-level only) Flashcards","topicId":"16ccbc5b-26c7-4618-8df6-cda22620ea5b","topicSlug":"partial-fractions","cards":[{"id":"0f8c1937-9b19-400b-bc32-0122e7dccb4f","cardType":"cloze","front":"A rational function has [ ].","back":"A rational function has polynomials in both its numerator and denominator.","points":null,"mcqOptions":null},{"id":"013215ed-d99d-4cbd-acdc-f66d692c8f55","cardType":"basic","front":"Is $\\frac{2x+1}{x^2+3x+2}$ proper or improper?","back":"Proper - numerator degree $1$ is less than denominator degree $2$.","points":2,"mcqOptions":null},{"id":"36d60ad2-cd63-4fd8-8a20-052ee134adb4","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":"4883ee8c-3974-4098-973c-7bb0e614b72b","cardType":"cloze","front":"Before decomposing an improper rational function, use [ ].","back":"Before decomposing an improper rational function, use polynomial division.","points":null,"mcqOptions":null},{"id":"1f7cec7e-5cc0-4e74-bc32-fd653e79c2e2","cardType":"basic","front":"What should be done to a denominator before choosing a partial-fraction form?","back":"Factorise it completely.","points":1,"mcqOptions":null},{"id":"032bf953-4764-46f4-9375-2d292b907861","cardType":"basic","front":"What partial-fraction form corresponds to denominator $(x-a)(x-b)$, where $a\\ne b$?","back":"$\\frac{A}{x-a}+\\frac{B}{x-b}$","points":1,"mcqOptions":null},{"id":"a4ec4cf6-26e1-4bc6-a433-d450e955a9e2","cardType":"basic","front":"What partial-fraction form corresponds to denominator $(x-a)(x-b)(x-c)$?","back":"$\\frac{A}{x-a}+\\frac{B}{x-b}+\\frac{C}{x-c}$","points":1,"mcqOptions":null},{"id":"092740ff-23b4-45e6-8699-2fd7c1df8883","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":"2fa3db42-2d36-451e-9ed4-86ee6ce1d1c9","cardType":"basic","front":"What partial-fraction form is required for denominator $(x+3)^2(x-4)$?","back":"$\\frac{A}{x+3}+\\frac{B}{(x+3)^2}+\\frac{C}{x-4}$","points":2,"mcqOptions":null},{"id":"a53878df-6ea2-4b38-b783-a72899440a91","cardType":"cloze","front":"After clearing the denominator, the resulting equation is an [ ], true for every permitted value of $x$.","back":"After clearing the denominator, the resulting equation is an identity, true for every permitted value of $x$.","points":null,"mcqOptions":null},{"id":"48b69386-69b2-497e-9402-f00834275479","cardType":"basic","front":"Why are roots of denominator factors substituted into the cleared identity?","back":"They eliminate terms, isolating individual constants.","points":2,"mcqOptions":null},{"id":"7b8abaf3-3ca0-4bd4-a959-6a9f04e2a10a","cardType":"cloze","front":"Values excluded from the original fractions may be substituted into the [ ].","back":"Values excluded from the original fractions may be substituted into the cleared polynomial identity.","points":null,"mcqOptions":null},{"id":"f7f33dd5-6baf-457a-a4ce-0b851a42b158","cardType":"basic","front":"Use polynomial division to rewrite $\\frac{x^2+3x+5}{x^2+x-2}$ as a polynomial plus a proper fraction.","back":"$1+\\frac{2x+7}{x^2+x-2}$","points":2,"mcqOptions":null},{"id":"e4498b94-d107-4cd8-8984-537f472cfdf6","cardType":"basic","front":"In $5x

1.5.10 Partial fractions (A-level only) Flashcards

1.5.10 Partial fractions (A-level only) Flashcards