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Questions include solving trigonometric equations in specified intervals, determining circle equations from a point and centre, finding standard position angles and coterminal angle measures, and extracting ranges of sine-based functions. Additional problems address logarithm simplification, intercepts and algebraic equation solving, estimation and solving with logarithms, and application-style tasks such as arrangements, combinations, and real-world constraints.",{"@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/pre-calculus-12-practice-exam-2/453894/",{"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/pre-calculus-12-practice-exam-2/453894.png","ImageObject",300,407,{"name":92,"@type":93},"noah","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-22","2026-09-30",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",11,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What topics are included in this Pre-Calculus 12 practice exam?","Question",{"text":113,"@type":114},"It includes multiple-choice questions on trigonometric equations and angles, circle equations, function ranges, logarithm rules and estimation, and some combinatorics/application problems.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"Are calculators allowed for this exam?",{"text":118,"@type":114},"The document indicates that a calculator is permitted for the first multiple-choice section and not permitted for a later section.",{"name":120,"@type":111,"acceptedAnswer":121},"How are answers presented in the exam?",{"text":122,"@type":114},"Each question is followed by multiple-choice options labeled with letters (a, b, c, d), and some questions also require correct reasoning.","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},453894,1790792349,{"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":29,"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":145},1099529839121,"https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d","Pre-Calculus 12 Practice Exam 2  \nMULTIPLE-CHOICE (Calculator permitted )  \nπ  \n1. Solve cos3x = sin x, 0 ≤ x ≤  \n2  \na. 0.39 b. 0.40, 1.25 c. 0.79 d. 0.79, 1.18  \n2. Determine the equation of a circle with centre (0,0) passing through the point P (− 2,5)  \na. x 2 + y 2 = 3 c. x 2 + y 2 = 21  \nb. x 2 + y 2 = 9 d. x 2 + y 2 = 29  \n3. Determine the measure of the standard position angle θ if the point P (− 4,3) is on the terminal arm of angleθ , where 0° ≤ θ \u003C 360°  \na. 37˚ b. 53˚ c. 127˚ d. 143˚  \n4. Express as a single logarithm: loga − logb − 3logc  \n a   a   ac 3   ac 3  \na. log bc 3 b. log b 3c 3 c. log b d. log b 3  \n5. Determine the x − intercept of y = 5x − 3  \na. -2 b. 0.008 c. 0.6 d. 0.68  \n6. An investment earns 2.25% per annum compounded daily. How many years would be required for an investment to triple in value? Assume all years have  \n365 days.  \na. 4.88 b. 5.41 c. 48.83 d. 49.37  \n7. Determine the number of different arrangements of all the letters in the word TRIGONOMETRY.  \na. 4 989 600 c. 119 750 400  \nb. 59 875 200 d. 479 001 600  \n8. An area code is the first 3 digits in a phone number and indicates the location of either the province orthe city. In Canada, the following area codes exist:  \nNotice that there are 3 area codes for British Columbia: 250, 604 and 778. It will be necessary to add another area code as the population increases. The new area code cannot be the same as an existing code, it must begin with a 3 and end in an even number. Determine the number of  \npossible area codes to choose from.  \na. 40 b. 44 c. 49 d. 50  \n9. In a standard deck of 52 cards, determine the number of 5-card hands that must contain at least  \n3 queens.  \na. 4512 b. 4560 c. 4704 d. 4752  \n10. A dance group has twelve people from which five need to be chosen to compete in a national competition. Bob and Nancy are in the group of twelve and have recently obtained gold at a regional competition. They are therefore required to be among the five selected for the national competition. Given this requirement, how many different fivemember teams are possible?  \na. 120 b. 220 c. 252 d. 792  \n11. Determine the 5th term in the expansion of (3x + 2 y)n , where n ≥ 6  \na. n C4 (3x)n−4 (2 y)4  \nb. n C5 (3x)n−5 (2 y)5  \nc. n C4 (3x)4 (2 y)n−4  \nd. n C5 (3x)5 (2 y)n −5  \n12. A sheet of metal 12 cm × 12 cm will be used to make an open-top box by removing a square of length x in each corner and turning up the sides as shown in the diagram.  \nWhat is the volume of the box as a function of x?  \na. V = x 3 c. V = 144 − 4x2  \nb. V = x (12 − x)2 d. V = x (12 − 2x)2  \n13. Determine all solutions to the equation x + 4 = 3x  \na. -0.61, 0.72 b. -0.61 c. 0.72 d. 1.33  \n14. Which equation represents the graph of f ( x) after it is horizontally stretched by a factor of 12 ?  \na. y = f (2x) c. y = f (~~ ~~12~~ ~~ x)  1  \nb. y = 2 f ( x) d. y = f ( x) 2  \nMULTIPLE-CHOICE (Calculator NOT permitted)  \n15. Determine the equivalent expression for 22 C8  \na. 8 C22 b. 20 C6 c. 22 C14 d. ~~22~~1P~~8~~4  \n16. The graph of y = asinbx is shown. Determine the values of a and b.  \na. a = −3 , b = 2  \nb. a = −3 , b = π  \nc. a = 3 , b = 2  \nd. a = 3 , b = π  \n17. The terminal arm of angle θ in standard position intersects the circle at the point (x , y) . Which expression represents cotθ ?  \na. ~~ ~~yx~~ ~~ b. ~~ ~~xy~~ ~~ c. x d. y  \n18. Which expression represents the measure of all angles in radians that are coterminal with angle θ ?  \na. 2π + nθ, n ∈Z c. θ + πn, n ∈Z π  \nb. θ + n , n ∈Z d. θ + 2πn, n ∈Z 2  \n19. Determine the range of the function y = −5sin 2x − 3  \na. − 8 ≤ y ≤ 2 c. − 5 ≤ y ≤ 5  \nb. − 8 ≤ y ≤ −2 d. − 2 ≤ y ≤ 8  \n20. Determine the general solution for sin 4x = −1  \na. x = π8~~ ~~ + ~~ ~~πn2~~ ~~ , n ∈Z 3π   πn  \nb. x = + , n ∈Z 8 2  \nc. x = π8~~ ~~ + 2πn, n ∈Z  \nd. x = ~~ ~~3π8~~ ~~ + 2πn , n ∈Z  \ncscθ + secθ  \n21. Chantal simplified the expression ~~ ~~ as  \nsinθ + cosθ  \nshown below. In which step is Chantal’s first error?  \n22. Determine all n","cbCaiqJVXXRQrjJx","https://ap.wps.com/l/cbCaiqJVXXRQrjJx","pdf",428743,"English","# Multiple-Choice Practice Questions\n## Trigonometry and Angles\n## Circles and Functions\n## Logarithms and Algebra\n## Combinatorics and Applications","[{\"question\":\"What topics are included in this Pre-Calculus 12 practice exam?\",\"answer\":\"It includes multiple-choice questions on trigonometric equations and angles, circle equations, function ranges, logarithm rules and estimation, and some combinatorics/application problems.\"},{\"question\":\"Are calculators allowed for this exam?\",\"answer\":\"The document indicates that a calculator is permitted for the first multiple-choice section and not permitted for a later section.\"},{\"question\":\"How are answers presented in the exam?\",\"answer\":\"Each question is followed by multiple-choice options labeled with letters (a, b, c, d), and some questions also require correct reasoning.\"}]","Pre-Calculus 12 Practice Exam 2 | PDF",1790739781,15]