nd functions (A-level only) Flashcards","topicId":"d7f4132b-f1c9-4715-8e71-33ad639e4c9d","topicSlug":"algebra-and-functions-22","cards":[{"id":"b19fab8d-5013-4771-959f-acfe6276fa32","cardType":"basic","front":"Evaluate $|3-8|+|-4|$.","back":"$9$","points":1,"mcqOptions":null},{"id":"c381fd37-3123-4897-a8c3-f7b7abea4b69","cardType":"cloze","front":"For every real number $A$, $\\text{[...]}$.","back":"For every real number $A$, $\\boxed{|A|\\ge 0}$.","points":null,"mcqOptions":null},{"id":"ed3b58b8-d335-405d-913d-7237e7b44472","cardType":"cloze","front":"$$|A|=0$ only when $\\text{[...]}$.","back":"$$|A|=0$ only when $\\boxed{A=0}$.","points":null,"mcqOptions":null},{"id":"5d7e70d0-c125-47a3-acf2-2cd238451867","cardType":"basic","front":"How many real solutions does $|2x+1|=-3$ have?","back":"No real solutions, since modulus cannot be negative.","points":1,"mcqOptions":null},{"id":"0b5e9915-d98d-4220-8207-9234bbee7b99","cardType":"basic","front":"Solve $|x-4|=3$.","back":"$x=1$ or $x=7$.","points":2,"mcqOptions":null},{"id":"94416aab-9a97-4572-a960-9b37154e7ecc","cardType":"basic","front":"What is the shape of the graph $y=|x|$?","back":"A V-shape.","points":1,"mcqOptions":null},{"id":"ca0fdd85-de79-4f2f-be08-a6820a4d74df","cardType":"basic","front":"Where is the vertex of $y=|x|$?","back":"At the origin, $(0,0)$.","points":1,"mcqOptions":null},{"id":"b3584db9-ccfb-4f9b-b0f5-c760a20326ed","cardType":"cloze","front":"To obtain $y=|x|$, the part of $y=x$ below the horizontal axis is [ ].","back":"To obtain $y=|x|$, the part of $y=x$ below the horizontal axis is reflected upwards.","points":null,"mcqOptions":null},{"id":"c2dd0367-3dd3-4b55-9d76-873ba1f80300","cardType":"basic","front":"Where is the vertex of $y=|ax-b|$, where $a\\ne0$?","back":"At $\\left(\\frac{b}{a},0\\right)$.","points":1,"mcqOptions":null},{"id":"9e4942e3-b5b6-4e0d-8084-ab9eff82870a","cardType":"cloze","front":"Each branch of $y=|ax-b|$ has gradient magnitude $\\text{[...]}$.","back":"Each branch of $y=|ax-b|$ has gradient magnitude $\\boxed{|a|}$.","points":null,"mcqOptions":null},{"id":"60e2c7d4-4378-42fb-9a3c-b2e477d4e335","cardType":"basic","front":"Write $f(x)=|2x-4|$ in piecewise form.","back":"$$f(x)=\\begin{cases}4-2x,&x<2,\\\\2x-4,&x\\ge2.\\end{cases}$$","points":3,"mcqOptions":null},{"id":"9a00c9e8-fd8b-4392-8aa4-3ee74bd7c711","cardType":"basic","front":"For $c>0$, which two equations must be solved when $|A|=c$?","back":"

$A=c$
$A=-c$

","points":3,"mcqOptions":null},{"id":"ac67dfb6-4504-4d6c-a73c-36212f406dea","cardType":"basic","front":"Solve $|3x-5|=7$.","back":"$x=4$ or $x=-\\frac{2}{3}$.","points":3,"mcqOptions":null},{"id":"d41a36ba-800b-477c-9c20-ad9fc5d98b56","cardType":"cloze","front":"For $c>0$, $|A|$\\text{[...]}$.","back":"For $c>0$, $|A|$\\boxed{-c.","points":null,"mcqOptions":null},{"id":"25fbf0b2-3ac7-4bc6-820b-ee2938286d7e","cardType":"basic","front":"Solve $|2x-4|<3$.","back":"$\\frac{1}{2}.","points":3,"mcqOptions":null},{"id":"8f90845e-aada-47f9-82c8-cb4551142a41","cardType":"basic","front":"Why are the endpoints excluded when solving $|2x-4|<3$?","back":"Because $<$ is a strict inequality.","points":2,"mcqOptions":null},{"id":"b553599b-edd1-4dab-9918-a3fae3a280a6","cardType":"cloze","front":"For $c\\ge0$, $|A|\\le c\\Longleftrightarrow$ $\\text{[...]}$.","back":"For $c\\ge0$, $|A|\\le c\\Longleftrightarrow$ $\\boxed{-c\\le A\\le c}$.","points":null,"mcqOptions":null},{"id":"3b474c11-880c-44c5-801a-85f353f8ad4f","cardType":"ba

3.1.6 Algebra and functions (A-level only) Flashcards

3.1.6 Algebra and functions (A-level only) Flashcards