tions (A-level only) Flashcards","topicId":"cf267704-7cc7-4f60-bfc4-52d1d03de079","topicSlug":"partial-fractions","cards":[{"id":"6c8a2788-a3c5-431a-9dfe-d5e88e1ad01e","cardType":"basic","front":"What is the degree of $4x^2-3x+7$?","back":"The degree is 2.","points":1,"mcqOptions":null},{"id":"d7723ee4-a4a9-4fd6-8588-3ddc14f3942f","cardType":"basic","front":"Why is $\\dfrac{2x+3}{x^2-4}$ a proper algebraic fraction?","back":"The numerator's degree, 1, is lower than the denominator's degree, 2.","points":2,"mcqOptions":null},{"id":"0c3679d9-f3ad-4a20-a9f3-19f3dd7f2c9e","cardType":"cloze","front":"An algebraic fraction is proper when the numerator's degree is [ ].","back":"An algebraic fraction is proper when the numerator's degree is lower than the denominator's degree.","points":null,"mcqOptions":null},{"id":"8d5c19d7-7acc-47e0-be8c-80f5cb02bed4","cardType":"cloze","front":"Before decomposing an improper algebraic fraction, first use [ ].","back":"Before decomposing an improper algebraic fraction, first use polynomial division.","points":null,"mcqOptions":null},{"id":"f55fb85c-e292-43de-a547-c7e5c0395150","cardType":"basic","front":"Rewrite $\\dfrac{x^2+3x+5}{x^2+x-2}$ as a polynomial plus a proper fraction.","back":"$$\\displaystyle 1+\\frac{2x+7}{x^2+x-2}$","points":2,"mcqOptions":null},{"id":"2eb280ff-4278-4c0e-b728-737bdbd23487","cardType":"cloze","front":"Before choosing the partial-fraction form, [ ].","back":"Before choosing the partial-fraction form, factorise the denominator completely.","points":null,"mcqOptions":null},{"id":"5444351d-f411-4bfa-ad95-42eb122f57fe","cardType":"basic","front":"What partial-fraction form is required for denominator $(x-a)(x-b)$, where the factors are distinct?","back":"$$\\displaystyle \\frac{A}{x-a}+\\frac{B}{x-b}$","points":1,"mcqOptions":null},{"id":"a5439a1c-6ea7-4e67-a0e2-2746aaf31ecf","cardType":"basic","front":"After clearing denominators in $\\dfrac{5x+1}{(x-1)(x+2)}=\\dfrac{A}{x-1}+\\dfrac{B}{x+2}$, what identity results?","back":"$$\\displaystyle 5x+1\\equiv A(x+2)+B(x-1)$","points":1,"mcqOptions":null},{"id":"0143530c-2775-4c02-a194-250926d8f612","cardType":"basic","front":"In $5x+1\\equiv A(x+2)+B(x-1)$, why is $x=1$ a useful substitution?","back":"It makes the $B$ term zero, isolating $A$.","points":2,"mcqOptions":null},{"id":"b5d3235a-8462-4519-88ca-add02dfe5645","cardType":"basic","front":"For $\\dfrac{5x+1}{(x-1)(x+2)}$, what coefficient is found by substituting $x=1$?","back":"$$\\displaystyle A=2$","points":1,"mcqOptions":null},{"id":"3398aa93-0ef6-4a61-8cf3-41a40490407b","cardType":"basic","front":"For $\\dfrac{5x+1}{(x-1)(x+2)}$, what coefficient is found by substituting $x=-2$?","back":"$$\\displaystyle B=3$","points":1,"mcqOptions":null},{"id":"a8ec331c-6b89-417c-aedf-d0ffd6e40ab9","cardType":"cloze","front":"A polynomial identity is true for [ ].","back":"A polynomial identity is true for every permitted value of the variable.","points":null,"mcqOptions":null},{"id":"07b95101-c561-4f44-b050-e37ee07b9f9f","cardType":"basic","front":"Where is the decomposition of $\\dfrac{5x+1}{(x-1)(x+2)}$ not valid?","back":"At $x=1$ and $x=-2$, where the denominator is zero.","points":1,"mcqOptions":null},{"id":"7c4348cc-83b4-43e7-9f66-b42102b9301e","cardType":"basic","front":"What partial-fraction terms are required for the repeated factor $(x-a)^2$?","back":"$$\\displaystyle \\frac{A}{x-a}+\\frac{B}{(x-a)^2}$","points":2,"mcqOptions":null},{"id":"08100903-fc

1.2.17 Partial fractions (A-level only) Flashcards

1.2.17 Partial fractions (A-level only) Flashcards