cdeb-4055-8ded-29f60f898e7e","cardType":"basic","front":"What partial-fraction form is required for denominator $(x+1)(x-2)^2$?","back":"$\\frac{A}{x+1}+\\frac{B}{x-2}+\\frac{C}{(x-2)^2}$","points":2,"mcqOptions":null},{"id":"6e556e98-ba49-45aa-af3c-0d8c56782e90","cardType":"basic","front":"After clearing denominators, why are roots of denominator factors useful substitutions?","back":"Each root usually eliminates all but one unknown constant.","points":2,"mcqOptions":null},{"id":"e406b6ab-4984-484b-8efd-64ca41114314","cardType":"cloze","front":"Two polynomial expressions are identical for every permissible $x$ only when corresponding [ ].","back":"Two polynomial expressions are identical for every permissible $x$ only when corresponding coefficients are equal.","points":null,"mcqOptions":null},{"id":"6004524c-bf7a-4e8a-8993-dc599cc5d7cb","cardType":"basic","front":"From $5x+1=(A+B)x+(A-2B)$, what equations follow by comparing coefficients?","back":"

$A+B=5$
$A-2B=1$

","points":

3.1.8 Algebra and functions (A-level only) Flashcards

3.1.8 Algebra and functions (A-level only) Flashcards