Instructions: Read Each Question Carefully and Select the Correct Answer s1

SD 9-12 Algebra
03/20/2009

Student Name: ______

Class: ______

Date: ______

Instructions: Read each question carefully and select the correct answer.

SD Algbra-Questions, Answer Key, Study Guide Page 9 of 102

1. The number of mosquitos in Kylie's backyard varies directly as the amount of water in a puddle. When there are 4 gallons of water in the puddle, there are 120 mosquitos in the yard. How many mosquitos would be in the yard if there was 1 gallon of water in the puddle?

A. 116 mosquitos

B. 480 mosquitos

C. 30 mosquitos

D. 481 mosquitos

2. Calculate the slope of the line between the points (- 4, 10) and (3, 8).

A. 2

3. Factor completely.
4x2 - 36

A. (2x + 6)(2x - 6)

B. 2(x + 9)(x - 16)

C. (4x + 18)(x - 2)

D. 4(x + 3)(x - 3)

4. Simplify.

5. A riding stable charges $150 per month to board a horse plus $6.75 per bale of hay that the horse eats. What is the maximum number of hay bales that Shiloh eats in a month if his monthly boarding cost is at least $225.00 and at most $255.00? Round your answer to the nearest whole bale that satisfies the inequality.

A. 12 bales

B. 11 bales

C. 16 bales

D. 15 bales

6. The electrical resistance (R) of a wire varies directly with its length (L) in meters, and indirectly with the square of its diameter (d) in millimeters. The equation that represents this relationship is given by
where k is the constant for wire made out of a specific metal. If the resistance of a 50 meter long wire is 8.64 ohms when its diameter is 5 millimeters, what is the resistance of a 200 meter long wire when its diameter is 8 millimeters?

A. 13.5 ohms

B. 14.3 ohms

C. 15.4 ohms

D. 17.9 ohms

7. Find the range of the following relation r.

8. Which function rule relates the values of the input variable, x, to the values of the output variable, y, in the table below?

A. y = x - 4

B. y = x + 5

C. y = x + 7

D. y = x - 1

A. Q

B. R

C. S

D. T

10. Simplify.

A. 3

B. 9

C. 324

11. Subtract the following.

12. Evaluate the expression with y = 18.
3 - 2(4y - 5)

A. -131

B. -151

C. 137

D. 157

13. Two sides of a rectangular picture frame are each 7 inches shorter than the other two sides. The perimeter of the picture frame measures 88 inches. What is the length of the shortest two sides of the frame?

A. 25.5 in.

B. 30 in.

C. 18.5 in.

D. 37 in.

14. Salim had a square picture that he enlarged. He increased the length by 3 inches and the width by 1 inch so that the area of the picture is 35 in2 . What was the length of the picture's sides before he enlarged it?

A. 31 in

B. 5 in

C. 4 in.

D. 7 in.

15. Which of the following points, if removed from the set, would make the set a function?

A. (- 9, 9)

B. (5, - 9)

C. (- 5, 5)

D. (9, - 5)

16. Solve for k.
kl - 4 = 2k

17. Solve for h.

18. Find the missing number.
9 + (4 + 7) = 4 + (9 + ?)

A. 9

B. 4

C. 7

D. 20

19. Solve for the value of x.

A. x = 36

B. 6 < x < 7

C. x = 6

D. 5 < x < 6

20. To get a certain shade of orange, Raul needs to mix red paint with yellow paint in the ratio of 5:2.
Which of the following equations shows how many quarts of red paint Raul needs to mix with 4 quarts yellow paint?

A. 5/2 = x/4

B. 5/2 = 4/x

C. 5/8 = x

D. 8/5 = x

21. Complete the following linear function table.

A. 3

B. 4

C. 1.5

D. 4.5

22. What is the value of x in the given statement?

23. If f(x) = 0.5x + 3.1 and g(x) = 0.6x - 1.86, find g(f(x)).

A. 0.3x2 + 0.93x - 5.766

B. 1.1x + 1.24

C. 0.3x + 2.17

D. 0.3x

24. Write the absolute value function, f(x) = |-3x - 4|, as a compound function.

25. Find the area of an ellipse with a major axis of 8 in. and a minor axis of 2 in. Express your answer in terms of .

A. 8 in.2

B. 64 in.2

C. 4 in.2

D. 16 in.2

26. Solve by completing the square.
x2 - 3x - 21 = 0

A. x = - 7 or x = 3

D. No Real Roots

27. Solve for x.

A. 1

B. -128

C. -2

D. -8

28. What is the value of y?
y + 8 - 11 = 17

A. -2

B. 20

C. 46

D. -2

29. What is the value of x?
x
0.2 = --
15

A. 7.5

B. 75

C. 3

D. 3.3

30. Solve the inequality.
n + 8 < -7

A. n > -1

B. n < -15

C. n > -15

D. n < -1

31. What is the value of n?
5n + 15 = 100

A. n = 575

B. n = 425

C. n = 23

D. n = 17

32. What is the value of y?
x = 9y
z = 10y

A. y = 90

B. y = 1 1/9

C. y = 1

D. Problem cannot be solved with the given information.

33. Which of the following is true?

34. Find the missing symbol.
(8 x 8) ? (7 x 7) = 15

A. +

B. -

C. x

D. ÷

35. Round to the nearest cent when necessary.
Which of the following is the best price?

A. 8 for $3.99

B. 7 for $3.55

C. 6 for $3.49

D. 9 for $4.20

36. Which of the following best completes the number sentence?
2 = (18 x 2) + (14 x 2)

A. (18 x 14) +

B. (18 x 14) x

C. (18 + 14) x

D. (18 + 14) +

37. Simplify

A. A

B. B

C. C

D. D

38. Which relation is written as a function?

A. x equals negative y squared

B. y equals negative x to the fourth power

C. x equals negative y to the second power

D. x equals 3y squared

39. Four pancakes and three eggs at Candy's Cafe cost $7.95. Two pancakes and three eggs at Burger Palace cost $5.95. Which option shows the best method for calculating the amount that each restaurant is charging for each pancake and each egg?

A. -2p = $13.90

B. 6p = $13.90

C. 4p + 3e = $7.95 and 2p + 3e = $5.95

D. 4 + 3(p + e) = $7.95 and 2 + 3(p + e) = $5.95

40. Given the points O(-3, 4), Q(-2, 6), write an equation for the line OQ and find the y-coordinate for point P (3, y) on the line OQ.

A. P(3, 2)

B. P(3, 4)

C. P(3, 44/5)

D. P(3, 16)

41. The length of a rectangle is four more than three times the width. The perimeter is sixty-four meters. Find the length and the width.

A. l = 21.5; w = 10.5

B. l = 25; w = 7

C. l = 26.5; w = 5.5

D. l = 28; w = 4

42. Factor completely.
6x2 - 3x - 30

A. 3(2x - 5)(x + 2)

B. 3(2x - 2)(x + 5)

C. 3(2x + 5)(x - 2)

D. 3(2x + 2)(x - 5)

43. Solve the following using the quadratic formula.
- 2x2 + 3x + 4 = 0

44.

45. Simplify.

A. A

B. B

C. C

D. D

46. Simplify.
(a + b)(3a + 2b)

47. Simplify.

A. A

B. B

C. C

D. D

48. Find the solution set and choose the corresponding description: 12 - (10 - 8 - 3x) < 8 - 10 + 2x

A. all points to the left of -2

B. all points to the left of -12, including -12

C. all points to the left of -12

D. all points to the left of -2, including -2

49. Solve for x.
|8x + 12| - 13 = 23

A. x = 6 or x = - 3

B. x = 6

C. x = 3

D. x = 3 or x = - 6

SD 9-12 Algebra
Answer Key
03/20/2009

1. C Direct Variation

2. D Slope

3. D Factoring: Difference of Two Squares

4. C Radicals: Addition/Subtraction - A

5. D Inequalities - C

6. A Joint and Combined Variation

7. A Domain/Range

8. C Function Rules

9. A Exponential Functions

10. A Exponential Notation - F

11. A Polynomials: Subtraction

12. A Equations: Order of Operations

13. C Functions: Linear

14. C Quadratic Equations: Real World Problems

15. A Functions/Relations - A

16. A Equations With Two Variables

17. D Literal Equations

18. C Missing Elements - D

19. C Radicals and Roots

20. A Ratio/Proportion - C

21. B Function/Pattern - C

22. D Inequalities - A

23. D Functions: Quadratic

24. B Functions: Absolute Value

25. C Irrational Numbers: Pi

26. B Non-Linear Equations

27. B Rational Numbers: Equations

28. B Equations: Addition/Subtraction

29. C Equations: Multiplication/Division

30. B Inequalities - B

31. D Equations: Two-Step

32. D Solving Equations: Substitution

33. C Exponential Notation - D

34. B Missing Elements - E

35. D Rates

36. C Properties - E

37. A Radicals: Simplifying

38. B Functions/Relations - B

39. C Equations: Systems

40. D Equations of a Line

41. B Number Relation Problems

42. A Factoring

43. B Quadratic Formula

44. D Polynomials: Addition

45. C Exponential Notation - E

46. C Polynomials: Multiplication

47. B Polynomials: Division

48. C Sets/Subsets/Solution Sets

49. D Absolute Value: Solve

SD Algbra-Questions, Answer Key, Study Guide Page 9 of 102

Study Guide
SD 9-12 Algebra
03/20/2009

Direct Variation
Variation equations are formulas that show how one quantity changes in relation to one or more other quantities. There are four types of variation: direct, indirect (or inverse), joint, and combined.
Direct variation equations show a relationship between two quantities such that when one quantity increases, the other also increases, and when one quantity decreases, the other also decreases. We can say that y varies directly as x, or y is proportional to x. Direct variation formulas are of the form y = kx, where the number represented by k does not change and is called a constant of variation.
Indirect variation equations are of the form y = k/x and show a relationship between two quantities such that when one quantity increases, the other decreases, and vice versa.

This skill focuses on direct variation. The following is an example of a direct variation problem.
The amount of money in a paycheck, P, varies directly as the number of hours, h, that are worked. In this case, the constant k is the hourly wage, and the formula is written P = kh. If the equation is solved for k, the resulting equation shows that P and h are proportional to each other.
Therefore, when two variables show a direct variation relationship, they are proportional to each other. Direct variation problems can be solved by setting up a proportion in the form below.

Example 1: The amount of fuel needed to run a textile machine varies directly as the number of hours the machine is running. If the machine required 8 gallons of fuel to run for 24 hours, how many gallons of fuel were needed to run the machine for 72 hours? Round your answer to the nearest tenth of a gallon, if necessary.

Step 1: Set up the proportion. Since the machine used 8 gallons of fuel in 24 hours, the left side of the proportion should be 8 gallons over 24 hours. The number of gallons that the machine used in 72 hours needs to be found, so the right side of the proportion should be g gallons over 72 hours.
Step 2: Cross-multiply across the equal sign.
Step 3: Set up the cross-multiplication equation.
Step 4: Divide both sides of the equation by 24 hours to isolate g gallons.
Step 5: Reduce the fractions on both sides of the equal sign.
Step 6: Simplify by multiplying the numbers remaining on the right side of the equal sign (8 gallons 3).
Answer: 24 gallons
Example 2: The price of jellybeans, j, varies directly as the number of pounds, p, that are purchased. Find the equation that relates the two variables if jellybeans are $1.95 per pound.
(1) y = kx, j = kp
(2) j = 1.95p
Step 1: Remember that the formula for direct variation is: y = kx and substitute the variables from the question into the appropriate places.
Step 2: Since the jellybeans are always $1.95 per pound, the constant, k, equals 1.95. Substitute 1.95 into the equation for k.
Answer: j = 1.95p
Activities that can help reinforce the concept of direct variation are as follows.
1. Have students solve the equation y = kx for k, and then substitute two sets of (x, y) values into the equation and compare the values for k. If they are the same, then x and y have a direct variation relationship.
2. Have the student think of scenarios that show a direct variation relationship. Then, make up numbers to go with the relationships and have the students practice solving them.