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The material practices core skills including function domains and distance, function identification, average rate of change, parity and symmetry, and finding inverse functions. It also covers solving inequalities, piecewise evaluation, polynomial factored forms, secant line equations, vector operations, logarithm expansion, and several trigonometry tasks including identities, inverse trig evaluation, and triangle problem solving. The short-answer section adds difference quotients, transformations, compositions, factoring and zeros, asymptotes and domain, exponential and logarithmic equations, and trigonometric modeling from graphs.",{"@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/math-150-pre-calculus-final-exam-review-fall-2024/434878/",{"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/math-150-pre-calculus-final-exam-review-fall-2024/434878.png","ImageObject",300,407,{"name":92,"@type":93},"BigDaveOnline","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-19","2026-09-29",true,{"@type":102,"interactionType":103,"userInteractionCount":44},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What topics are emphasized in the multiple-choice section?","Question",{"text":112,"@type":113},"The multiple-choice questions emphasize domains and distance, identifying which equations define y as a function of x, average rate of change, parity and symmetry, inverse functions, inequalities, piecewise functions, polynomial equation from a graph, secant line equations, vector dot products and angles, logarithm expansion, and trigonometry including inverse trig and triangle solving.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What kinds of tasks appear in the short-answer section?",{"text":117,"@type":113},"The short-answer section requires work and covers difference quotients, function transformations, function compositions and inverse relationships, factoring polynomials and identifying zeros and end behavior, finding intercepts and sketching graphs, asymptotes and domain, and solving exponential/logarithmic and trigonometric equations.",{"name":119,"@type":110,"acceptedAnswer":120},"Does the review include both algebraic and trigonometric problems?",{"text":121,"@type":113},"Yes. It includes algebra topics such as inverses, factoring, zeros, and asymptotes, and it also includes trigonometry problems involving identities, inverse trigonometric evaluation, triangle sides/angles, and writing sine functions that match given graphs.","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},434878,1790694673,{"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":44,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"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":41},962090896214,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","Math 150 – Pre-Calculus  \nFinal Exam Review (Fall 2024)  \nPart I. Multiple Choice: Choose the best possible answer.  \n1. Find the domain of the function: 􀝂 (􀝔) = √2􀝔 + 10 − 4  \na. (−∞, −5] ∪ [−4, ∞) b. (−5, −∞) c. [−5, ∞) d. [−4 . , ∞)  \n2. Find the distance between the points: 􀜲 = (−7 , 3) & 􀜳 = (4 , 5)  \na. √13 b. 5√5 c. √17 d. √17􀝅  \n3. Which of the following equations represent y  as a function of x?  \na. 􀯫42 − 􀯬92 = 1 b. 􀝕 = 3􀝔2 + 9 c. |􀝕| = 􀝔 − 10 d. 􀝔 2 + 􀝕 2 = 16  \n4. Find the average rate of change of the function 􀝂(􀝔) = 􀝔 2 − 2􀝔 + 8 from  \n􀝔1 = 2 to 􀝔2 = 5 .  \na. 5 b. 3 c. −5 d. 11  \n5. Is 􀝂(􀝔) = 􀝔 4 − 2􀝔2 + 3 even, odd, or neither? Does it have any symmetry?  \na. Odd with origin symmetry b. Even with x-axis symmetry  \nc. Neither with no symmetry d. Even with y-axis symmetry  \n6. Find the inverse function 􀝂−1(􀝔) of 􀝂(􀝔) = 􀯫􀯫12  \na. 􀝂 −1(􀝔) = 2􀯫􀯫 b. 􀝂 −1(􀝔) = −2􀯫+11  \nc. 􀝂 −1(􀝔) = 􀝔􀝔21 d. 􀝂 −1(􀝔) = 2􀯫􀯫  \n7. Solve for 􀝔 : 2􀝔2 − 5􀝔 + 3 ≥ 0  \na. (−∞ , 1] ∪ [32 , ∞) b. [ 1 , 32] c. (−∞ , 1) ∪ (32 , ∞) d. ( 1 , 32 )  \n8. Given the following piecewise function, find 􀝂(1): 􀝂 (􀝔) = {􀝔􀝔3+−4􀝔  \na. 3 b. 5 c. 2 d. 0 9. Find the equation of the polynomial graphed below.  \n􀝔 ≤ 1  \n􀝔 > 1  \na. 􀝕 = (􀝔 − 2)2 (􀝔 + 3)(􀝔 + 4) b. 􀝕 = (􀝔 + 2)2 (􀝔 − 3)(􀝔 − 4)  \nc. 􀝕 = (􀝔 − 2)(􀝔 + 3)(􀝔 + 4) d. 􀝕 = (􀝔 + 2)(􀝔 − 3)(􀝔 − 4)  \n10. Find the equation of the secant line for 􀝂(􀝔) = 􀝔 2 + 3􀝔 + 1 on the interval [2 , 7] .  \na. 􀝕 = 2􀝔 − 13 b. 􀝕 = 12􀝔 − 13  \nc. 􀝕 = 12􀝔 − 130 d. 􀝕 = 12􀝔 − 17  \nGiven 􀢛 = 〈−2 , 5〉 and 􀢜 = 〈−1 , 8〉 , answer questions 11 and 12.  \n11. Find the dot product: 􀢛 ∙ 􀢜  \na. −38 b. 41 c. 42 d. 60  \n12. Find the angle between the vectors to the nearest tenth of a degree:  \na. 138.4° b. 14.7° c. 36. 2° d. 14.67°  \n13. Expand the expression by using the properties of logarithms:  \n􀝈􀝋􀝃 2 (4􀝉􀝌√2􀝊)  \na. 􀝈􀝋􀝃 24 + 􀝈􀝋􀝃 2􀝉 + 12 􀝈􀝋􀝃 2􀝊 − 2􀝈􀝋􀝃2􀝌 b. 􀝈􀝋􀝃 24􀝉 + 12 􀝈􀝋􀝃 2􀝊 − 2􀝈􀝋􀝃2􀝌  \nc. 􀝈􀝋􀝃 24 + 􀝈􀝋􀝃 2􀝉 + 12 􀝈􀝋􀝃 2􀝊 + 2􀝈􀝋􀝃2􀝌 d. 2 + 􀝈􀝋􀝃 2􀝉 + 12 􀝈􀝋􀝃 2􀝊 − 2􀝈􀝋􀝃2􀝌  \n14. Given cos 􀝑 = − 27 and 􀰗2 \u003C 􀝑 \u003C 􀟨 , find cos 􀯨2 and sin 2􀝑 .   \na. cos 􀯨2 = − 704 b. cos 􀯨2 = 704  \nsin 2􀝑 = 6√75 sin 2􀝑 = − 6√75  \nc. cos 􀯨2 = 3√1144 d. cos 􀯨2 = 704  \nsin 2􀝑 = − 12√495 sin 2􀝑 = − 12√495  \nFor problems 16 and 17, let sin 􀜣 = − 725 with Ain Quadrant III and cos 􀜤 = − 45 with B in Quadrant III.  \n15. Find sin(􀜣 + 􀜤)  \na. − 45 b. ~~ ~~35 c. ~~ ~~45 d. − 35  \n16. Find tan(􀜣 − 􀜤)  \na. ~~ ~~100117 b. − 4475 c. ~~ ~~4475 d. − ~~ ~~44117 sec 􀰏−1  \n17. Simplify the trigonometric expression:  \n1−cos 􀰏  \na. sec 􀟠 b. cos 􀟠 c. ~~ ~~secs􀰏i2co􀰏s~~ ~~􀰏~~ ~~ d. −1  \n18. Simplify the trigonometric expression: cos1􀯫+1 + cos1􀯫−1  \na. sec 􀝔 b. −2 csc 􀝔 cot 􀝔 c. −2 csc 2 􀝔 d. ~~ ~~cos22􀯫−1  \n19. Evaluate tan−1(−1)  \na.  3􀰗   7􀰗  b.  7􀰗  c. − 􀰗  d.  3􀰗  \n4 , 4 4 4 4  \n20. Evaluate 􀝏􀝅􀝊 (cos −1 ( − 12))          \na. √3 b. − √3 c. √3 − √3 d. √3 􀰗  \n2 2 2 , 2 2  \n21. In triangle ABC, if 􀜽 = 3.7 􀜿􀝉, 􀜿 = 6.4 􀜿􀝉, 􀜽􀝊􀝀 􀜤 = 23°, find b.  \na. 4.1 cm b. 3.3 cm c. 5.7 cm d. 11.1 cm  \nPart II. Short Answer Section: Show your work.  \n1. Find the difference quotient: 􀯙 (􀯫+ℎ)−􀯙(􀯫) ℎ ≠ 0 for 􀝂(􀝔) = 5􀝔 − 􀝔 2 ℎ , .  \n2. The graph of 􀝂(􀝔) = √􀝔 is shifted up 3 units, right 4 units, reflected about they-axis, and compressed vertically by a factor of 3. Name the resulting function 􀝃 , then write an equation for 􀝃(􀝔) in terms of 􀝂 .  \n3. Describe the transformations that would produce the graph of 􀝃 from the graph of 􀝂 . Be specific and detailed. If more than one transformation is needed, specify the order in which the transformations should be applied.  \na. 􀝃 (􀝔) = 􀝂 (2􀝔) + 7  \nb. 􀝃 (􀝔) = −􀝂(􀝔 − 3) − 5  \n4. Find the compositions (􀝂 ∘ 􀝃)(􀝔) and (􀝃 ∘ 􀝂)(􀝔) using the following functions:􀝂 (􀝔) = 3√􀝔 − 5 and 􀝃(􀝔) = 􀝔 3 + 1 . Are 􀝂(􀝔) and 􀝃(􀝔) inverse functions of each other? Explain why or why not.  \n5. Given the function. 􀝂 (􀝔) = 􀝔 3 + 2􀝔2 + 4􀝔 + 8.  \na. Factor the polynomial over the real numbers as the product of linear factors or irreducible quadratic factors.  \nb. State all zeros (real and imaginary) and their associated ","cbCaiv0KCdfLYapj","https://ap.wps.com/l/cbCaiv0KCdfLYapj","pdf",205319,12,"English","# Part I. Multiple Choice\n## Questions 1-21\n# Part II. Short Answer Section\n## Questions 1-12","[{\"question\":\"What topics are emphasized in the multiple-choice section?\",\"answer\":\"The multiple-choice questions emphasize domains and distance, identifying which equations define y as a function of x, average rate of change, parity and symmetry, inverse functions, inequalities, piecewise functions, polynomial equation from a graph, secant line equations, vector dot products and angles, logarithm expansion, and trigonometry including inverse trig and triangle solving.\"},{\"question\":\"What kinds of tasks appear in the short-answer section?\",\"answer\":\"The short-answer section requires work and covers difference quotients, function transformations, function compositions and inverse relationships, factoring polynomials and identifying zeros and end behavior, finding intercepts and sketching graphs, asymptotes and domain, and solving exponential/logarithmic and trigonometric equations.\"},{\"question\":\"Does the review include both algebraic and trigonometric problems?\",\"answer\":\"Yes. It includes algebra topics such as inverses, factoring, zeros, and asymptotes, and it also includes trigonometry problems involving identities, inverse trigonometric evaluation, triangle sides/angles, and writing sine functions that match given graphs.\"}]","Math 150 - Pre-Calculus - Final Exam Review - Fall 2024 | PDF",1790670931]