Arithmetic Operations Rules and Operations
Part I – Arithmetic Operations Rules and Operations
1. -11 - 7 =
a) -4 b) -18 c) 18 d) 4 e) none of these
2. 3/5 ÷ 2/3 =
a) 2/5 b) 15/6 c) 7/9 d) 9/10 e) none of these
3. What is the greatest common factor for : 12 and 20
a) 1 b) 2 c) 4 d) 6 e) none of these
4. .035 x 1.1 =
a) .0385 b) .00385 c) .385 d) 3.85 e) none of these
5. -5 - │ -3 + 4 │ =
a) 2 b) -6 c) 6 d) -4 e) none of these
6. Round to the nearest ten thousandth: .0035475
a) .0035 b) .00355 c) .004 d) .003548 e) none of these
7. Convert to scientific notation: .0000567
a) 56.7 x 104 b) 5.67 x 10-4 c) 5.67 x 105 d) 5.67 x 10-5 e) none of these
8. Evaluate -2Y3 – 2Y2 – 2Y – 2 for the value Y = -2
a) -16 b) 10 c) 26 d) 12 e) none of these
9. Transform into a fraction: .0045
a) 45/100 b) 45/1000 c) 9/2000 d) 3/700 e) none of these
10. Six is thirty percent of what number?
a) 30 b) 20 c) 36 d) 28 e) none of these
Part II – Equations and Inequalities
11. Identify the solution region for: 3Q + 7 < Q - 1
a) Q > -4 b) Q < 4 c) Q < -4 d) Q > 4 e) none of these
12. Solve for Y: 2Y2 - 5Y = 12
a) -3/2 b) -4 c) 3/2 d) 12 e) none of these
13. Find the value of Z in the equation: 2/3 Z + 5 = Z + 7
a) 3 b) -3 c) -6 d) -9 e) none of these
14. Find B in this system of equations: 2A + 2B = -2 and 5A - B = 13
a) -3 b) 2 c) 3 d) -2 e) none of these
15. Solve for X: (3X - 1) (3X - 2) = 0
a) 1/3, -2/3 b) 1/3, 2/3 c) -1/3, -2/3 d) -1/3, 2/3 e) none of these
16. Solve for A: 1/5 A + 2 < 2A + 11
a) < -5 b) < 5 c) > 5 d) > -5 e) none of these
17. Solve for G in the following system: 2G - 2H = -6 3G + H = 3
a) 0 b) -3 c) 3 d) -5 e) none of these
18. Find the value of Q: 5Q + 3 = 2Q - 9
a) 4 b) -4 c) 3 d) -3 e) none of these
19. For the equation: X2 + X - 2 = 0, solve for X
a) 1 b) ½ c) -1 d) 0 e) none of these
20. Solve for Y: 3/7 Y = 3
a) 7 b) 3 c) -3 d) -7 e) none of these
Part III – Evaluation of exponential, radical, and graphical operations
21. Identify the slope for the line given by: -Y = -5/8 + 3
a) -3 b) -5/8 c) 5/8 d) -3 e) none of these
22. What is the Y intercept for the line described by: 2X + 3Y = -15
a) -2/3 b) 5 c) -15 d) -5 e) none of these
23. Find the slope for this line: 3Y - 6X = 12
a) 2 b) 12 c) 4 d) -2 e) none of these
24. Multiply: X-3 ● X4 ● X-1 ● X ● X2 ● X0 =
a) X2 b) X3 c) X d) X0 e) none of these
25. Write with no negative exponents: -2Y-2Z =
X-3
a) -2X3Y2Z b) X3Z c) -2X3 d) -2X3Z e) none of these
-2Y2 Y2Z Y2
26. Divide: Z-4 ÷ Z-5 =
a) Z-1 b) Z-9 c) Z d) Z9 e) none of these
27. (-4X2Y3)3 =
a) -4X6Y9 b) -64X6Y9 c) 16X6Y9 d) -4XY15 e) none of these
______ _____
28. √ 108 - √ 75 =
_____ _____ _____ _____
a) √ 33 b) 3 √ 2 c) 3 √ 11 d) √ 3 e) none of these
_____ ______
29. √ 15 ● √ 20 =
_____ ____ ____ ____
a) 10 √ 3 b) 3 √ 10 c) 12 √ 5 d) 15 √ 20 e) none of these
_____
30. √ 18 =
____________
√ 2
____ _____
a) 2 √ 3 b) √ 90 c) 3 d) 6 e) none of these
2
Part IV – Operations with Polynomials
31. Multiply: (2X – 3)(3X - 2)
a) 6X2 – 6 b) 6X2-13X-6 c) 6X2-13X+6 d) 6X2+13X+6 e) none of these
32. Factor: 6Y2 - 5Y + 1
a) (3Y-1)(2Y-1) b) (6Y-1)(Y+1) c) (3Y+1)(2Y-1) d) (3Y+1)(2Y+1) e) none of these
33. Multiply: (3Q-4) (3Q+4) =
a) 9Q2–12Q-16 b) 9Q2-16 c) 9Q2+23Q-16 d) 9Q+16 e) none of these
34. Multiply: (2X + 3)(3X – 5) =
a) 6X2+X-15 b) 6X2-X+15 c) 6X2-X-15 d) 6X2+X+15 e) none of these
35. Factor: X2 + XY + 5X + 5Y
a) (X+Y)(X+5) b) (X+1)(X+5Y) c) (X+Y)(Y+1) d) (X+5Y)(X+1) e) none of these
36. Factor: 81Q2 - 1
a) (9Q – 1)2 b) (9Q-1)(9Q-1) c) (9Q+1)(9Q-1) d) (27Q-1)(3Q-1) e) none of these
37. Factor: (4Y – 3) (5Y + 2) =
a) 20Y2-15Y-6 b) 20Y2-7Y-6 c) 20Y2+8Y-6 d) 20Y2+7Y-6 e) none of these
38. Multiply: (11 – R)(11 + R) =
a) 121 - R2 b) 121 + R2 c) 121 + 22R - R2 d) 121 – 22R - R2 e) none of these
39. Multiply: (Z – 3)(Z – 3) =
a) Z2 – 6Z + 9 b) Z2 - 9 c) Z2 + 9 d) Z2 + 18Z + 9 e) none of these
40. Factor: 12Y2 - 35Y - 3
a) (3Y+1)(4Y-3) b) (6Y-1)(Y+3) c) (12Y+1)(Y-3) d) (4Y-3)(3Y+1) e) none of these
Part V – Word Problems
41. A bag of coins contains quarters, dimes and nickels. There are twice as
many nickels as dimes and five less quarters than dimes. The total value of
the coins is $3.25. How many of the coins are dimes?
a) 10 b) 12 c) 20 d) 15 e) none of these
42. The perimeter of a triangle forty-two inches. The longest side is one less
than twice the length (in inches) of the next longest (middle) side. The
shortest side is five inches less than length of the middle side. What is the
length of the middle side?
a) 23 b) 21 c) 24 d) 12 e) none of these
43. A 15 foot ladder leans against a wall. It reaches 3 feet higher than it stands
from the base of the wall. How high does the ladder reach up the wall?
a) 12 b) 9 c) 15 d) 10 e) none of these
44. The sum of two numbers is one and their difference is seven. What is the
value of the smaller number?
a) 3 b) -3 c) 4 d) -4 e) none of these
45. Dad is three years less than three times his daughter’s age. In five years the
sum of their ages will be sixty-seven. How old is Dad?
a) 15 b) 35 c) 42 d) 51 e) none of these
46. The perimeter of a rectangle is less than 68. The length is 5 less than twice
the width. Find the length of the rectangle.
a) <13 b) <18 c) <21 d) <24 e) none of these
47. The sum of two integers is less than negative four. Their difference is less
than negative eighteen. What must be the value of the larger number?
a) < -7 b) < 11 c) < -11 d) < 7 e) none of these
48. The sum of two consecutive odd integers is greater than minus twenty-four.
What are the possible values for the larger integers?
a) > -15 b) > -13 c) >-11 d) > -9 e) none of these
49. The area of a triangle is 63 square inches. The base is 4 less than twice the
height. Using the formula A = 1/2bh, find the base.
a) 7 b) 9 c) 11 d) 14 e) none of these
50. The product of, a number increased by five, and the same number decreased
by five is 375. Find the number.
a) 10 b) 15 c) 20 d) 25 e) none of these