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 is equivalent to

a. .b. .c. .d. .

4. The product of and its conjugate isa. .b. .c. 1.d. 0.

5. Which equation does not have any real roots?

a.b.c.d.

6. The solution set of the equationis

a. .b. .c. .d. .

7. Generally if a is positive, then < a is equivalent to

a. –a < x < a.b. x < -a or x > a.c. x > a.d. x < a.

8. The line has a slope ofa. ab.

b. .

c. .

d. .

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 hasa. 3 real roots.b. 2 real roots.c. 1 real root.d. no real roots.

13. The expression is equivalent to

a. .

b. -1.

c. .

d. 1.

14. The eccentricity of a circle is equal toa. the square of the length of its radius.b. the length of its radius.c. 0.d. 1.

15. is equivalent toa. .b. .c. .d. .

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.

17. Right triangle XYZ whose hypotenuse is is isosceles if is

a. 0.b. between 0 and 1.c. 1.d. more than 1.

18. The slope of a line is equal toa. 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.

19. The graph of isa. a wave.b. a circle.c. a line.d. an irregular curve.

20. The graph of the polar equation

is

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 +

… isa. 0.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. is a factor of where k > 0, k is an integer.

a. Always trueb. Sometimes truec. Never true

24. The binomial hasa. One prime factor.b. Two prime factors.c. Three prime factors.d. Four prime factors.

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%.

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.

27. The equation is the representation

ofa. a point.b. a circle.c. an ellipse.d. a hyperbola.

28. Suppose , and .

Then is

a. 12.b. 20.c. 8.d. not determinable.

29. The sum of the reciprocals of two distinct

numbers is 4. One number is . The other

number isa. 2.b. 4.

c. .

d. .

30. The graph of the function has

a. a vertical asymptote.b. no vertical asymptotes.c. no horizontal asymptotes.d. 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 isa. 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

a. 45.b. 100.c. 20.d. 90.

35. If and , then the numerical value

of is

a. .

b. 64.c. 8.d. 4.

36. The line perpendicular to among the choices is

a. .b. .c. .d. .

37. The parabola that opens to the left among the choices is

a. .b. .c. .d. .

38. The ellipse isa. 2 units long.b. 3 units long.

c. unit long.

d. unit long.

39. Two numbers whose sum is x has a maximum possible product of

a. .b. .

c. .

d. .

40. The expression is equivalent to

a. [2(10) + 2(15)]2.b. 2(10 + 15)2.c. [2(10) + 15]2.d. [10 + 2(15)]2.

41. If g and h are numbers that satisfy the equation , 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

isa. True.b. False.

46. Arcsin has

47. The reciprocal of csc 20 is48. The reciprocal of cot 135 is49. A and B are measures of the acute angles in

a right triangle. Hence, sin A =50. In triangle