[PDF] College Algebra Review for Accuplacer Placement Exam - GCC.pdf | Plain Text

Glendale Community College, AZ College Algebra Review for Accuplacer Placement Exam This exam is intended as an overall review and includes problems similar to what you may expect on the Accuplacer exam. However, it is NOT a sample exam. Accuplacer Exam Info  Consult the following web site for the most up-to-date information on placement testing at GCC. http://www.gccaz.edu/testingservices/ Google “GCC Testing Services.”  The most recent version of this exam should be available at http://www.gccaz.edu/math/Placement.htm .  Please send any comments to walter.kehowski@gccaz.edu Please include the following information in your email: LAST COMPILED DATE: April 30, 2013.This review was created by the GCC Mathematics Placement Exam Review Committee (GCCMPERC): Walter A. Kehowski (Chair), Jason Bright, Anne Dudley, Miriam Pack.

Glendale Community College, AZ College Algebra Review for Accuplacer Placement Exam 1. Simplify 3a 2 bc 4 4 ab 2! 3 (a) 3 a 6 c 12 4 b 2 (b)3 a 3 c 12 4 b 3 (c)27 a6 c 12 64 b3 (d)27 a3 c 12 64 b3 2. Simplify 64 x9 y 3
1=3 (a) 64 x3 y 3 (b) 192x27 y9 (c)4x 3 y (d)4 x 3 y 3. Simplify x 2 1 x ‚ 2
x 2 ‚ 5x ‚ 6 x 2 ‚ 4x ‚ 3 (a) x 1 (b)„x 1…„x ‚3… „x ‚2…„x 3… (c) x‚ 1 (d)„x 1…„x ‚1…„x ‚6… „x ‚2…„x 3… 4. A jogger started a course and jogged at an average speed of 4 mph. One hour later, a cyclist started the same course and cycled at an average speed of 11 mph. How long after the jogger started did the cyclist overtake the jogger? (a) 15 7 hours (b)5 7 hour (c)14 7 hours (d)4 7 hour 5. A chemist mixes an 8% hydrochloric acid solution with a 5% hydrochloric acid solution. How many milliliters of the 5% solution should the chemist use to make a 750-milliliter solution that is 7% hydrochloric acid? (a) 400 ml (b)250 ml (c)500 ml (d)300 ml 6. Solve by factoring: 6 z2 7z 3ƒ 0. (a) 2 3 ; 1 3 (b) 3 2 ; 1 3 (c) 3 2 ; 1 3 (d) 2 3 ; 6 7 7. Use the quadratic formula to solve y2 ‚ 10 y‚20 ƒ0 (a) 10 p 10 2 (b) 4;5 (c)5  p 5 (d) 4; 5 8. Solve by factoring: x3 ƒ 81 x. (a) 9;0 ;9 (b)3;0 ;3 (c)9;9 (d)0;81 9. Solve the inequality 2x 3< 6. Write the solution using set notation. (a) fx jx < 3=2 g (b)fx jx > 9=2 g (c)fx jx < 9=2 g (d)fx jx > 3=2 g 2

10. Given that pvaries inversely as the square root of qand that pƒ 3 when qƒ 9, nd pwhen q ƒ 16. (a) 9 4 (b) 3 4 (c) 4 3 (d) 9=2 11. Given that nvaries directly with the square of pand inversely as the square of q, and that nƒ 12 when pƒ 3, qƒ 2, nd nwhen pƒ 6, qƒ 4. (a) 12 (b)4=3 (c)9=16 (d)16=9 12. Determine the xand yintercepts of the graph of 5 x‚ 2y ƒ10. (a) „5 ;0 …; „ 0;2 … (b)„2 ;0 …; „ 0;5 … (c)„5 ;0 …; „ 2;0 … (d)„0 ;5 …; „ 0;2 … 13. Given f „x…ƒ2x 4, nd f „4…. (a) 4 (b)4 (c)32 (d)12 14. Given g„x…ƒx2 1, nd g„h‚2…. (a) h2 ‚ 4h ‚ 5 (b)h2 ‚ 4h ‚ 3 (c)h2 ‚ 1 (d)h2 ‚ 2h ‚ 3 15. Determine the domain of the function f „x…ƒ3 p x 2. (a) „1 ;2 … [ „2 ;1 … (b)†2 ;1 … (c)„1 ;2 ‡ [ †2 ;1 … (d)„2 ;1 … 16. A van was purchased for $29 ;000. Assuming that the van depreciates at a constant rate of $4000 per year (straight-line depreciation) for the rst 7 years, write the value vof the van as a function of time t, 0 t 7, and calculate the value of the van 3 years after purchase. (a) v „t… ƒ29 ;000 4000 t; v „ 3… ƒ 17 ;000 (b)v „t… ƒ4000 t; v „ 3… ƒ 12 ;000 (c) v „t… ƒ29 ;000 ‚4000 t; v „ 3… ƒ 41 ;000 (d)v „t… ƒ4000 3 t ; v „ 3… ƒ 444 :44 17. Find the equation of the line with slope 3 =5 and y-intercept „0 ; 5…. (a) yƒ 3 5 x 3 (b)yƒ 5 3 x 5 (c)yƒ 3 5 x 5 (d)yƒ 5 3 x ‚ 5 18. Find the equation in slope-intercept form of a line that passes through „ 3;5 … and „6 ;8 …. (a) yƒ 1 3 x ‚ 6 (b) yƒ3x ‚ 10 (c)yƒ3x ‚ 14 (d)yƒ 1 3 x 14 3 19. Find the value of xin the domain of f „x…ƒ4x ‚ 1 for which f „x…ƒ 1. (a) 3 (b)0 (c)1=4 (d)1=2 3

20. Graph f „x…ƒ2„x ‚1…2 . (a) (b) (c) (d) 21. Solve the equation x3 5x 2 4x ‚ 20 ƒ0. (a) 2;2 ;5 (b)5;2 i; 2i (c)5; 2;2 (d)5;2 i; 2i 22. Graph f „x…ƒx 2 4 3 x ‚ 9 (a) (b) (c) (d) 23. Graph f „x…ƒ 1‚ log 2x . (a) (b) (c) (d) 24. Write log by 2 xz 5 in terms of log bx , log by , and log bz . (a) 2 log by 5 log bxz (b)2 log by log bx ‚ 5 log bz (c) 2 log by log bx 5 log bz (d)2 log by ‚log bx ‚ 5 log bz 25. Write log 10„x ‚3… 4 log 10x as a single logarithm. (a) log 10†„x ‚3… ‚ x4 ‡ (b)log 10„x ‚3…x 4 (c) log 10x ‚ 3 x 4 (d) log 10x ‚ 3 4 x 4

26. Solve 5 x ƒ 94. (a) log 94 log 5 (b) log 5 log 94 (c) 94 5 (d) 5 p 94 27. Solve log x‚ log „x15 …ƒ 2. (a) 5 (b)5;20 (c)20 (d)No solution. 28. Solve log 10 4 x 3 ƒ 7. (a) 2:5 (b)1 (c)0:4542 (d)No solution. 29. Ifis an acute angle of a right triangle and cot ƒ 12 =5, nd csc . (a) 12=13 (b)5=13 (c)13=12 (d)13=5 30. Find the exact value of sin 30  sin 45  cos 45  . (a) 0 (b)1=2 (c)1 (d)2 31. Evaluate sin 20  6 . (a) p 3 2 (b) p 3 2 (c) 1 2 (d) 1 2 32. Find the values of all six trigonometric functions with the angle in standard position with the terminal side passing through the point P „24 ; 7…. (a) sinƒ 7=25 cos ƒ 24=25 tan ƒ 7=24 csc ƒ 25=7 sec ƒ 25=24 cot ƒ 24=7 (b) sinƒ 7=25 cos ƒ 24=25 tan ƒ 7=24 csc ƒ 25=7 sec ƒ 25=24 cot ƒ 24=7 (c) sinƒ 24=25 cos ƒ 7=25 tan ƒ 24=7 csc ƒ 25=24 sec ƒ 25=7 cot ƒ 7=24 (d) sinƒ 7=25 cos ƒ 24=25 tan ƒ 24=7 csc ƒ 25=7 sec ƒ 25=24 cot ƒ 7=24 33. Find the exact value of cos 2 180  sin 2 120  . (a) 1=4 (b)7=4 (c)1=4 (d)3=4 34. Write cos 8 cos 3 ‚ sin 8 sin 3 in terms of a single trigonometric function. (a) sin 5 (b)cos 11 (c)cos 5 (d)sin 11 35. Find an exact radian value for sin 1  1 2  . (a)  6 (b)  6 (c)  3 (d)  3 5

36. Solve the equation 2 cos 2 x ‚ sin x‚ 1ƒ 0, 0 x 2 . (a)  (b)3  2 (c)  3 ;  ; 5  3 (d)  3 ; 5  3 37. Solve the system of equations ( 2x 3y ƒ 5 3x ‚ yƒ 4. (a) „1 ; 1… (b)Dependent (c)Inconsistent (d)„ 1;1 … 38. Graph the inequality 3 x‚ y 2. (a) (b) (c) (d) 6

College Algebra Review for Accuplacer Placement Exam ANSWER KEY 1. d 2. c 3. a 4. c 5. b 6. b 7. c 8. a 9. b 10. a 11. a 12. b 13. d 14. b 15. d 16. a17. c 18. a 19. d 20. a 21. a 22. b 23. d 24. c 25. c 26. a 27. c 28. a 29. d 30. a 31. b 32. a33. c 34. c 35. a 36. b 37. d 38. a 7