[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-1-en-105":3,"doc-seo-572016-105":53,"doc-detail-572016-en":127},{"code":4,"msg":5,"data":6},0,"success",[7,14,19,24,29,34,39,44,49],{"id":8,"doc_module":9,"doc_module_name":10,"category_name":11,"show_sort_weight":12,"slug":13},11,1,"Template","Presentations",90,"presentations",{"id":15,"doc_module":9,"doc_module_name":10,"category_name":16,"show_sort_weight":17,"slug":18},12,"Resumes",80,"resumes",{"id":20,"doc_module":9,"doc_module_name":10,"category_name":21,"show_sort_weight":22,"slug":23},14,"Invoices",70,"invoices",{"id":25,"doc_module":9,"doc_module_name":10,"category_name":26,"show_sort_weight":27,"slug":28},15,"Posters",60,"posters",{"id":30,"doc_module":9,"doc_module_name":10,"category_name":31,"show_sort_weight":32,"slug":33},16,"Social Media",50,"social-media",{"id":35,"doc_module":9,"doc_module_name":10,"category_name":36,"show_sort_weight":37,"slug":38},17,"Forms",40,"forms",{"id":40,"doc_module":9,"doc_module_name":10,"category_name":41,"show_sort_weight":42,"slug":43},18,"Letters",30,"letters",{"id":45,"doc_module":9,"doc_module_name":10,"category_name":46,"show_sort_weight":47,"slug":48},21,"Paper Templates",5,"papers-templates",{"id":50,"doc_module":9,"doc_module_name":10,"category_name":51,"show_sort_weight":4,"slug":52},158,"General","general-158",{"code":4,"msg":54,"data":55},"ok",{"site_id":56,"language":57,"slug":58,"title":59,"keywords":60,"description":61,"schema_data":62,"social_meta":120,"head_meta":122,"extra_data":124,"updated_unix":126},105,"en","algebra-ii-regents-exam-summary-key-math-topics-radicals-fractions-probability-functions-quadratics","Algebra II Regents Exam Summary - Key Math Topics - Radicals, Fractions, Probability, Functions, Quadratics","","Study guide for Algebra II Regents Exam topics, organized into key algebra and pre-calculus skills. Covers simplifying and combining radicals, adding/subtracting rules, multiplying/dividing radicals, conjugates, rationalizing denominators, and solving equations with radicals by isolating, squaring, then checking. Includes fraction equation-solving with LCD, domain/range and function tests (vertical/horizontal line), inverse functions, domain restrictions, conditional and independent probability formulas, and quadratic equation solving using factoring or the quadratic formula plus discriminant-based root types.",{"@graph":63,"@context":119},[64,80,102],{"@type":65,"itemListElement":66},"BreadcrumbList",[67,71,74,77],{"item":68,"name":69,"@type":70,"position":9},"https://docshare.wps.com","Home","ListItem",{"item":72,"name":10,"@type":70,"position":73},"https://docshare.wps.com/template/",2,{"item":75,"name":51,"@type":70,"position":76},"https://docshare.wps.com/template/general/",3,{"item":78,"name":59,"@type":70,"position":79},"https://docshare.wps.com/template/algebra-ii-regents-exam-summary-key-math-topics-radicals-fractions-probability-functions-quadratics/572016/",4,{"url":78,"name":59,"@type":81,"image":82,"author":87,"headline":59,"publisher":90,"fileFormat":93,"inLanguage":57,"description":61,"dateModified":94,"datePublished":95,"encodingFormat":93,"isAccessibleForFree":96,"interactionStatistic":97},"DigitalDocument",{"url":83,"@type":84,"width":85,"height":86},"https://docshare.wps.com/thumbnails/algebra-ii-regents-exam-summary-key-math-topics-radicals-fractions-probability-functions-quadratics/572016.png","ImageObject",442,249,{"name":88,"@type":89},"Sophia Brooks","Person",{"url":68,"name":91,"@type":92},"DocShare","Organization","application/pdf","2026-10-23","2026-10-13",true,{"@type":98,"interactionType":99,"userInteractionCount":101},"InteractionCounter",{"@type":100},"ViewAction",6,{"@type":103,"mainEntity":104},"FAQPage",[105,111,115],{"name":106,"@type":107,"acceptedAnswer":108},"How do you simplify an expression with radicals?","Question",{"text":109,"@type":110},"Find factors under the radical that include a perfect square, then simplify by moving the square root of the perfect square outside. If there is a coefficient, multiply it through the simplified radical parts.","Answer",{"name":112,"@type":107,"acceptedAnswer":113},"What steps are used to solve equations that include radicals?",{"text":114,"@type":110},"Isolate the radical first, square both sides to remove the radical, then solve for x. Afterward, check solutions in the original equation and reject any that fail.",{"name":116,"@type":107,"acceptedAnswer":117},"How can you determine the type of roots for a quadratic equation without fully solving it?",{"text":118,"@type":110},"Compute the discriminant b2 - 4ac. If it is negative, the roots are imaginary; if zero, roots are equal; if positive, roots are real and distinct.","https://schema.org",{"og:url":78,"og:type":121,"og:title":59,"og:site_name":91,"og:description":61},"article",{"robots":123,"canonical":78},"index,follow",{"doc_id":125,"site_id":56},572016,1792086195,{"code":4,"msg":5,"data":128},{"doc_id":125,"user_id":129,"nickname":88,"user_avatar":130,"doc_module":9,"category_id":50,"category_name":51,"doc_title":59,"doc_description":61,"doc_content":131,"file_id":132,"file_url":133,"file_type":134,"file_size":135,"view_count":101,"is_deleted":4,"is_public":9,"is_downloadable":9,"audit_status":9,"page_count":30,"language":136,"language_code":57,"site_id":56,"html_lang":57,"table_of_contents":137,"faqs":138,"seo_title":139,"seo_description":61,"update_tm":140,"read_time":101},962084925636,"https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d","| Things to Know for the Algebra II Regents Exam |  |\n| --- | --- |\n| RADICALS | Simplifying Radicals: find two numbers that multiply to the number under the radical where one number must be a  perfect square. (If  thereis a coefficient, it will multiply) Ex) 5√32 = 5√16√2 = 5 · 4√2= 20√2 Adding/Subtracting: Two radicals must have the SAME number under the radical. If  so, add/subtract coefficients and leave common radical alone. Ex) √27 − 5√12 = √9√3 - 5√4√3= 3√3 − 5 ∙ 2√3 = -7√3 Multiplying/Dividing: Any two radicals can mult/divide (do not have to be the same) . Mult/divide the coefficients and mult/divide theradicands.\u003Cbr>RULE: √􀢞 · √􀢞  = 􀢞\u003Cbr>Ex) Multiply and express result in simplest radical form:  9√6 ∙ 7√3 = 63√18 = 63√9√2 = 63 ∙ 3√2 = 189√2\u003Cbr>Ex) Divide: 322 = 3√16 = 3 ∙ 4 = 12\u003Cbr>Conjugates: to find the conjugate, change the MIDDLE sign. The product of a number and its conjugate will always be a rational number (no √ ) .        \u003Cbr>Ex) conjugate of 2 + √5 is 2- √5 and (2 + √5)( 2- √5) = 4 – 5 = -1 Rationalizing Denominators: we can never leave a radical in the denominator of a fraction. To get rid of it…\u003Cbr>If there is only one term… Multiply by the same radical on top & bottom Ex)  = ∙2 = 4√22 = 2√2\u003Cbr>If there are two terms… Multiply by the Conjugate of the denominator Equations with Radicals: Step 1 : Get the radical alone. Step 2; Square BOTH sides to get rid of radical. Step 3 : Solve for x and CHECK solution(s) in original eqn.  \u003Cbr>Ex) Solve: √􀝔 + 7 − 􀝔 = 1  CHECK: x = -3\u003Cbr>|\n| FRACTIONS | Equations: Step 1 : Find LCD for all fractions. (FACTOR them if\u003Cbr>necessary) Step 2 : Multiply each fraction by what it is “missing”. Step 3 : Cancel out all common denominators. Step 4 : Solve equation. Step 5 : CHECK Solution(s) and REJECT any that make a fraction undefined.\u003Cbr>Ex) 􀯫~~ ~~1 + 􀯫~~ ~~1 = 􀯫~~ ~~21  􀯫~~ ~~1 + 􀯫~~ ~~1 = (􀯫+12)(􀯫−1)(􀯫1(􀢞)−)􀫚) + (􀯫~~ ~~1(􀢞)~~ ~~+(􀫚􀢞+)~~ ~~􀫚) = (􀯫+12)(􀯫−1)  􀝔 − 1 + 􀝔 + 1 = 2\u003Cbr>CHECK: x = 1 2􀝔 = 2 􀝔 = 1\u003Cbr>makes 􀯫~~ ~~1 undefined since it’s 10 ∴ reject!\u003Cbr>Solution: ∅ (empty set – there is NO solution) |\n|  | Probability Formula: 􀢔􀢛􀢓􀢚􀢕􀢈􀢚􀢋􀢇􀢘􀢒􀢕􀢔􀢌􀢛􀢌􀢓􀢇􀢈􀢜􀢋􀢕􀢘􀢘􀢕􀢇􀢈􀢌􀢒􀢕􀢋􀢛􀢕􀢛􀢚􀢉􀢕􀢚􀢉􀢓􀢕􀢋􀢓􀢙􀢋􀢙 |\n\n\n| PROBABILITY | Conditional Probability: finds the probability of an event (􀜧2)\u003Cbr>occurs GIVEN that another event ( 􀜧1) already occurred…\u003Cbr>􀯉 (􀮾2 􀯔􀯡􀯗 􀮾1 )\u003Cbr>􀜲 (􀜧2 􀜧1 ) =\u003Cbr>􀯉 (􀮾1 )\u003Cbr>Ex) The probability a student takes computers and Spanish is .15. The probability the student takes computers if 0.4. What is the probability t the student takes Spanish given that he/she takes computers?\u003Cbr>\u003Cbr>Answer:\u003Cbr>.15\u003Cbr>0.4\u003Cbr>= .375\u003Cbr>Ex) The table below has information regarding the percent of people (either with or without children in college) and how affordable they feel college is or is not)\u003Cbr>What the probability that person thinks college is too expensive\u003Cbr>that they child college?\u003Cbr>􀯇􀯨􀯠􀯕􀯘􀯥 􀯪ℎ􀯢 ℎ􀯔􀯩􀯘 􀯖ℎ􀯜􀯟􀯗􀯥􀯘􀯡 􀯜􀯡 􀯖􀯢􀯟􀯟􀯘􀯚􀯘 􀮺􀯇􀮽 􀯧ℎ􀯜􀯡􀯞 􀯜􀯧􀯦 􀯘􀯫􀯣􀯘􀯡􀯦􀯜􀯩􀯘 .55 ~~ ~~ = ~~ ~~􀯍􀯢􀯧􀯔􀯟 􀯡􀯨􀯠􀯕􀯘􀯥 ℎ􀯔􀯩􀯜􀯡􀯚 􀯖ℎ􀯜􀯟􀯗􀯥􀯘􀯡 􀯜􀯡 􀯖􀯢􀯟􀯟􀯘􀯚􀯘 .59\u003Cbr>Independent Events: when occurrence of 1 event does not change the occurrence of another.\u003Cbr>If independent then: 􀜲 (􀜣 􀜤) = 􀜲 (􀜣)\u003Cbr>If independent then: 􀜲 ( 􀜣 􀜽􀝊􀝀 􀜤) = 􀜲 (􀜣) ∙ 􀜲 (􀜤)\u003Cbr>Ex) This table shows favorite subjects. Does it appear that choosing math as a favorite subject is dependent on gender?\u003Cbr>If independent then P( math female) = P(math)\u003Cbr>􀯉 ( ℎ 􀯙􀯘􀯠􀯔􀯟􀯘  = P(math)\u003Cbr>􀯉 (􀯠􀯔􀯧ℎ)\u003Cbr>830 = 1857 No!\u003Cbr>∴ 􀝊􀝋􀝐 􀝅􀝊􀝀􀝁􀝌􀝁􀝊􀝀􀝁􀝊􀝐, 􀝉􀝑􀝏􀝐 􀜾􀝁 􀝀􀝁􀝌􀝁􀝊􀝀􀝁􀝊􀝐\u003Cbr>|\n| --- | --- |\n\n| FUNCTIONS | To determine if a relation is a function…\u003Cbr>Graphs: must pass the “Vertical Line Test”(no vertical line can ever intersect the graph more than once)\u003Cbr>Points: All x-values must be DIFFERENT in a function.\u003Cbr>f(x) notation: If f(x) is given and we want to find ”f(some number)”, we substitute the number in place of x on the right side of the equation.\u003Cbr>Ex) If f(x) = 2x2-3x + 1, then f(5) = 2(5)2-3(5) + 1 = 36 Domain: a list of the x-values used in the relation/function.\u003Cbr>Range: a list of the y-values used in the rela","cbCaiidIJbFQFHWE","https://ap.wps.com/l/cbCaiidIJbFQFHWE","pdf",1187072,"English","# Radicals\n## Simplifying, Adding/Subtracting, Multiplying/Dividing\n## Conjugates and Rationalizing Denominators\n## Equations with Radicals\n# Fractions\n## Equation Solving with LCD and Checking\n# Probability\n## Conditional Probability\n## Independent Events\n# Functions\n## Function Tests and Notation\n## Domain/Range and Restricted Domains\n## Inverse Functions and One-to-One\n# Quadratic Equations\n## Solving and Quadratic Roots via Discriminant","[{\"question\":\"How do you simplify an expression with radicals?\",\"answer\":\"Find factors under the radical that include a perfect square, then simplify by moving the square root of the perfect square outside. If there is a coefficient, multiply it through the simplified radical parts.\"},{\"question\":\"What steps are used to solve equations that include radicals?\",\"answer\":\"Isolate the radical first, square both sides to remove the radical, then solve for x. Afterward, check solutions in the original equation and reject any that fail.\"},{\"question\":\"How can you determine the type of roots for a quadratic equation without fully solving it?\",\"answer\":\"Compute the discriminant b2 - 4ac. If it is negative, the roots are imaginary; if zero, roots are equal; if positive, roots are real and distinct.\"}]","Algebra II Regents Exam Summary - Key Math Topics - Radicals, Fractions, Probability, Functions, Quadratics | PDF",1791925064]