[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-434874-105":59,"doc-detail-434874-en":130},{"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":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","practice-frq-4-ap-precalculus","Practice FRQ 4 - AP Precalculus","","This document provides a set of symbolic manipulation practice questions specifically designed for the AP Precalculus curriculum. The content focuses on testing students' mastery of algebraic and trigonometric identities, logarithmic properties, and solving transcendental equations. Students are required to simplify expressions, rewrite functions using specific identities, and solve equations for variables within defined domains without the use of a calculator. This resource is an essential tool for exam preparation, helping students practice the critical thinking and precision required for advanced mathematics examinations. It emphasizes logical deduction and the application of mathematical rules to arrive at exact values and simplified functional forms.",{"@graph":69,"@context":122},[70,84,105],{"@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/practice-frq-4-ap-precalculus/434874/",{"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/practice-frq-4-ap-precalculus/434874.png","ImageObject",300,407,{"name":92,"@type":93},"404brain","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-18","2026-09-29",true,{"@type":102,"interactionType":103,"userInteractionCount":34},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What is the goal of the practice question regarding the function f(x)?","Question",{"text":112,"@type":113},"The student is required to rewrite the function f(x) = tan x (1 - sin^2 x) / cos x into a single expression containing only one trigonometric function.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How should the function h(x) be simplified according to the instructions?",{"text":117,"@type":113},"The function h(x) = log_3(x^2) + 10 log_9 x must be rewritten as a constant multiple of log_3 x.",{"name":119,"@type":110,"acceptedAnswer":120},"What is required to solve the equation involving the function p(x)?",{"text":121,"@type":113},"To solve p(x) = 1/2, the student must identify all values of x within the domain of the function p(x) that satisfy the equation.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},434874,1790792362,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":34,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":8,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":81},1099529839291,"https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","Practice Question 4 : Symbolic Manipulations  \nDirections:  \n• Unless otherwise specified, the domain of a function 􀀲 is assumed to be the set of all real numbers 􀀣 for which 􀀲(􀀣) is a real number. Angle measures for trigonometric functions are assumed to be in radians.  \n• Solutions to equations must be real numbers. Determine the exact value of any expression that can be obtained without a calculator. For example, log\" 8 , cos 0\\#\"1 , and sin$%(1) can be evaluated without a calculator.  \n• Unless otherwise specified, combine terms using algebraic methods and rules for exponents and logarithms, where applicable. For example, 2􀀣 + 3􀀣 , 5\" ⋅ 5& ,'\"! , and ln 3 + ln 5 should be rewritten in equivalent forms.  \n'  \nh part of the questi  \n(A) The functions 􀀡 and ℎ are given by  \n􀀡 (􀀤) = tan 􀀤 (1 − sin! 􀀤)  \ncos 􀀤  \nℎ (􀀤) = log\" (􀀤 ! ) + 10 log\\# 􀀤  \n(i) Rewrite 􀀡(􀀣 ) as a single expression including only one trigonometric function.  \n(ii) Rewrite ℎ(􀀣 ) as a constant multiple of log3 􀀤 .  \n(B) The functions 􀀴 and 􀀵 are given by  \n$  \n􀀴 (􀀤) = 􀀶~~ ~~%  \n􀀵 (􀀤 ) = cos &'(5􀀤)  \n(i) Solve 􀀩(􀀣 ) = 􀀶 for values of 􀀤 in the domain of 􀀴 .  \n(ii) Solve 􀀫 (􀀣) = 2􀀩3 for values of 􀀤 in the domain of 􀀵 .  \n(C) The function 􀀬 is given by  \n􀀬 (􀀣 ) = 6 csc 0􀀤 − 1  \nFind all values in the domain of 􀀬 that yield an output of 12.","cbCail9HseW1XvfU","https://ap.wps.com/l/cbCail9HseW1XvfU","pdf",197735,"English","# Symbolic Manipulations\n## Functions and Identities\n## Equation Solving","[{\"question\":\"What is the goal of the practice question regarding the function f(x)?\",\"answer\":\"The student is required to rewrite the function f(x) = tan x (1 - sin^2 x) / cos x into a single expression containing only one trigonometric function.\"},{\"question\":\"How should the function h(x) be simplified according to the instructions?\",\"answer\":\"The function h(x) = log_3(x^2) + 10 log_9 x must be rewritten as a constant multiple of log_3 x.\"},{\"question\":\"What is required to solve the equation involving the function p(x)?\",\"answer\":\"To solve p(x) = 1/2, the student must identify all values of x within the domain of the function p(x) that satisfy the equation.\"}]","Practice FRQ 4 - AP Precalculus | PDF",1790670922]