nd functions (A-level only) Flashcards","topicId":"07eae98f-8800-4beb-b283-80b5e3f8376e","topicSlug":"algebra-and-functions-17","cards":[{"id":"f5ef277d-ad6c-4874-84a7-54cd74e5e788","cardType":"basic","front":"Factorise $x^2+3x-10$.","back":"$$\\strong{(x-2)(x+5)}$","points":1,"mcqOptions":null},{"id":"11aa8384-4c8f-47e3-bb18-b0850b921c6d","cardType":"cloze","front":"The difference of two squares factorises as $\\text{[...]}$.","back":"The difference of two squares factorises as $\\boxed{a^2-b^2=(a-b)(a+b)}$.","points":null,"mcqOptions":null},{"id":"4b083e2e-4cba-461d-a344-3d7fe7034cf6","cardType":"basic","front":"Factorise $2x^2-7x+3$.","back":"$$\\strong{(2x-1)(x-3)}$","points":2,"mcqOptions":null},{"id":"13757ab4-6b27-4e60-8dcf-fce598cec65e","cardType":"cloze","front":"A rational expression $\\frac{P(x)}{Q(x)}$ requires $\\text{[...]}$.","back":"A rational expression $\\frac{P(x)}{Q(x)}$ requires $\\boxed{Q(x)\\neq0}$.","points":null,"mcqOptions":null},{"id":"e8bf2e40-fd61-4910-b55e-fd3fe7d2f4a4","cardType":"basic","front":"When is a rational expression undefined?","back":"When its denominator equals zero.","points":1,"mcqOptions":null},{"id":"2c38193b-9393-432e-bac8-71ec9bda0b69","cardType":"basic","front":"Which values are excluded from the domain of $\\frac{x^2-9}{x^2+x-6}$?","back":"$x\\neq-3,\\ 2$","points":1,"mcqOptions":null},{"id":"7395fcd6-5d8c-4917-a8b6-55207edfd518","cardType":"basic","front":"Why can the $x$ terms in $\\frac{x+2}{x+5}$ not be cancelled?","back":"They are terms in sums, not common factors.","points":2,"mcqOptions":null},{"id":"b570b4dd-de7a-4579-972c-51b1e906237f","cardType":"cloze","front":"The cancellation $\\frac{AB}{AC}=\\frac{B}{C}$ is valid provided $\\text{[...]}$.","back":"The cancellation $\\frac{AB}{AC}=\\frac{B}{C}$ is valid provided $\\boxed{A\\neq0}$.","points":null,"mcqOptions":null},{"id":"aac273c9-a8a9-4074-8658-de099829a9dc","cardType":"basic","front":"Simplify $\\frac{x^2-9}{x^2+x-6}$.","back":"$\\frac{x-3}{x-2}$","points":2,"mcqOptions":null},{"id":"23dbcc00-2284-4436-ad80-e7d039a1bfce","cardType":"basic","front":"Why does $x=-3$ remain excluded after cancelling $x+3$?","back":"It made the original denominator zero.","points":2,"mcqOptions":null},{"id":"2f0eded1-2915-4af9-bb50-107e74e64c79","cardType":"basic","front":"Simplify $\\frac{3x^2-12x}{x^2-16}$.","back":"$\\frac{3x}{x+4}$","points":2,"mcqOptions":null},{"id":"72c145e0-1c7d-44d1-b44a-078c5d14a95c","cardType":"basic","front":"Which values are excluded from the domain of $\\frac{3x^2-12x}{x^2-16}$?","back":"$x\\neq4,\\ -4$","points":1,"mcqOptions":null},{"id":"fc27ac86-e14b-4b40-99b7-bae82171e3f8","cardType":"basic","front":"Simplify $\\frac{x^2-4x}{x^2-16}$.","back":"$\\frac{x}{x+4}$","points":2,"mcqOptions":null},{"id":"1c0c7b44-13d7-43d4-86eb-af8c6c38e15f","cardType":"cloze","front":"Polynomial division satisfies $\\text{[...]}$.","back":"Polynomial division satisfies $\\boxed{\\text{dividend}=(\\text{divisor})(\\text{quotient})+\\text{remainder}}$.","points":null,"mcqOptions":null},{"id":"9b70c9b6-b4e8-4fb6-8813-042993aff662","cardType":"basic","front":"How must the degree of a polynomial division remainder compare with the divisor?","back":"It must be lower than the divisor's degree.","points":1,"mcqOptions":null},{"id":"f968308d-409a-4219-a02d-69b00cd5ce52","cardType":"basic","front":"How should $x^3-4x+1$ be written for long division?","back":"$x^3+0x^2-4x+1$","points":1,"mcqOptions":null},{"id":"2fb4036c-ab71-4f83-bd22-219a05dbfe2a","cardType":"basic","front":"What is the first quotient term when $2x^3+3x^2-11x-6$ is divided by $x+3$?","back":"$2x^2$","points":1,"mcqOptions":null},{"id":"62d28fe8-d322-47f0-9bb4-3244872b846c","cardType":"basic","front":"Divide $2x^3+3x^2-11x-6$ by $x+3$.","ba

3.1.1 Algebra and functions (A-level only) Flashcards

3.1.1 Algebra and functions (A-level only) Flashcards