Q1. Evaluate (7x - 11y)/7 given that x = 8 and y = 3.

a. 67/7

b. 89/7

c. 45/7

d. 23/7

Q2. Evaluate |x| + |y| given that x = -6 and y = 3.

a. -3

b. 3

c. 9

d. -9

Q3. Evaluate -10xy + 8y - 9 given that x = 1 and y = -3.

a. 15

b. -63

c. -3

d. 6

Q4. Write the expression 2i¹⁵ - i⁷ in the standard form a + bi.

a. -1

b. i

c. -i

d. 1

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

a. {8}

b. {49}

c. {7}

d. {64}

Q7. Solve x² - 2x - 24 = 0 by using completing the square.

a. {5, -1}

b. {-6, 4}

c. {-20, -4}

d. {6, -4}

Q8. Solve P-5Q/3=(P+7)/2+1 for P.

a. P = (15 - 10Q)/3

b. P = (27 + 10Q)/3

c. P = (27 - 10Q)/3

d. P = (15 + 10Q)/3

Q9. Find the real solutions of the equation (2x - 1)² - 10(2x - 1) + 24 = 0.

a. {5/2, -3/2}

b. {-5/1, 3/2}

c. {-7/2, -5/2}

d. {7/2, 5/2}

Q10. 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)}

Q11. 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

Q12. Find the real solutions of the equation 2x⁴ - 128x² = 0 by factoring.

a. {-82, 0, 82}

b. {0}

c. {-8, 0, 8}

d. {-8, 8}

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. 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.

Q15. Solve the inequality. Express your answer using interval notation. Graph the solution set.

7 2x + 3 15

a. (-6, -2)

b. [-6, -2]

c. [2, 6]

d. (2, 6)

Q16. 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

Q17. Solve the linear equation 3(x + 3) = 4(x-6)

a. {-15}

b. {33}

c. {4}

d. {-33}

Q18. 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, )

Q19. 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

Q20. Solve the rational equation x/(x-1)+6=1/(x-1)

a. {-1}

b. {1,-1}

c. {1}

d. no solution

Q21. Solve the equation x² + 144 = 0 in the complex number system.

a. {-12, 12}

b. {12}

c. {12i}

d. {-12i, 12i}

Q22. During a hurricane evacuation from the east coast of Georgia, a family traveled 210 miles west. For part of thetrip, they averaged 50 mph, but as the congestion got bad, they had to slow to 10 mph. If the total time of travel was 8 hours, how many miles did they drive at the reduced speed?

a. 57.5 mi

b. 42.5 mi

c. 52.5 mi

d. 47.5 mi

Q23. 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

Q24. 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

Q25. 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

Q26. 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

Q27. List the intercepts for the graph of the equation y = 4x.

a. (0, 0)

b. (0, 4)

c. (4, 4)

d. (4, 0)

Q28. 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

Q29. Write 17x + 3y = 10 in slope-intercept form.

a. y = 17x/3 + 10/3

b. y = 17x - 10

c. y = 17x/3 - 10/3

d. y = -17x/3 + 10/3

Q30. Graph the circle with radius r = 2 and center (h, k) = (-4, -1).

a.

b.

c.

d.

Q31. If (-5, -5) is the endpoint of a line segment, and (-10, -7) is its midpoint, find the other endpoint.

a. (5, -1)

b. (-15, -9)

c. (-9, -15)

d. (-15, -3)

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

a.

b.

c.

d.

Q33. 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

Q34. 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

Q35. The lengths of the sides of a triangle are given. Determine if the triangle is a right triangle. If it is, identify the hypotenuse.

8, 16, 20

a. right triangle; 8

b. right triangle; 16

c. right triangle; 20

d. not a right triangle

Q36. Graph the line containing the point P = (-2, -8) and having slope m = 1/2.

a.

b.

c.

d.

Q37. Graph the following equation by plotting points: y = 1/x.

a.

b.

c.

d.

Q38. 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

Q39. Find an equation for the line that is parallel to the line 8x + 7y = 98 and contains the point (7, 0).

a. 8x - 7y = 56

b. 8x + 7y = 56

c. 7x + 8y = 0

d. 7x + 7y = 98

Q40. Find the midpoint of the line segment joining the points P₁ and P₂.

P₁ = (-1, 6); P₂ = (-5, 3)

a. (-6, 9)

b. (2, 3/2)

c. (4, 3)

d. (-3, 9/2)