Q1. Write the expression 6/(2 + 8i) in the standard form a + bi.

a. -1/5 + 4i/5

b. 3/17 + 12i/17

c. -1/5 - 4i/5

d. 3/17 - 12i/17

Q2. Use U = universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} andB = {2, 3, 5, 7} to find the set B.

a. {0, 1, 4, 6, 9}

b. {0, 1, 4, 6, 8, 9}

c. {0, 1, 4, 6, 7, 8, 9}

d. {1, 4, 6, 8, 9}

Q3. Choose the graph of the number line that represents x > -7.

a.

b.

c.

d.

Q4. Evaluate -10xy + 8y - 9 given that x = 1 and y = -3.

a. 15

b. -63

c. -3

d. 6

Q5. Solve (2x - 3)² = 49 by using the Square Root Method.

a. {4, -10}

b. {5, -2}

c. {10, -4}

d. (2, -5}

Q6. A bank loaned out $70,000, part of it at the rate of 12% per year and the rest at a rate of 6% per year. If the interest received was $5760, how much was loaned at 12%?

a. $44,000

b. $26,000

c. $43,000

d. $27,000

Q7. Find the real solutions of the equation x³ - 5x² + 6x = 0 by factoring.

a. {0, -2, -3}

b. {2, 3}

c. {-2, -3}

d. {0, 2, 3}

Q8. Solve the equation x² + 144 = 0 in the complex number system.

a. {-12, 12}

b. {12}

c. {12i}

d. {-12i, 12i}

Q9. An inheritance of $210,000 is to be divided among Chris, Kelly, and Julie in the following manner: Kelly is to receive 3/5 of what Chris gets, while Julie gets 1/2 of what Chris gets. How much does Kelly receive?

a. $20,000

b. $60,000

c. $100,000

d. $50,000

Q10. Solve x² - 6x - 27 = 0 by factoring.

a. {-3, 9}

b. {-3, -9}

c. {3, 9}

d. (3, -9}

Q11. Multiply each side of the inequality 2 - 4x -2 by 5. What is the resulting inequality?

a. 10 - 20x -10

b. 10 - 20x -10

c. 10 - 4x -10

d. 10 - 4x -10

Q12. The net income y (in millions of dollars) of Pet Products Unlimited from 1997 to 1999 is given by the equation y = 9x² + 15x + 52, where x represents the number of years after 1997. Assume this trend continues and predict the year in which Pet Products Unlimited's net income will be $598 million.

a. 2005

b. 2004

c. 2003

d. 2006

Q13. Find the real solutions, if any, of the equation 9x² - 32 = 12x. Use the quadratic formula.

a. {8/9, -4/9}

b. {-8/3, 4/3}

c. {8/3, -4/3}

d. {-4/9, -28/9}

Q14. The manager of a candy shop sells chocolate covered peanuts for $6 per pound and chocolate covered cashews for $15 per pound. The manager wishes to mix 100 pounds of the cashews to get a cashew-peanut mixture that will sell for $8 per pound. How many pounds of peanuts should be used?

a. 225 lb

b. 450 lb

c. 175 lb

d. 350 lb

Q15. Solve the equation 8x² - 3x + 1 = 0 in the complex number system.

a. {(-3/16) - (23i/16), (-3/16) + (23i/16)}

b. {(-3/16) - (23i/16), (3/16) + (23i/16)}

c. {(3/16) - (23i/16), (-3/16) + (23i/16)}

d. {(3/16) - (23i/16), (3/16) + (23i/16)}

Q16. Translate the following sentence into a mathematical equation. Be sure to identify the meaning of all symbols.

The profit derived from the sale of x video cameras is $370 per unit less the sum of $2700 costs plus $160 per unit.

a. If P is profit and x the units sold, then P = 370x - (2700 + 160x) or P = 210x - 2700.

b. If P is profit and x the units sold, then P = 370x + 2700 - 160x or P = 210x + 2700.

c. If P is profit and x the units sold, then P = 370x - (2700 - 160x) or P = 530x - 2700.

d. If P is profit and x the units sold, then P = 370/x - (2700 + 160/x) or P = 210/x - 2700.

Q17. Find the real solutions of the equation x + x = 56.

a. {8}

b. {49}

c. {7}

d. {64}

Q18. Fill in the blank with the correct inequality symbol. If x < 6, then -3x ____ -18.

a. <

b.

c.

d. >

Q19. Solve the inequality. Express your answer using interval notation. Graph the solution set.

4x + 1 > 3x - 4

a. (-, -5]

b. (-3, )

c. [-5, )

d. (-5, )

Q20. Tracy can wallpaper 2 rooms in a new house in 8 hours. Together with her trainee they can wallpaper the 2 rooms in 6 hours. How long would it take the trainee working by herself to do the job?

a. 8 hr

b. 30 hr

c. 22 hr

d. 44 hr

Q21. Solve the rational equation (4x-1)/(2x+3)=(6x+8)/(3x-4)

a. {28/15}

b. {-28/53}

c. {-20/53}

d. {4/3}

Q22. Find the real solutions of the equation (x + 3)^1/3 = -2.

a. {1}

b. {-9}

c. {-11}

d. no real solution

Q23. The lengths of the sides of a triangle are given. Determine if the triangle is a right triangle. If it is, identify the hypotenuse.

15, 36, 39

a. right triangle; 39

b. right triangle; 15

c. right triangle; 36

d. not a right triangle

Q24. List the intercepts of the graph. Tell whether the graph is symmetric with respect to the x-axis, y-axis, origin, or none of these.

a. intercepts: (0, -5) and (0, 5); symmetric with respect to y-axis

b. intercepts: (-5, 0) and (5, 0); symmetric with respect to origin

c. intercepts: (0, -5) and (0, 5); symmetric with respect to x-axis, y-axis, and origin

d. intercepts: (-5, 0) and (5, 0); symmetric with respect to x-axis, y-axis, and origin

Q25. Find the center (h, k) and radius r of the circle with the equation x² - 16x + 64 + (y + 9)² = 36.

a. (h, k) = (8, -9); r = 6

b. (h, k) = (9, -8); r = 36

c. (h, k) = (-9, 8); r = 6

d. (h, k) = (-8, 9); r = 36

Q26. Graph the follwing equation by plotting points: 5x + 2y = 10.

a.

b.

c.

d.

Q27. Write the standard form of the equation of the circle with radius r = 2 and center (h, k) = (0, 0).

a. x² + y² = 4

b. x² + y² = 2

c. (x - 2)² + (y - 2)² = 2

d. (x - 2)² + (y - 2)² = 4

Q28. List the intercepts and type(s) of symmetry, if any for y² = -x + 9.

a. intercepts: (-9, 0), (0, 3), (0, -3); symmetric with respect to x-axis

b. intercepts: (0, -9), (3, 0), (-3, 0); symmetric with respect to y-axis

c. intercepts: (9, 0), (0, 3), (0, -3); symmetric with respect to x-axis

d. intercepts: (0, 9), (3, 0), (-3, 0); symmetric with respect to y-axis

Q29. Graph the following equation by plotting points: y = x³.

a.

b.

c.

d.

Q30. Find an equation for the line that is perpendicular to the line 3x - y = 6 and contains the point (0, 2).

a. y = x/3 + 2

b. y = -x/3 + 6

c. y = -x/3 + 2

d. y = 5/3

Q31. Find the distance d(P₁, P₂) between the points P₁ and P₂.

P₁ = (1, 7); P₂ = (-7, -2)

a. 17

b. 1

c. 145

d. 72

Q32. Graph the follwing equation by plotting points: y = 3x + 6.

a.

b.

c.

d.

Q33. Find the slope of the line containing the points (-7, 1) and (-8, -5).

a. -1/6

b. -6

c. 1/6

d. 6

Q34. Find the general form of the equation of the circle with center at the point (2, -3) containing the point (5, -3).

a. x² + y² + 4x - 6y + 4 = 0

b. x² + y² - 4x + 6y + 22 = 0

c. x² + y² + 4x - 6y + 22 = 0

d. x² + y² - 4x + 6y + 4 = 0

Q35. Graph the following equation by plotting points: y = 1/x.

a.

b.

c.

d.

Q36. Find an equation for the line in general form Containing the points (-5, -7) and (0, 4).

a. 11x - 5y = -20

b. -2x + 4y = -16

c. -11x - 5y = -20

d. 2x - 4y = -16

Q37. List the intercepts for the graph of the equation y = 4x.

a. (0, 0)

b. (0, 4)

c. (4, 4)

d. (4, 0)

Q38. Find the slope and y-intercept of the line -x + 10y = 70.

a. slope = 10; y-intercept = -70

b. slope = -1; y-intercept = 70

c. slope = - 1/10; y-intercept = 7

d. slope = 1/10; y-intercept = 7

Q39. Graph the equation (x + 2)² + (y + 3)² = 9.

a.

b.

c.

d.

Q40. Find the center (h, k) and radius r of the circle with the given equation (x - 6)² + (y - 2)² = 16.

a. (h, k) = (2, 6); r = 16

b. (h, k) = (6, 2); r = 4

c. (h, k) = (2, 6); r = 4

d. (h, k) = (6, 2); r = 16