nd Functions (A-level only) Flashcards","topicId":"d93b21b8-093d-40b8-ab43-ae7433d3d9c7","topicSlug":"algebra-and-functions-16","cards":[{"id":"706898f2-754c-44e2-af0a-7c9169f89fb8","cardType":"basic","front":"Evaluate $|3x-7|$ when $x=-2$.","back":"$13$","points":1,"mcqOptions":null},{"id":"8b9459c2-fa12-404a-a5d2-065063441e40","cardType":"basic","front":"Why is $|x|$ never negative for real $x$?","back":"It represents a distance from zero.","points":2,"mcqOptions":null},{"id":"d730cdcf-a33f-4433-9a86-a724618dce81","cardType":"basic","front":"If $x<0$, what expression gives $|x|$?","back":"$-x$","points":1,"mcqOptions":null},{"id":"181ae84f-d758-44e3-8197-b03b1b7b2216","cardType":"basic","front":"What is the shape of the graph $y=|x|$?","back":"V-shaped","points":1,"mcqOptions":null},{"id":"3ba3af7f-7958-47f1-b3e2-45af7d867d2e","cardType":"basic","front":"What line of symmetry does $y=|x|$ have?","back":"The vertical axis, $x=0$.","points":1,"mcqOptions":null},{"id":"4fab266e-154c-46ca-90b1-115d2275384d","cardType":"basic","front":"What happens to the part of $y=ax+b$ below the horizontal axis when forming $y=|ax+b|$?","back":"It is reflected in the horizontal axis.","points":2,"mcqOptions":null},{"id":"1d9ae2b7-bb6c-49a1-917f-9698a706e49e","cardType":"basic","front":"What happens to the part of $y=ax+b$ on or above the horizontal axis when forming $y=|ax+b|$?","back":"It remains unchanged.","points":1,"mcqOptions":null},{"id":"5967b952-ed8a-4ef5-a79e-335c64d147ab","cardType":"cloze","front":"For $a\\ne0$, the vertex of $y=|ax+b|$ occurs at $\\text{[...]}$.","back":"For $a\\ne0$, the vertex of $y=|ax+b|$ occurs at $\\boxed{x=-\\frac{b}{a}}$.","points":null,"mcqOptions":null},{"id":"6231f56c-c657-400e-b62a-3fe4ac990724","cardType":"cloze","front":"The vertical-axis intercept of $y=|ax+b|$ is $\\text{[...]}$.","back":"The vertical-axis intercept of $y=|ax+b|$ is $\\boxed{y=|b|}$.","points":null,"mcqOptions":null},{"id":"9cf23f6a-f905-4f68-97f5-dd4650fe285c","cardType":"basic","front":"What are the gradients of the two arms of $y=|ax+b|$?","back":"$a$ and $-a$","points":1,"mcqOptions":null},{"id":"3cacedca-2955-4e41-b464-98ee7c64ed06","cardType":"basic","front":"Why does $|ax+b|=-3$ have no real solutions?","back":"A modulus is never negative.","points":2,"mcqOptions":null},{"id":"cc3da00c-420f-47dd-94a1-944ae0bf3c58","cardType":"basic","front":"How many solutions does $|ax+b|=0$ normally have when $a\\ne0$?","back":"One, found from $ax+b=0$.","points":1,"mcqOptions":null},{"id":"f6c01c0f-2669-4988-af35-a25f1b9dc0ee","cardType":"cloze","front":"For $k>0$, $|ax+b|=k$ becomes [ ].","back":"For $k>0$, $|ax+b|=k$ becomes $ax+b=k$ or $ax+b=-k$.","points":null,"mcqOptions":null},{"id":"466e48d5-9d79-4571-831d-6fcb00756500","cardType":"basic","front":"Graphically, what represents the solutions of $|ax+b|=k$?","back":"The horizontal coordinates of intersections of $y=|ax+b|$ and $y=k$.","points":1,"mcqOptions":null},{"id":"a86de7d0-b3ad-4180-8dea-bcba25dac6a6","cardType":"cloze","front":"For $k>0$, $|ax+b|$\\text{[...]}$.","back":"For $k>0$, $|ax+b|$\\boxed{-k.","points":null,"mcqOptions":null},{"id":"448b5e69-62d9-4feb-bfe5-ca0a5be80d50","cardType":"cloze","front":"For $k>0$, $|ax+b|\\le k$ is equivalent to $\\text{[...]}$.","back":"For $k>0$, $|ax+b|\\le k$ is equivalent to $\\boxed{-k\\le ax+b\\le k}$.","points":null,"mcqOptions":null},{"id":"25de9e9e-1315-48f6-9ce8-53f2c99a69e2","cardType":"cloze","front":"For $k>0$, $|ax+b|>k$ is equivalent to [ &

3.2.2 Algebra and Functions (A-level only) Flashcards

3.2.2 Algebra and Functions (A-level only) Flashcards