M110 PreCalculus Diagnostic Test

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M110 PreCalculus Diagnostic TestSuccess in a first year Calculus class is highly dependent on your algebra skills. The following is a selfdiagnostic test to be taken by students prior to entering a Math 110 Calculus class (note that there is aseparate test for students entering Math 103).Instructions:Complete the following test in no more than 90 minutes.Do not use a calculator for any questions.Do not refer to books, notes, or other material while completing the test.Only select one answer per question.Once you have completed all 40 questions, refer to the last page for scoring and recommendations.

1 2 4 3 222411667614471. 2 a)b)c)d)e)2. Expressa)b)c)121 2 2 3 as a single fraction:2yx y x yx2 y 2 y 2 1x2 y344 6x yx 2yx2 y3d)x2 3 yx2 y 2e)x 4 y 4 2 xy 5 x 2x4 y6 2xy 3. Simplify x y 2 32a) 6xy 4b) 8x 7 y86 y3c)x8 y3d)x8 y4e)x2

14. 16 4 40 a) 212c) 0b)d) 12e) 25. One factor ofa) 3x 1b) x 4c) 3x 1d) x 2e) 3x 46. Factor x 2 2 x 8a)b)c)d)e) x 2 x 4 x 8 x 1 x 8 x 1 x 2 x 4 x 4 x 2 7. If x 2 4 x 1 0 , then x a)2 3 , 2 3b) 2 3 , 2 3c)d)2 5 , 2 53, 3e) None of the above.8. If 2 x 3 9 , then x a)b)c)d)e) 6 or 3 6 or 36 or 36 or 3None of the above.is

9. If x 3 5 , thena) 2 x 8b) 8 x 2c) x 8 x 2d) x 2 x 8e) x 8 x 210. If x 2 2 x 3 0 , thena) x 1 x 3b) x 3 x 1c) 3 x 1d) 1 x 3e) 1 x 311. Solve the following pair of equations for x and y : 2 x y 5 and 4 x y 7a)x 2 , y 1x 2 , y 1c) x 1 , y 3d) x 6 , y 17e) x 2 , y 1b)12.a)b)c)d)e)1 1xy 1 y x2 xyxxy1 xyxxyxy 1

1x 22 x 18 x 81 1a)2 x 9 13.b) 3 x 3 2 x 9 x 9 c) 12 x 9 d) 9 x 9 x 9 e)1 x x 9 x 7 14. If x 11 and y 25 , then x y a) 6b) 611551d)61e) 6c)15. Factor 16 x 4 1a) 2 x 1 2 x 1 22c) 4 x 1 4 x 1 2 x 1 2 x 1 4 x2 1 d) 2 x 1 2 x 1 2 x2 1 e) 2 x 1 2 x 1 2 x2 1 b)22 12

, then x 16. Ifa)b)c)d)e)2 88 2None of the above.17. Ifa)b)c)d)e)18. Leta)b)c)d)e)thenandand19. The graph of the equationa) a parabola with vertexb) a parabola with vertexc) a line with slopeand interceptd) a line with slope and intercepte) a circle with radius 220. The graph of the equationa) a parabola with vertexb) a parabola with vertexc) a line with slopeand interceptd) a line with slope and intercepte) a circle with radius 2. Evaluateisis

21. Find the equation of the straight line through pointsa)b)c)d)e)and22. Find the equation of the line perpendicular toa)b)c)d)e)23. Which graph best represents the equationa)(2,5)b)c)through the point(-2,5)d)e)andb)andc)d)(-2,5)intersects the parabolaa).?(2,5)24. The line.atandande) None of the above.25. The parabolasa)andb)andc)andd)ande) none of the aboveandintersect at points26. After a 20% price decrease, the cost of an item is 4.20. What was the original price?a) 4.40b) 5.04c) 5.00d) 4.96e) 5.25(2,-5)

27. Adam can shovel a driveway in two hours. Bev can shovel the same driveway in three hours. Howlong would it take them working together?a) 2 hours 30 minutesb) 2 hours 20 minutesc) 48 minutesd) 1 hour 12 minutese) 1 hour 36 minutes28. A car leaves Regina at 1 PM and drives along Highway #1 at constant speed 85 km/h. A 2nd car leavesRegina at 1:30 PM and follows the same highway at constant speed 110 km/h. At what time will it passthe first car?a) 1:47 PMb) 2:07 PMc) 2:42 PMd) 3:12 PMe) 3:30 PM29. A cell phone plan costs 20 a month and includes 200 free minutes. Each additional minute costs 5cents. Assume you use your cell phone for at least 200 minutes a month. If x is the total number ofminutes a month, then your total cost C is given bya)b)c)d)e)30. Find the area of the triangle that has sides with length 3, 4, and 5.a) 6b) 7.5c) 10d) 12e) 1531. Find the distance between pointsa) 5b)c)d)e)and

32. Find the total area of the given shape, a square with side length 2 topped by a semi-circle.a)b)c)d)e)33. How many degrees is radians?a)b)c)d)e)1809060453034.a) 0b)c)d)e) 135.a)b)c)d)e) None of the above.

36. The angle(in radians) in the given diagram isa)b)c)d)e)37. In the given diagram,a) 5/12b) 5/13c) 12/13d) 12/5e) 13/538. Which of the following values is largest?a)b)c)d)e)39. At what points in the intervala)andb)andc)d)e)andandand40.a) 0b)c) 1d)e) None of the above.doesintersect?

Answers and ScoringThe answer key is given as d35d36b37a38d39b40cAdd up your correct answers for all 40 questions.Your score: out of 40Recommendations:If you scored 31 or more points, you are likely ready for Calculus. However, you will want to review anyareas of weakness that arose while you were working on this test. Refer to the resources section forsome review suggestions.If you scored between 20 and 30 points, and are planning to enroll in Calculus, you should definitelyreview relevant PreCalculus material as soon as possible. Refer to the resources section for some reviewsuggestions. If you do not feel comfortable doing this on your own, you may wish to consider enrollingin PreCalculus Math 102 instead.If you scored less than 20 points, you will likely have a difficult time with the material in a Calculuscourse and face a high probability of failure. You should consider enrolling in PreCalculus Math 102instead.Note: While your score on this test is a good indication of how well you might do in a Calculus class, itis of course not a guarantee of either your success or failure.

Resources1. Google TermsThe following is a list of relevant terms for each of the 40 questions in this diagnostic test. If you haddifficulties with specific questions, you may wish to google the given term below to look for usefulresources, including online examples, YouTube videos, and more.1. Google: “fraction arithmetic”2. Google: “simplify algebraic expressions involving fractions”3. Google: “simplify algebraic expressions involving exponents”4. Google: “exponent arithmetic”5. Google: “factoring trinomials”6. Google: “factoring trinomials”7. Google: “quadratic formula”8. Google: ”solving equations involving absolute values”9. Google: “solving inequalities involving absolute values”10. Google: “solving quadratic inequalities”11. Google: “solving two linear equations”12. Google: “simplify algebraic expressions involving complex fractions”13. Google: “simplify algebraic expressions involving common denominators”14. Google: “exponent arithmetic”15. Google: “difference of squares”16. Google: “solving rational equations”17. Google: “evaluating functions”18. Google: “function composition examples”19. Google: “equation of a line”20. Google: “equation of a parabola”21. Google: “equation of a line through two points”22. Google: “equation of a perpendicular line”23. Google: “finding the vertex of a parabola”24. Google: “intersection of line and parabola example”25. Google: “intersection of two parabolas”26. Google: “working with percentages”27. Google: “shared work word problems”28. Google: “distance speed time problems”29. Google: “linear cost function examples”30. Google: “area of triangles”31. Google: “distance between two points”32. Google: “area of squares and circles”

33. Google: “convert radians to degrees”34. Google: “trigonometry of right triangles”35. Google: “trigonometry with angles larger than pi”36. Google: “trigonometry of right triangles”37. Google: “trigonometry of right triangles tangent”38. Google: “trigonometric functions”39. Google: “intersect of sine and cosine”40. Google: “trigonometric identities”2. Text ResourcesIf you require more in-depth review (and have elected not to enrol in Math 102), you should alsoconsider working through a PreCalculus text.The following are online open text (i.e. free) resources: Precalculus, 3rd Edition: http://www.stitz-zeager.com/Precalculus: An Investigation of Functions: http://www.opentextbookstore.com/precalc/The following are relatively inexpensive PreCalculus books that can be ordered through onlinebooksellers (such as Amazon). Just-in-Time Algebra and Trigonometry for Calculus, by Mueller, BrentSchaum’s Outline of PreCalculus, by Safier

M110 PreCalculus Diagnostic Test Success in a first year Calculus class is highly dependent on your algebra skills. The following is a self-diagnostic test to be taken by students prior to entering a Math 110 Calculus class (note that

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