[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-411632-105":59,"doc-detail-411632-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","complex-number-system-polynomial-expressions-equations-and-inequalities-functions-data-and-probability","Complex Number System, Polynomial Expressions, Equations and Inequalities, Functions, Data and Probability","","Mathematics learning objectives covering core algebra concepts and problem-solving skills. Students represent and use complex numbers, simplify imaginary-number expressions, apply complex ideas to polynomial identities and quadratic equations, and perform arithmetic with complex quantities. The document also specifies work with polynomial and rational expressions, including factoring, simplification, and relationships between zeros and factors. Additional objectives include creating and solving varied equation types, interpreting functions, modeling with multiple representations, and analyzing data using graphs and scatter plots.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/complex-number-system-polynomial-expressions-equations-and-inequalities-functions-data-and-probability/411632/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/complex-number-system-polynomial-expressions-equations-and-inequalities-functions-data-and-probability/411632.png","ImageObject",300,407,{"name":92,"@type":93},"hdkawk","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-06","2026-09-28",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",16,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What complex number skills are emphasized in this document?","Question",{"text":113,"@type":114},"Students learn to represent and use imaginary numbers in equivalent forms, simplify/evaluate expressions involving imaginary numbers, and perform arithmetic with complex numbers. They also apply complex-number concepts to polynomial identities and quadratic equations to solve problems.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What abilities are listed for polynomial and rational expressions?",{"text":118,"@type":114},"Students practice arithmetic operations on polynomials, solve equations involving rational expressions, and understand the relationship between zeros and factors. They also rewrite rational expressions and use polynomial identities to solve, including simplifying or factoring expressions involving polynomials.",{"name":120,"@type":111,"acceptedAnswer":121},"How does the document address functions and data topics?",{"text":122,"@type":114},"It requires interpreting and applying functions using context and notation, creating and analyzing functions with graph/table/equation representations, and modeling relationships between quantities. For data, it includes analyzing patterns in sets of data, summarizing single- and two-variable data, and analyzing/interpreting scatter plots to make predictions such as regression.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},411632,1791055457,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":19,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":52,"preview_page_count":4},3985747859855,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","| Concepts | Competencies | Key Vocabulary |\n| --- | --- | --- |\n| Complex Number System | Represent and/or use imaginary numbers in equivalent forms.\u003Cbr>Simplify/evaluate expressions involving imaginary numbers.\u003Cbr>Perform arithmetic operations and apply to complex numbers.\u003Cbr>Apply concepts of complex numbers in polynomial identities and quadratic equations to solve problems.\u003Cbr>References:\u003Cbr>PACCS\u003Cbr>(CC.2.1.HS.F.6),(CC.2.1.HS.F.7)\u003Cbr>EC\u003Cbr>(A2.1.1.1.1),(A2.1.1.1.2),(A2.1.1.2.1),(A2.1.1.2.2) | Absolute Value Arithmetic Sequence Asymptote Binomial Combination Common Logarithm\u003Cbr>Complex Number System Compound Events Dependent/Independent Events\u003Cbr>Difference of Squares Dilation\u003Cbr>Domain Exponential\u003Cbr>Exponential Decay\u003Cbr>Exponential Function\u003Cbr>Exponential Growth Expression\u003Cbr>Extrema Fundamental Counting Principle\u003Cbr>Geometric Sequence Imaginary Number Increasing/Decreasing Intervals\u003Cbr>Intercept\u003Cbr>Inverse of a Function Linear\u003Cbr>Logarithm Mean Median Mode Monomial\u003Cbr>Natural Logarithm Negative Exponents Observational Study Odds\u003Cbr>Outcomes\u003Cbr>Perfect Square Trinomial Permutation Polynomial\u003Cbr>Polynomial Identity |\n| Polynomial and Rational Expressions | Perform arithmetic operations on polynomials Solve equations involving rational expressions\u003Cbr>Understand the relationship between zeros and factors of polynomials\u003Cbr>Rewrite rational expressions\u003Cbr>Use polynomial identities to solve problems Simplify/factor expressions involving polynomials\u003Cbr>References:\u003Cbr>PACCS\u003Cbr>(CC.2.1.HS.F1),(CC.2.1.HS.D1),(CC.2.1.HS.D2),(CC.2.1.HS.D.3),(CC.2.1.HS.D.4),(CC.2.1.HS.D.5),(CC.2.1.HS.D.6),\u003Cbr>EC |  |\n\n\n| Concepts | Competencies | Key Vocabulary |\n| --- | --- | --- |\n|  | (A2.1.2.1.2),(A2.1.3.1.2),(A2.1.2.2.1),(A2.1.2.2.2) | Probability\u003Cbr>Quadratic Formula Quadratic Function Radical Functions Range (Note: 2 different meanings)\u003Cbr>Rational Functions Reflection Regression Models Root Functions Sample Survey Scatterplot Standard Deviation Statistical Experiment Transformation\u003Cbr>Translations\u003Cbr>Trinomial Unit Circle |\n| Equations and Inequalities | Create and/or solve equations (including literal, polynomial, rational, radical, exponential, and logarithmic) both algebraically and graphically.\u003Cbr>Use and/or explain reasoning while solving equations, and justify the solution method.\u003Cbr>Determine how a change in one variable relates to a change in a second variable.\u003Cbr>Use exponents, roots, and/or absolute values to represent equivalent forms or to solve problems.\u003Cbr>References:\u003Cbr>PACCS\u003Cbr>(CC.2.1.HS.F.1),(CC.2.1.HS.D.1),(CC.2.1.HS.D.2), EC\u003Cbr>(A2.1.2.1.3),(A2.1.2.1.4),(A2.1.2.2.2),(A2.1.3.1.1),\u003Cbr>(A2.1.3.1.3),(A2.1.3.1.4),(A2.1.3.2.1),(A2.1.3.2.2),\u003Cbr>(A2.2.2.1.2),(A2.2.2.1.3) |  |\n| Equations and Inequalities | Create and/or solve equations (including literal, polynomial, rational, radical, exponential, and logarithmic) both algebraically and graphically.\u003Cbr>Use and/or explain reasoning while solving equations, and justify the solution method.\u003Cbr>Determine how a change in one variable relates to a change in a second variable.\u003Cbr>Use exponents, roots, and/or absolute values to represent equivalent forms or to solve problems.\u003Cbr>(CC.2.2.HS.D.7),(CC.2.2.HS.D.8),(CC.2.2.HS.D.9),(CC.2.2.HS.D.10)\u003Cbr>EC\u003Cbr>(A2.1.2.1.3),(A2.1.2.1.4),(A2.1.2.2.2),(A2.1.3.1.1),\u003Cbr>(A2.1.3.1.3),(A2.1.3.1.4),(A2.1.3.2.1),(A2.1.3.2.2),\u003Cbr>(A2.2.2.1.2),(A2.2.2.1.3) |  |\n| Functions | Use the concept and notation of function to interpret and apply them in terms of their context. |  |\n\n\n| Concepts | Competencies | Key Vocabulary |\n| --- | --- | --- |\n|  | Create and/or analyze functions using multiple representations (graph, table, and equation) .\u003Cbr>Create a function and/or sequence that models a relationship between two quantities.\u003Cbr>Create new functions from existing functions (transformations and/or inverses of functions) .\u003Cbr>Construct and compare linear, quadratic, exponential, and logarithmic models to solve problems.\u003Cbr>Interpret functions in terms of the sit","cbCaip9vK1W8L2k8","https://ap.wps.com/l/cbCaip9vK1W8L2k8","pdf",338035,"English","# Concepts\n## Complex Number System\n## Polynomial and Rational Expressions\n## Equations and Inequalities\n## Functions\n## Data and Probability","[{\"question\":\"What complex number skills are emphasized in this document?\",\"answer\":\"Students learn to represent and use imaginary numbers in equivalent forms, simplify/evaluate expressions involving imaginary numbers, and perform arithmetic with complex numbers. They also apply complex-number concepts to polynomial identities and quadratic equations to solve problems.\"},{\"question\":\"What abilities are listed for polynomial and rational expressions?\",\"answer\":\"Students practice arithmetic operations on polynomials, solve equations involving rational expressions, and understand the relationship between zeros and factors. They also rewrite rational expressions and use polynomial identities to solve, including simplifying or factoring expressions involving polynomials.\"},{\"question\":\"How does the document address functions and data topics?\",\"answer\":\"It requires interpreting and applying functions using context and notation, creating and analyzing functions with graph/table/equation representations, and modeling relationships between quantities. For data, it includes analyzing patterns in sets of data, summarizing single- and two-variable data, and analyzing/interpreting scatter plots to make predictions such as regression.\"}]","Complex Number System, Polynomial Expressions, Equations and Inequalities, Functions, Data and Probability | PDF",1790589194]