[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-434872-105":59,"doc-detail-434872-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","ap-precalculus-solve-the-problems-without-consulting-a-text","AP Precalculus - Solve the problems without consulting a text","","AP Precalculus practice problems cover core algebra and pre-calculus skills: evaluating linear functions, graphing lines and parabolas, finding intercepts, determining slopes, solving systems and inequalities, simplifying rational expressions, working with exponents and radicals, and handling polynomial equations including factoring and the quadratic formula. The set also includes complex numbers, functions and composition, domain and range in interval notation, asymptotes, and selected trigonometry tasks such as cosine, cotangent, identities, and graphing.",{"@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/ap-precalculus-solve-the-problems-without-consulting-a-text/434872/",{"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/ap-precalculus-solve-the-problems-without-consulting-a-text/434872.png","ImageObject",300,407,{"name":92,"@type":93},"noah","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-20","2026-09-29",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",12,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What is the general instruction for solving this AP Precalculus set?","Question",{"text":113,"@type":114},"Solve the problems without consulting a text. For any problems not solved correctly, use the provided correct answers to become familiar with the question type.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What kinds of math skills are included?",{"text":118,"@type":114},"The problems span linear equations and inequalities, rational expressions, exponents and radicals, polynomials and equations, functions (including domain/range and composition), and trigonometry.",{"name":120,"@type":111,"acceptedAnswer":121},"Are graphing questions included?",{"text":122,"@type":114},"Yes. The set includes graphing lines and inequalities, as well as graphing functions such as parabolas and other function forms.","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},434872,1790710848,{"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":140,"language":141,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":67,"update_tm":145,"read_time":26},1099529839121,"https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d","AP Precalculus \nDue August 11th, 2025 \nSolve the problems without consulting a text. If you can solve at least half the problems correctly, you will likely do OK in Precalculus. For problems which you do not solve correctly, the questions should at least look familiar, and you should be able to solve such problems with the aid of a text and armed with the correct answers. \n1. If y = 3 − 4x, determine the value of y corresponding to x = −2. \n 7 \n2. Given f (x) = 3x +14 , determinef(2) . \n3. Graph y = −3x +2. \n4. Find the x-and y-intercepts of the line 5x − 3y = 15 . \n5. Find the slope of the line containing the points P1 (3 , −2) and P2 (5 , 6) . \n6. Determine the slope of the line 5x − 3y = 15 . \n7. Find an equation for the line that contains the point (−2, 3) and has slope 5 \n7 . \n8. Are the lines 4x − 2y = 3 and 7x +3y = 7 perpendicular? \n9. Graph the solution set to 2x − 3y ≤ 12. \n10. Solve the system ! yy 2x3x 48 . \n11. By factoring the numerator and denominator, simplify xx22~~ ~~x2x63 . \n12. Multiply and simplify x2 − x − 6 · xy 3 \nx2 y x2 − 6x +9 . \n13. Divide and simplify x2 − 4 ÷ x2 +2x − 8 \nx4 y 3 x4 y 2 . \n14. Add: 5 + 4 \nx − 2 x − 2 . \n 2x +1 x − 2 \n15. Subtract and simplify: − \nx2 + x − 6 x2 + x − 6 . \n16. Add and simplify : x2~~ ~~−5x + x~~ ~~~~ ~~2 . \n17. Solve: 3x~~ ~~2 = 5 . \n18. Solve: 2 = 3 \nx +4 x +1 . \n19. Solve: x~~ ~~+3~~ ~~6 = 27 . \n20. Solve for r: s = r + rt. \n21. Simplify: (x3 y 9 ) 43 . \n2 5 8 \n22. Simplify: x − 3 (x 3 − x 3 ) . \n23. Add: √80 − √20. \n24. Multiply: (a +2b)(a − 2b) . \n25. Multiply the complex numbers: (2 + 4i)(3 − 2i) . \n26. Divide the complex numbers: 2+4i \n3 − 2i . \n27. Solve by factoring: 3x2 − 11x − 4 = 0 . \n28. Solve by using the quadratic formula: 2x2 +10x +3 = 0 . \n29. Solve the inequality: (x − 5)(x +2) ≤ 0. \n30. Graph the parabola f(x) = x2 +2x − 3. \nAnswers \n(1) 11 (2) 720 (3) The straight line through 2 on the y-axis and 23 on the x-axis. \n(4) x-intercept: 3, y-intercept: −5 (5) 4 (6) 5/3 \n(7) Several different forms of the answer are possible. Reasonable choices are 7y = 5x + 31, or 5 31 \n5x − 7y = −31, or y = 7 x + 7 . \n(8) No \n(9) The part of the plane on and above the line through −4 on the y-axis and 6 on the x-axis. \n(10) x = −12, y = −28 (11) xx~~ ~~−~~ ~~21 (12) yx2((xx23)) (13) y~~ ~~x(x24) (14) x~~ ~~~~ ~~2 \n(15) x~~ ~~~~ ~~2 (16) x~~ ~~~~ ~~3 (17) x = 45 (18) x = −10 (19) x = − 367 \n(20) r = 1~~ ~~~~ ~~t (21) x4 y 12 (22) x − x2 (23) 2 √5 (24) a2 − 4b2 (25) 14 + 8i \n(26) − ~~ ~~213 + 1613i (27) x = 4 , − 13 (28) x = −5~~ ~~√~~ ~~19 \n(29) The interval [−2, 5] (30) the parabola opens upwards and its vertex is at the point (−1, −4) \nTopic I 􀀨 Rational Expressions Simplify the following: \n1. §¨© ~~ ~~9x2x2􀀐1􀀎21x~~ ~~ ·¹¸¨§© ~~ ~~9x22x􀀎26􀀎x~~ ~~~~ ~~24·¹¸ \n§¨1 􀀐 3 ·¸ \n© x ¹ \n2. 9 􀀐 x2 \n§ 6v 3 · § 􀀐uv ·§ 1 · \n3. ¨© u 2 ¹¸ ¨© 2v ¹¸ ¨© 7v2 ¹¸ \n􀀐4 2x 􀀎1 \n4. 9 􀀐 x2 􀀐 x2 􀀐 3x \n 3 2 1 \n5. 􀀋 x 􀀎 2b 􀀌􀀋 x 􀀐 b 􀀌 􀀎 􀀋3b 􀀐 x􀀌􀀋 x 􀀎 2b 􀀌 􀀎 􀀋 x 􀀐 3b 􀀌􀀋b 􀀐 x 􀀌 \n§ 2a b ·􀀐2 \n6. ¨© b 􀀐 a~~ ~~ ¹¸ \n§ xy 2 · \n¨ ~~ ~~ ¸ \n © x 􀀎 y ¹ \n7. § x 􀀐 y ·¨© x2 􀀐 y2 ¹¸ \n§ m 2m ·¨© m 􀀐 3 􀀐 m2 􀀐 2m 􀀐 3¹¸ \n8. § 2 1 · \n¨© m 􀀎1 􀀐 m ¹¸ \nTopic II 􀀨 Exponents and Radicals \n9. Evaluate: 81􀀐 34 Simplify the following: \n10. 6 15 \n11. \n 􀀋 a 􀀎 b 􀀌 􀀋 a2 􀀐 b2 􀀌 \n12. 16x2 􀀎 24y 2 􀀎 36z2 \n􀀋 3xy 12 􀀌 􀀋 4x2y 􀀌 􀀐2 13. 32 \nxy \n a􀀐2b3 c \n14. a􀀐1b􀀐2c 0 \n3 x 􀀎2 \n15. ~~ ~~aa4􀀐x~~ ~~ \n16. 􀀋 mb􀀎1 􀀌 b􀀐1 \n17. §¨ 43 x321y 43 ·¸ 􀀐 2 ¨© 16x 􀀐 2y 2 ¹¸ \n2 \n18. 􀀋􀀐125x18 y 24 􀀌 􀀐 3 \n19. 􀀋 4 m 6 􀀌􀀋2m m 􀀌 \n20. 2 12 􀀎 27 􀀐 48 Rationalize the following: \nx \n21. 5 4 \n3 x \n22. \n23. Solve for x: 35 x 􀀎2 27x 􀀐4 \nTopic III 􀀨 Linear Equations, Inequalities, and Absolute Value 24. Solve for x: 3x ~~ ~~ab~~ ~~ 􀀋 x 􀀐1􀀌 \n25. Solve for a: a 􀀐 2 􀀎 3 7 \n3 2 5x 􀀎 3 \n26. Solve for x: x 􀀐 x 􀀎 1 x 􀀎 1 \n2x 􀀎 3y \n27. Solve this system of equations: ®¯5x 􀀐 2y \n3x \n28. Solve this system of equations: ®¯2x 􀀎 3y \n2","cbCaiiBV19MtFuLe","https://ap.wps.com/l/cbCaiiBV19MtFuLe","pdf",382132,24,"English","# Problems\n## Topics I-VI","[{\"question\":\"What is the general instruction for solving this AP Precalculus set?\",\"answer\":\"Solve the problems without consulting a text. For any problems not solved correctly, use the provided correct answers to become familiar with the question type.\"},{\"question\":\"What kinds of math skills are included?\",\"answer\":\"The problems span linear equations and inequalities, rational expressions, exponents and radicals, polynomials and equations, functions (including domain/range and composition), and trigonometry.\"},{\"question\":\"Are graphing questions included?\",\"answer\":\"Yes. The set includes graphing lines and inequalities, as well as graphing functions such as parabolas and other function forms.\"}]","AP Precalculus - Solve the problems without consulting a text | PDF",1790670920]