PRACTICE PLACEMENT TEST - Barton College

BARTON COLLEGEPRACTICE PLACEMENT TEST1. Simplify:20 43 (!8)a) 42. Simplify:b) ‐4c) 12d) ‐10.5c) a – 11d) 7a ‐17(2a – 4) 2(a – 5) – 3(a 1)a) 7a – 11b) a – 173. Evaluate the expression: 4a 2 ! 4ab b 2 , when a 2 and b 5a) ‐14b) 1c) 66d) 814. Firefighters use the formula S 0.5P 26 to compute the horizontal range S in feet of water from aparticular hose, where P is the nozzle pressure in pounds. Find the horizontal range if pressure is 90 lb.a) 44 feet5. Simplify:(2 x 2 !3 x 26. Simplify:a)w2 v 44u 7c) 19 feetd) 71 feetb) 18x8c) !18x12d) !54x83)a) 54x12" 2u !5v 2 # %& 8w 'b) 450 feet!2b)16v 4w2u10c)16w2u10v4d)u 7v 44 w27. Express in scientific notation: 0. 0000056a) 5.6 " 10!6b) 5.6 ! 106c) 5.6 " 10!5d) 5.6 " 10!7b) 1200000c) 120000d) 120008. Expand: 1.20 ! 105a) 12000000PAGE 1 OF 12

BARTON COLLEGEPRACTICE PLACEMENT TEST15 3x! 48 89. Solve:a) x 4b) x 210. Solve:11. Solve for m: F d) x 14b) x 28c) x ‐8d) x ‐18b) m Frv 2c) m Fv 2rd) m Frv2c) P A1 rtd) P A2rtmv 2rFrv 2A P Pr t12. Solve P:b) P a) P A ! rt13. Solve:128(x – 2) – 5(x 4) 20 xa) x 9a) m c) x A ! rt264 x !5 xa) x ‐5b) x ‐6c) x ‐10d) x 214. Solve: 2 x ! 3 5b) x a) x 4, 015. Solve: 3 !a) x 416. Simplify:a) x – 2yx4 x!4 4! x1 11,2 2c) x 0,11212d) x ! , !b) x ‐4c) x 1d) No solutionb) x(x 3y)c) x(x‐2y)d) x 3yx3 x 2 y ! 6 xy 2x 2 ! 2 xyPAGE 2 OF 12112

BARTON COLLEGEPRACTICE PLACEMENT TEST17. Simplify:4x2 !12 x2 5x ! 3a) Cannot be simplifiedb)2x !1x 3c)2x 1x !3d)2x 1x 318. Solve: ‐3(2x – 3) 27a) x ‐619. Solve:b) x ‐6c) x ‐3d) x ‐3b) x ‐2c) x ‐2d) x 22 x 4 3 5 15a) x 220. John averaged 82 out of 100 on his first three tests. What was John’s score on the fourth test if his averageafter the fourth test dropped to 79 out of 100?a) Cannot be foundb) 80c) 75d) 7021. The sales tax rate in Wilson County is 6.75%. Suppose total price of an item that you bought in WilsonCounty including taxes is 14.93, what is the price (rounded to two decimal places) before tax?a) 12.93b) 13.99c) 15.94d) 8.9122. The long term parking rate at Raleigh‐Durham Airport is 2 per hour (or part of an hour) with 10 dailymaximum (12:00 a.m. to 12:00 a.m.). Suppose you park your car on Friday afternoon at 8:30 p.m. and pick it upon the following Tuesday at 9:30 a.m., what will be you parking fee?a) 58b) 50c) 48d) 3823. Solve: 2x(10x 8) ‐3(x 1)a) x 3 1,4 53 14 53415b) x ! ,c) x ! , !b) x 3, ‐2c) x !3 2 2d) x 3 1,!4 5d) x !3 2 22224. Solve: (2 x ! 3) ! 8 0a) x 3 2 22PAGE 3 OF 12

BARTON COLLEGEPRACTICE PLACEMENT TEST25. The profit, P, realized by a company varies directly as the number of products s it sells. If a company makesa profit of 7800 on the sale of 325 products, what is the profit when the company sells 5000 products?a) 120,000b) 100,000c) 80,000d) 60,00026. If the voltage, V, in an electric circuit is held constant, the current I, is inversely proportional to theresistance, R. If current is 120mA (milliampere) when resistance is 5 ohms, find the current when theresistance is 15 ohms.a) 40mAb) 357mAc) 360mAd) 200mA27. A 36 foot long tube is cut into two pieces with ratio 4:5. Find the length of the shorter piece.a) 9 feetb) 16 feetc) 12 feetd) 20 feet28. A large square pizza has 49 pieces (square slices). John, Jack and Jane ate all the pieces in the ratio 4:2:1respectively. How many pieces did Jack eat?a) 10 pieces29. Solve:b) 12 piecesd) 18 piecesc) x ‐1d) x c) V ! hr 2d) V r ! h1! 2x 1 3b) x !a) x 030. Solve for V given r a) V c) 14 piecesr!h3212V!hb) V !hr231. Find the equation of the straight line passing through the points (2,‐4) and (1,0).a) y ‐ 4x 4b) y 4x – 4c) y 4x 4d) y ‐4x ‐ 432. Determine the x and y intercepts of the graph of 7x – 5y 35a) (5, 0) and (0, ‐7)b) (‐5, 0) and (0, 7)c) (‐5, 0) and (0, ‐7)PAGE 4 OF 12d) (5, 0) and (0, 7)

BARTON COLLEGEPRACTICE PLACEMENT TEST33. The linear relationship between the Fahrenheit scale and Centigrade scale for temperatures is givenby F 9C 32 . Which of the following statements, if any, are TRUE?5A. 68 o F corresponds to 20o Ca) Only Ab) Only BB. 40 o C corresponds to 78o Fc) Both A and Bd) Neither A nor B34. John (J) is 5 years older than his sister Mary (M) who is 2 years younger than her brother Paul (P). If J, Mand P denote their ages, which one of the following represents the given information?!J M 5 P M # 2!J M 5#M P 2a) "b) "!M J 5 P M # 2c) "!J M 5 M P # 2d) ""3 x ! 5 y !4 3x ! y 435. Solve the system: #a) (‐2, ‐10)b) (2, 2)!&2"5'c) 2, # %!4%3"&d) # ,0 36. The sum of two numbers is 31. Twice the smaller number is 11 more than the larger number. The positivedifference between the numbers isa) 4b) 3c) 2d) 137. Find the coordinates of a point A whose distance from the origin (0, 0) is 5 units.a) A (3, 3)b) A(-3, 2)c) A(4, -3)d) A(1, 4)38. Consider the circle given by the equation (x – 2)2 (y 1) 2 5. Find the center and radius.a) (‐2, 1); 5b) (2, ‐1); 5c) (2, ‐1); 5d) (‐2, 1); 5c) x 0 or x 16d) 0 x 1639. The inequality 8 ! x 8 is equivalent toa) x 0b) x 0PAGE 5 OF 12

BARTON COLLEGEPRACTICE PLACEMENT TEST40. The inequality x 4 ! 1 is equivalent toa) x ‐5b) x ‐3 or x ‐541. The interval solution to the inequalitya) (2, ! )b)c) x ‐5d) ‐5 x -3x!2 0 isx 1(!", 2 )c) (!", !1) # (2, " )d) (!1, 2 )42. Let f ( x) 1 ! 2 x . Find f (a ! 1)1 ! 2a ! 1a)b)1 ! 2ac)3 ! 2a!2ad)43. Let f (x ) 2 ! x 2 and g (x ) 2 x ! 1 . Which of the following, if any, is false?a)( f g )(0) !2b)(f! g )(1) 0c)( fg )(2 ) !6! f " (1) 1%g&d) #44. Let f (x ) 2 ! x 2 and g (x ) 2 x ! 1 . Which of the following, if any, is true?( f o g )(0 ) !2c) ( f o f )( x) 4 ! 4 x 2 x 4b) (g o f)(0 ) 3d) (g o g )( x) 4 x 2 ! 4 x 1a)45. Let f (x ) 3 ! 2 x . Find the difference quotienta) 1b) 2hf (x h ) ! f (x )hh ! 4xc)hd) ‐246. Consider the quadratic function f (x ) 2 x 2 ! 4 x 1 . Find the vertex of the graph of f (x ).a) (‐2, 1)b) (2, 1)c) (1, ‐1)d) (‐1, 7)47. The temperature, in degrees Fahrenheit, over a twelve hour period is given by the functionT(t) ‐0.5t2 6t 30, where t 0 denotes 6:00 a.m. When is the morning temperature 47.5o F?a) 12 noonb) 11:00 a.m.c) 10 a.m.PAGE 6 OF 12d) 9:00 a.m.

BARTON COLLEGEPRACTICE PLACEMENT TEST48. Simplify and express in the form a bi: (‐2 i)(3 2i)a) ‐8 0ib) ‐8 2i49. Simplify and express in the form a bi:a) 2 – 2ia) all real numbersd) ‐6 2ic) 4 – 4id) ‐4 4i!4i1 ib) ‐2 – 2i50. Find the domain of the function f ( x) c) ‐8 – ix 3.x2 1b) x 1, ‐1c) x ‐351. Find the equation of horizontal asymptote of the function f ( x) a) y 1b)y ‐152. Find the inverse function for f(x) a) f ‐1(x) 6x 3x!2.3b) f ‐1(x) 3x 2c) y 3d) x ‐3, ‐1, 1x 3x2 !1d) y 0c) f ‐1(x) 2x 3d) f ‐1(x) 3x 653. Which of the following pairs of exponential and logarithmic forms is false?a) 3‐2 1/9 ; log3(1/9) ‐2b) (1/2) ‐2 4; log 4(1/2) ‐2c) 103 1000; log(1000) 3d) e2 x ; ln(x) 254. Write in terms of log(x), log(y), log(z):!y zlog ## 2% xa) log(y) – 0.5 log(z) – 2 log(x)b) log(y) 0.5 log(z) – 2log(x)" &c) log(y) 0.5 log(z) 2log(x)d) log(y) 0.5log(z) 2log(x) 55. Find the hydronium‐ion concentration, H , of a solution given pH 7.1a) 7.9 10 –8 moles per literc) 8.3 10 –4 moles per literb) 7.1 10 –9 moles per literd) 1.3 107 moles per literPAGE 7 OF 12Note: pH ‐log(H )

BARTON COLLEGEPRACTICE PLACEMENT TEST56. Solve: e 2 x!1 32a) x 1 ln (32 )2b) x 1 ! ln (32 )2c) x 1 ln (16 )d) x c) x 5/3d) x 01 ln (16 )257. Solve the equation: log 2 ( x 1) ! log 2 ( x ! 1) 2a) x 3b) x 5!1"58. Suppose the population of a town is given by the model P (t ) 17250 # %2&t /10, where t denotes thenumber years since 2000. Which of the following statements is true?a) The population in 2000 was 8625.b) The population doubles every 10 years.c) The population is halved every ten yearsd) The population is growing by 50% every ten years.59. If the angle " a) 0 ! 90o3!radians, then5b) 90o ! 180oc) 180o ! 270od) 270o ! 360o60. If the light beam makes one complete revolution every 20 seconds, how long will it take to sweep andangle of 150o?a) less than 3 secondsc) between 5 and 7 secondsb) between 3 and 5 secondsd) between 7 and 10 seconds61. Given an isosceles triangle with base length 32 cm and altitude 12 cm, find the length of the congruentsides.a) 24 cmb) 22 cmc) 20 cm62. If tan ! 3 and sin ! 0 , then cos ! equalsPAGE 8 OF 12d) 18 cm

BARTON COLLEGEPRACTICE PLACEMENT TESTa) !31063. If csc! a)310b)110110d) !13and cos ! 0 , then cot ! equals5125b) !125(o64. Find the exact value of csc 225a) ! 2b) !(o65. Find the exact value of cot 420a)c)32b)c)512c)2d)c)3d)d) !1312)2222)3312! 51",#%% , find the value of the functions 66&'66. If the angle ! in standard position meets the unit circle at sin (! ) and cos (! ) .a) sin ! c) sin ! "51and cos ! "66b) sin ! "51and cos ! 6667. Find the expression that is equal tod) sin ! 1 sin !1 " sin !PAGE 9 OF 1215and cos ! 6615and cos ! "66

BARTON COLLEGEPRACTICE PLACEMENT TESTa) sin ! cos 2 !b)csc! 1csc! " 1c) 0d) sec 2 ! tan 2 !c) 2cot 2 ! " 1d) sec 2 ! csc 2 !268. Find the expression that is equal to (tan ! cot ! )a) tan 2 ! cot 2 !b) 2 tan ! cot !69. The minute hand of a clock is 6cm long. How far does the tip of the minute hand travel in 15 minutes?a) 12! cmb) 9! cmc) 6! cmd) 3! cm70. Find the area of a sector of a circle with central angle θ 3 radians, if the radius of the circle is 6 in.a) 54 in2b) 36 in2c) 27 in2d) 18 in271. The area of the sector of a circle with central angle of 2 radians is 16m2. Find the radius of the circle.a) 16mb) 8mc) 4md) 2m72. Solve 4cos ! 6 5 (cos ! 1), 0 " ! 360oa) 0ob) 90od) 270oc) 180o73. Solve (2sin ! # 3)(cos ! 2 ) 0, 0 ! "!,03a) No solutionb) " 74. Solve 2sin 2 " sin " 1, #!! " 22! !b) " , #3 2a) " #! !,6 2c) " 0,c) " !2! !,#6 275. In a right triangle ABC with m !C 90o , if AC 12 and sin (B ) a) 20b) 6c) 2 14PAGE 10 OF 12d) " ! !,3 2d) " #3, find AB.5d) 8! !,3 2

BARTON COLLEGEPRACTICE PLACEMENT TEST76. In triangle ABC with m !A 30o , m !B 45o and BC 2 , find AC.a)2b) 2c) 3d) insufficient information77. In triangle ABC with m !A 30o , m !B 60o and AB 12, find BC.a) 6 3c) 12 3b) 6d) insufficient information!" x cos (t )" y 3 sin (t )78. Eliminate the parameter t in the given parametric equation #a) y 3 b) x 3 xyc) x 2 y 2 922d) x ( y ! 3) 1"! x sin (t )cos (t )" y sin (2t )79. Eliminate the parameter t in the given parametric equation #a) x 2yb) y 2xrc) xy 2d) xy 12r80. Given vectors u !4, !3 and v 2,1 , which if the following statements, if any, is false.ra) u 5rrrb) u 2v 0r rc) v ! u 6, 4PAGE 11 OF 12d) None of these

BARTON COLLEGEPRACTICE PLACEMENT TESTANSWER 78.79.80.bbdbb.PAGE 12 OF 12

BARTON COLLEGE PRACTICE PLACEMENT TEST PAGE 4 OF 12 25. The profit, P, realized by a company varies directly as the number of products s it sells. If a company makes a profit of 7800 on the sale of 325 products, what is the profit when the company sells 5000 products?