College Algebra And Trigonometry
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College Algebra and Trigonometry Level 1 (10 seconds each) 1. The number of permutations of the letters of the word PAINTS is a. 6. b. 720. c. 120. d. 360. 2. Which operation is not closed to integers? a. Addition. b. Subtraction. c. Multiplication. d. Division. 3. The expression a. b. c. d.
6nx 6 n is equivalent to 3nx 3n
2nx 3 . 2 x 3n . 2x 2 . 3nx 2 .
4. The product of a + b and its conjugate is a. a + b . b. a − b . c. 1. d. 0. 5. Which equation does not have any real roots? a. x 2 = x b. x 2 − 5 = 0 c. x 2 + 5 = 0 d. 5 − x 2 = 0 6. The solution set of the equation x 2 + 3 x − 10 = 0 is a. { − 5,2} . b. { − 2,5} . c. { − 10,3} . d. φ . 7. Generally if a is positive, then x < a is equivalent to a. –a < x < a. b. x < -a or x > a. c. x > a.
d. x < a. 8. The line ax + by + c = 0 has a slope of a. ab. b b. − . a b c. . a a d. − . b 9. Rona is twice as old as Nenita. Ten years ago, Rona is thrice as old as Nenita. How old is Rona? a. 30. b. 20. c. 10. d. 0. 10. A parabola opening downward has one zero if a. it touches the x-axis at two points. b. it touches the x-axis at one point. c. it touches the y-axis at one point. d. it does not touch the x-axis. 11. The graph of a cubic function has a maximum of a. 1. b. 2. c. 3. d. 4. 12. The equation x 3 − 8 = 0 has a. 3 real roots. b. 2 real roots. c. 1 real root. d. no real roots. 13. The expression i −7 is equivalent to 1 a. . i b. -1. 1 c. − . i d. 1. 14. The eccentricity of a circle is equal to a. the square of the length of its radius. b. the length of its radius.
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 inscribed in a semicircle whose one side is a diameter is a. always right. b. sometimes right. c. always acute. d. sometimes obtuse.
b. 225. c. 2-25. d. Infinite. 22. The sum of the infinite series … + (-10) + (-5) + 0 + 5 + 10 + … is a. 0. b. 5100. c. 5-100. d. Infinite. 23. x − y is a factor of x k − y k where k > 0, k is an integer. a. Always true b. Sometimes true c. Never true
17. Right triangle XYZ whose hypotenuse is YZ is isosceles if tan(m∠Y ) is a. 0. b. between 0 and 1. c. 1. d. more than 1.
24. The binomial 125 x 3 + y 9 has a. One prime factor. b. Two prime factors. c. Three prime factors. d. Four prime factors.
18. The slope of a line is equal to a. the sine of its angle of inclination to the positive x-axis. b. the cosine of its angle of inclination to the positive x-axis. c. the tangent of its angle of inclination to the positive x-axis. d. the cotangent of its angle of inclination to the positive x-axis.
25. Two solutions are mixed together. 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%.
19. The graph of cos(2 x − 4) = y is a. a wave. b. a circle. c. a line. d. an irregular curve.
26. Parabola A has a latus rectum of 3 inches, while Parabola B has that of 6 inches. This means that a. A is narrower than B. b. B is narrower than A. c. None of the choices. x2 27. The equation − y 2 = 1 is the 4 representation of a. a point. b. a circle. c. an ellipse. d. a hyperbola.
20. The graph of the polar equation 2 sin θ + cos θ = is r a. a line. b. a limacon. c. a circle. d. a lemniscate. Level 2 (45 seconds each) 21. The sum of the infinite series 2 + 4 + 6 + 8 + … is a. 0.
28. Suppose log a = 16 , log b = 4 and log c = 8 . ab Then log is c
a. b. c. d.
12. 20. 8. not determinable.
a. b. c. d.
29. The sum of the reciprocals of two distinct 1 numbers is 4. One number is . The other 2 number is a. 2. b. 4. 1 c. . 4 1 d. . 2 30. The graph of the function f ( x ) = 2 x + a. b. c. d.
1 has 9
a vertical asymptote. no vertical asymptotes. no horizontal asymptotes. no asymptotes at all.
31. An apprentice can make 10 handicraft 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 units in 3 days. b. 100 units in 3 days. c. 60 units a day. d. 40 units a day. 32. 100 square tiles fit a certain room. If the tiles have twice the length of each side as the original, a. 50 tiles would fit the room. b. 25 tiles would fit the room. c. 200 tiles would fit the room. d. 400 tiles would fit the room. 33. The numerical value of log10 ( log 2 1) is a. 0. b. 10. c. 2. d. not defined. 34. 10 persons joined a party. The maximum number of handshakes produced by the persons, assuming that no two persons shook their hands twice is
45. 100. 20. 90.
35. If a = 2 9 and b = 4 3 , then the numerical a value of is b 1 a. . 64 b. 64. c. 8. d. 4. 36. The line perpendicular 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 that opens to the left among the choices is a. x 2 + y = 2 x + 1 . b. y = x 2 + 2 x + 1 . c. y 2 + x = 2 y + 1 . d. x = y 2 + 2 y + 1 . 38. The ellipse 9 x 2 + 4 y 2 = 1 is a. 2 units long. b. 3 units long. 1 c. unit long. 2 1 d. unit long. 3 39. Two numbers whose sum is x has a maximum possible product of a. 2x 2 . b. x 2 . x2 c. . 2 x2 d. . 4 40. The expression 10 2 + 4(10 )(15) + 4(15) 2 is equivalent to
a. b. c. d.
[2(10) + 2(15)]2. 2(10 + 15)2. [2(10) + 15]2. [10 + 2(15)]2.
41. If g and h are numbers that satisfy the equation ax 2 − 16ax + 9 = 0 , then the numerical value of g + h is a. 16. b. 9. c. dependent on the value of a. d. not determinable. 42. Using the same information on item no. 41, the numerical value of gh is a. 16. b. 9. c. dependent on the value of a. d. not determinable. 43. The smaller of two numbers is 3 less 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 the truck 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 at a rate of 72 km/h and overtakes the truck in 8 h, what is the average speed of the truck? a. 56 km/h. b. 81 km/h. c. 64 km/h. d. 49 km/h. 45. The equation ( 2,999,999)( 3,000,001) = ( 3,000,000) 2 − 1 is a. True. b. False. 1 has 2 47. The reciprocal of csc 20° is 48. The reciprocal of cot 135° is 49. A and B are measures of the acute angles in a right triangle. Hence, sin A = 46. Arcsin
50. In triangle
6nx 6 n is equivalent to 3nx 3n
2nx 3 . 2 x 3n . 2x 2 . 3nx 2 .
4. The product of a + b and its conjugate is a. a + b . b. a − b . c. 1. d. 0. 5. Which equation does not have any real roots? a. x 2 = x b. x 2 − 5 = 0 c. x 2 + 5 = 0 d. 5 − x 2 = 0 6. The solution set of the equation x 2 + 3 x − 10 = 0 is a. { − 5,2} . b. { − 2,5} . c. { − 10,3} . d. φ . 7. Generally if a is positive, then x < a is equivalent to a. –a < x < a. b. x < -a or x > a. c. x > a.
d. x < a. 8. The line ax + by + c = 0 has a slope of a. ab. b b. − . a b c. . a a d. − . b 9. Rona is twice as old as Nenita. Ten years ago, Rona is thrice as old as Nenita. How old is Rona? a. 30. b. 20. c. 10. d. 0. 10. A parabola opening downward has one zero if a. it touches the x-axis at two points. b. it touches the x-axis at one point. c. it touches the y-axis at one point. d. it does not touch the x-axis. 11. The graph of a cubic function has a maximum of a. 1. b. 2. c. 3. d. 4. 12. The equation x 3 − 8 = 0 has a. 3 real roots. b. 2 real roots. c. 1 real root. d. no real roots. 13. The expression i −7 is equivalent to 1 a. . i b. -1. 1 c. − . i d. 1. 14. The eccentricity of a circle is equal to a. the square of the length of its radius. b. the length of its radius.
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 inscribed in a semicircle whose one side is a diameter is a. always right. b. sometimes right. c. always acute. d. sometimes obtuse.
b. 225. c. 2-25. d. Infinite. 22. The sum of the infinite series … + (-10) + (-5) + 0 + 5 + 10 + … is a. 0. b. 5100. c. 5-100. d. Infinite. 23. x − y is a factor of x k − y k where k > 0, k is an integer. a. Always true b. Sometimes true c. Never true
17. Right triangle XYZ whose hypotenuse is YZ is isosceles if tan(m∠Y ) is a. 0. b. between 0 and 1. c. 1. d. more than 1.
24. The binomial 125 x 3 + y 9 has a. One prime factor. b. Two prime factors. c. Three prime factors. d. Four prime factors.
18. The slope of a line is equal to a. the sine of its angle of inclination to the positive x-axis. b. the cosine of its angle of inclination to the positive x-axis. c. the tangent of its angle of inclination to the positive x-axis. d. the cotangent of its angle of inclination to the positive x-axis.
25. Two solutions are mixed together. 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%.
19. The graph of cos(2 x − 4) = y is a. a wave. b. a circle. c. a line. d. an irregular curve.
26. Parabola A has a latus rectum of 3 inches, while Parabola B has that of 6 inches. This means that a. A is narrower than B. b. B is narrower than A. c. None of the choices. x2 27. The equation − y 2 = 1 is the 4 representation of a. a point. b. a circle. c. an ellipse. d. a hyperbola.
20. The graph of the polar equation 2 sin θ + cos θ = is r a. a line. b. a limacon. c. a circle. d. a lemniscate. Level 2 (45 seconds each) 21. The sum of the infinite series 2 + 4 + 6 + 8 + … is a. 0.
28. Suppose log a = 16 , log b = 4 and log c = 8 . ab Then log is c
a. b. c. d.
12. 20. 8. not determinable.
a. b. c. d.
29. The sum of the reciprocals of two distinct 1 numbers is 4. One number is . The other 2 number is a. 2. b. 4. 1 c. . 4 1 d. . 2 30. The graph of the function f ( x ) = 2 x + a. b. c. d.
1 has 9
a vertical asymptote. no vertical asymptotes. no horizontal asymptotes. no asymptotes at all.
31. An apprentice can make 10 handicraft 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 units in 3 days. b. 100 units in 3 days. c. 60 units a day. d. 40 units a day. 32. 100 square tiles fit a certain room. If the tiles have twice the length of each side as the original, a. 50 tiles would fit the room. b. 25 tiles would fit the room. c. 200 tiles would fit the room. d. 400 tiles would fit the room. 33. The numerical value of log10 ( log 2 1) is a. 0. b. 10. c. 2. d. not defined. 34. 10 persons joined a party. The maximum number of handshakes produced by the persons, assuming that no two persons shook their hands twice is
45. 100. 20. 90.
35. If a = 2 9 and b = 4 3 , then the numerical a value of is b 1 a. . 64 b. 64. c. 8. d. 4. 36. The line perpendicular 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 that opens to the left among the choices is a. x 2 + y = 2 x + 1 . b. y = x 2 + 2 x + 1 . c. y 2 + x = 2 y + 1 . d. x = y 2 + 2 y + 1 . 38. The ellipse 9 x 2 + 4 y 2 = 1 is a. 2 units long. b. 3 units long. 1 c. unit long. 2 1 d. unit long. 3 39. Two numbers whose sum is x has a maximum possible product of a. 2x 2 . b. x 2 . x2 c. . 2 x2 d. . 4 40. The expression 10 2 + 4(10 )(15) + 4(15) 2 is equivalent to
a. b. c. d.
[2(10) + 2(15)]2. 2(10 + 15)2. [2(10) + 15]2. [10 + 2(15)]2.
41. If g and h are numbers that satisfy the equation ax 2 − 16ax + 9 = 0 , then the numerical value of g + h is a. 16. b. 9. c. dependent on the value of a. d. not determinable. 42. Using the same information on item no. 41, the numerical value of gh is a. 16. b. 9. c. dependent on the value of a. d. not determinable. 43. The smaller of two numbers is 3 less 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 the truck 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 at a rate of 72 km/h and overtakes the truck in 8 h, what is the average speed of the truck? a. 56 km/h. b. 81 km/h. c. 64 km/h. d. 49 km/h. 45. The equation ( 2,999,999)( 3,000,001) = ( 3,000,000) 2 − 1 is a. True. b. False. 1 has 2 47. The reciprocal of csc 20° is 48. The reciprocal of cot 135° is 49. A and B are measures of the acute angles in a right triangle. Hence, sin A = 46. Arcsin
50. In triangle
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