College Algebra and Trigonometry

8. The line ax + by + c = 0 has a slope of  a. ab.

College Algebra and Trigonometry Level 1 (10 seconds each)

 b.

1. The numbe numberr of permu permutat tation ionss of the the letter letterss of  the word PAINTS is a. 6 . b. 720. c. 120. d. 360. 2. Which Which operat operation ion is is not close closed d to integ integers ers?? a. Addition.  b.  b. Subt Subtra ract ctio ion. n. c. Mult Multip ipli lica cati tion on.. d. Division. 3. The The exp expre ress ssio ion n

6nx 6 n 3nx

3n

is equivalent to

3

a. 2 nx .  b. 2 x 3n . c. 2 x 2 . d. 3nx 2 . 4. The The pro produ duct ct of  a a. a + b .  b. a − b . c. 1 . d. 0 .

+

b

and its conjugate is

5. Which Which equat equation ion does not have any real real roots? a.  x 2 = x  b.  x 2 − 5 = 0 c.  x 2 + 5 = 0 d. 5 −  x 2 = 0 6. The soluti solution on set set of of the the equa equatio tion n 2  x + 3 x − 10 = 0 is a. {− 5, 2} .  b. {− 2,5} . c. {−10 ,3} . d. . 7. Gene Generrally ally if a f a is positive, then equivalent to a.  –a < x < a.  b.  x < -a or  x  x > a. c.  x > a. d.  x < a.

−

b a

c.

b . a

d.

−

a b

.

.

9. Rona Rona is twic twicee as old old as Neni Nenita. ta. Ten Ten year yearss ago, Rona is thrice as old as Nenita. How old is Rona? a. 30. b. 20. c. 10. d . 0. 10. A parabola parabola opening downward downward has one zero zero if  a. it touche touchess the the x-axi x-axiss at two points points..  b. it touch touches es the the x-axi x-axiss at one poin point. t. c. it touche touchess the the y-axi y-axiss at one poin point. t. d. it doe doess not not touc touch h the the x-ax x-axis is.. 11. The graph graph of a cubic functio function n has a maximum of  a. 1 . b . 2. c. 3 . d . 4. 12. The equat equation ion  x 3 − 8 = 0 has a. 3 re real ro roots.  b.  b. 2 rea reall roo rootts. c. 1 real root. d. no real eal roo roots ts.. 13. The expression expression i −7 is equivalent to a.

1 i

.

b. -1. c.

−1i .

d . 1.  x

< a is 14. The eccentricit eccentricity y of a circle circle is equal to a. the square square of the the lengt length h of its its radi radius. us.  b. the the len lengt gth h of its its radi radius us.. c. 0 . d . 1.

15. sin 400 ° is equivalent to a. sin 40 ° .  b. cos 40 ° . c. sin( −400 °) . d. cos( −400 °) . 16. A triangle triangle inscribed inscribed in a semicircl semicirclee whose one side is a diameter is a. alwa alway ys right ight..  b.  b. some someti time mess righ right. t. c. alwa alway ys acut acute. e. d. some someti time mess obtu obtuse se.. 17. Right triangle triangle XYZ whose whose hypotenuse hypotenuse is Y ) is YZ  is isosceles if  tan( m∠ a. 0 .  b.  b. betw betwee een n 0 and and 1. c. 1 . d. more th than 1. 18. The slope slope of a line is equal to a. the sine sine of its its angl anglee of incl inclina inatio tion n to the positive x-axis.  b. the cosi cosine ne of its angle angle of incl inclina inatio tion n to the positive x-axis. c. the tange tangent nt of of its its angle angle of of incli inclinat nation ion to the positive x-axis. d. the the cota cotange ngent nt of of its its angl anglee of  inclination to the positive x-axis. 19. The grap graph h of cos( 2 x − 4) =  y is a. a wave. b. a ci circle. c. a line. d. an irr irreg egul ular ar cur curve ve.. 20. The graph of of the polar polar equation equation sin θ  + cos cos θ  =

a. b. c. d.

2 r 

is

a line. a li limacon con. a circle. a lem lemni nisscat cate.

Level 2 (45 seconds each) 21. The sum of the infinit infinitee series 2 + 4 + 6 + 8 + … is a. 0 . b. 225. c. 2-25. d. Infinite.

22. The sum of the infinite series series … + (-10) + (-5) + 0 + 5 + 10 + … is a. 0 . b. 5100. c. 5-100. d. Infi nfinit nite. 23.  x − y is a factor of   x k  − y k  where k > k > 0, k is k is an integer. a. Always true  b.  b. Some Someti time mess true true c. Never true 24. The binom binomial ial 125  x 3 + y 9 has a. One One prim primee fact factor or..  b.  b. Two Two prim primee fact factor ors. s. c. Thre Threee prim primee fact factor ors. s. d. Four Four pri prime me fac facto tors rs.. 25. Two solutions solutions are mixed mixed together. Solution Solution A, with 9% concentration is mixed with 12% solution B. Solution A has twice the volume as Solution B. The resulting solution has a concentration of  a. 9.5%. b. 10%. c. 10.5%. d. 11%. 26. Parabola Parabola A has a latus rectum rectum of 3 inches, inches, while Parabola B has that of 6 inches. This means that a. A is is nar narro rowe werr tha than n B. B.  b. B is is nar narro rowe werr than than A. c. None None of the the cho choic ices es.. 27. The equat equation ion

 x 2 4

−

y2

=

1 is the representation

of  a. b. c. d.

a point. a ci circle. an ell ellipse. a hy hyperbol bola.

log a 28. Suppos Supposee log

=16

log b , log

 ab    is   c  

log  Then log

a. b. c. d.

12. 20. 8. not not det deter ermi mina nabl ble. e.

log = 4 and log

c

=8 .

29. The sum of the reciprocals reciprocals of two distinct distinct 1 numbers is 4. One number is . The other  2 number is a. 2 . b. 4 . c. d.

1 4

.

1 . 2

30. The graph graph of the the function function  f  ( x ) a.  b.  b. c. d.

=

2x +

1 9

has

a verti vertica call asym asympt ptot ote. e. no vert vertic ical al asym asympt ptot otes es.. no hor horiz izont ontal al asy asymp mpto tote tes. s. no asym asympt ptot otes es at all. all.

31. An apprentice apprentice can make 10 handicraft handicraft units units a day. If a master craftsman can make 90 units in 3 days, then 3 apprentices and a master  craftsman can make a. 300 300 uni units ts in 3 day days. s.  b.  b. 100 100 uni units ts in 3 days days.. c. 60 unit unitss a day day. d. 40 unit unitss a day day. 32. 100 square tiles fit a certain certain room. If the tiles have twice the length of each side as the original, a. 50 til tiles es woul would d fit fit the the room room..  b.  b. 25 til tiles es woul would d fit fit the the room room.. c. 200 tile tiless woul would d fit fit the the room room.. d. 400 til tiles es woul would d fit fit the the room room.. log 2 1) is 33. The numerica numericall value of log 10 ( log a. 0 . b. 1 0. c. 2 . d. not not de defined.

34. 10 persons persons joined a party. party. The maximum maximum number of handshakes produced by the  persons, assuming that no two persons shook  their hands twice is a. 4 5 . b. 100. c. 2 0 . d. 9 0.

2 9 and b a value of  is b

35. If  a

=

a.

1 64

= 4 3 , then the numerical

.

b. 64. c. 8 . d . 4. 36. The line line perpendicula perpendicularr to 2 x + 3 y + 5 = 0 among the choices is a. 3 x − 2 y +10 = 0 .  b. 3 x + 2 y −15 = 0 . c. 6 x + 9 y −15 = 0 . d. 4 x − 6 y +17 = 0 . 37. The parabola parabola that opens opens to the left among among the choices is 2 a.  x +  y = 2 x +1 . 2  b.  y =  x + 2 x +1 . 2 c.  y + x = 2 y +1 . d.  x =  y 2 + 2 y +1 . 38. The ellip ellipse se 9 x 2 + 4 y 2 = 1 is a. 2 un units lo long.  b.  b. 3 uni unitts lon long. g. 1 c. unit long. 2 d.

1 3

unit long.

39. Two numbers numbers whose whose sum sum is x is x has a maximum possible product of  a. 2 x 2 .  b.  x 2 .  x 2 c. . 2  x 2 d. . 4

)(15 ) + 4(15 ) is 40. The expression expression 10 2 + 4(10 )( equivalent to a. [2(10 2(10)) + 2( 2(15) 15)]2. b. 2(10 + 15) 2. c. [2(1 2(10) + 15]2. d. [10 + 2(1 2(15)] 5)]2. 2

 g and h are numbers that satisfy the 41. If  g and equation ax 2 − 16ax + 9 = 0 , then the numerical value of  g +  g + h is

a. b. c. d.

1 6. 9. depen depende dent nt on the the val value ue of a. not not dete determ rmin inab able le..

42. Using the same same information information on item no. 41, the numerical value of  gh  gh is a. 1 6 . b. 9 . c. depen depende dent nt on the the val value ue of a. d. not not dete determ rmin inab able le.. 43. The smaller smaller of two numbers numbers is 3 less than than the larger, and their sum is 43. the difference of  their squares is a. 116. b. 147. c. 129. d. 133. 44. One hour after after the truck has has left on an overnight haul, a messenger on a motorcycle leaves from the same starting point to overtake the truck. If the messenger travels km/h and overtakes the truck  at a rate of 72 km/ in 8 h, what is the average speed of the truck? a. 56 km/h. km/h. b. 81 km/h. km/h. c. 64 km/h. km/h. d. 49 km/h. km/h. 45. The equat equation ion

( 2,999 ,999 )( 3,000 ,001 ) = ( 3,000 ,000 ) 2 −1 is a. True. b. False. 1 has 2 47. The reciprocal reciprocal of of csc 20 is 48. The reciprocal reciprocal of of cot 135 135 is 49. A and B are measures measures of the acute angles angles in a right triangle. Hence, sin A = 50. In trian triangle gle

46. Arcs Arcsin in

°

°