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Intermediate Algebra Appeals Practice Test 6/07

Show all work and answers. Give all answers in simplest form.

1. Evaluate .

2. Evaluate .

3. Evaluate .

4. What is 15.2 percent of 76? Round answer to the nearest tenth.

5. 30 is 20% of what number?

6. 12 is what percent of 108? Round answer to the nearest tenth of a percent.

7. If 2.5 pounds of steak costs $12.50, how much will 4 pounds cost?

8. Evaluate -3 + 2 ∙ -4.

9. Evaluate (-2)2 – 3 ∙ -1.

10. Simplify .

11. Simplify .

12. Simplify .

13. Determine the common solution: x + y = 4 and 2x – y = 11.

14. Determine the common solution: 3x - 5y = 14 and 2x – 3y = 9.

15. Convert to a percent. Do not round your answer.

16. Determine if when feet and feet.

17. Determine the slope of the line through:

a. (2,-3) and (-1,5)

b. (4,-1) and (4,6)

c. (3,5) and (-3,5)

18. Write in slope-intercept form the equation of the line through:

a. (-4,-2) and (0,-3)

b. (-3,2) and (4,5)

c. (5,-1) and (2,-1)

19. Determine the slope for:a. the line b. the line c. the line


20. Write the equation of the line graphed below.

21. Determine (a) the domain and (b) the range of the function graphed below.

2

6-6

6

-6

6-6

6

-6


22. Graph the line .

23. Determine the distance between the points (-5,2) and (1,-5). Round your answer to the hundredths place.

24. State which of the following relations are functions (there may be more than one correct answer):a.

b.

c.

d.

25. Let . Determine (a) , (b) , (c)

26. Let . Determine (a) , (b) , (c) g(-2)

27. Solve for x by factoring:

a.

b.

c.

28. Solve for x using the quadratic formula:

a.

b.

c.

29. Let , represent the number of rabbits in a barn after t weeks. How many rabbits are there after (a) 1 week? (b) 3 weeks?

30. Simplify each of the following. Express each answer using positive exponents only.

a.

b.

c.

31. Compute .

32. Multiply, simplifying as much as possible: .

3


33. Divide, simplifying as much as possible: .

34. Add, simplifying as much as possible: .

35. Subtract, simplifying as much as possible: .

36. Draw a graph of . In your graph, clearly label and give both coordinates of the x-

intercepts, the y-intercept, and the vertex.

37. Compute .

38. Compute .

39. Determine the domain of the function .

40. Solve for x: .

41. Solve for x: .

4


Answers/Solutions for Intermediate Algebra Appeals Practice Test

1. Evaluate .

To add or subtract fractions as mixed numbers, you must find a common denominator for the fractions. The least common denominator for 3 and 7 is 21.

Add the fractions: [Add numerators, keep common denominators]

Add the whole numbers: 3 + 4 = 7

Add the two results:

Answer:

2. Evaluate .


Subtract the fractions: [subtract numerators, keep common denominators]

Subtract the whole numbers: 5 - 2 = 3

Answer:

3. Evaluate .


Subtract the fractions: You cannot subtract 3 from 2; you

must “borrow” 1 from 9 [ ] to get

Now, subtract the fractions:

Subtract the whole numbers: 8 - 4 = 4

Answer:

4. What is 15.2 percent of 76? Round answer to the nearest tenth.

Translate into a mathematical equation.What is 15.2 percent of 76? ↓ ↓ ↓ ↓ ↓ N = 0.152 • 76

Multiply 0.152 and 76 to get 11.552

11.552 rounded to the nearest tenth is 11.6.

Answer: 11.6

5. 30 is 20% of what number?

Translate into a mathematical equation.30 is 20% of what number? ↓ ↓ ↓ ↓ ↓30 = 0.20 • N or 0.2N = 30Solve for N: N = 30 ÷ 0.2 = 150

6. 12 is what percent of 108? Round answer to the nearest tenth of a percent.

Translate into a mathematical equation.12 is what percent of 108↓ ↓ ↓ ↓ ↓12 = N • 108 or 108N = 12Solve for N: N = 12 ÷ 108 = 0.1111Write N as a percent and round to the nearest tenth.

5


Answer: 150N = 0.1111 = 11.11% = 11.1%Answer: 11.1%

7. If 2.5 pounds of steak costs $12.50, how much will 4 pounds cost?

Let x = the cost of 4 pounds of steak.

Answer: The cost of 4 pounds of steak is $20.00

8. Evaluate -3 + 2 ∙ -4.

Order of operations: Multiply first, then add

-3 + 2 ∙-4 = -3 + (-8) = -11

Answer: -11

6


9. Evaluate (-2)2 – 3 ∙ -1. Answer: 7

10. Simplify

Answer: 5x-1111. Simplify .

Answer: x-4

12. Simplify

Answer:

13. Determine the common solution: x + y = 4 and 2x – y = 11.To find the common solution, eliminate one of the unknowns by addition or subtraction; then solve for the remaining unknown

So x = 15 ÷ 3 = 5. Substitute 5 for x in first equation: 5 + y = 4 y = 4 – 5 = -1Answer: (5,-1)

14. Determine the common solution: 3x – 5y = 14 and 2x – 3y = 9.To solve for y, multiply the first equation by -2 and the second equation by 3; then add the equations

Substitute -1 for y in the first equation:3x – 5(-1) =14 3x + 5 = 14 3x = 9 x = 3Check in the second equation: 2(3) -3(-1) = 6 + 3 = 9Answer: (3,-1)

15. Convert to a percent. Do not round your

answer.To convert a fraction to a percent, divide the numerator by the denominator; move the decimal point two places to the right and affix the % sign.

Answer: 56.25%

16. Determine if when feet and feet.

Answer: l = 100 feet

17. Determine the slope of the line through:a. (2,-3) and (-1,5)b. (4,-1) and (4,6)c. (3,5) and (-3,5)

The slope between 2 points, (x1, y1) & (x2,y2) is

; if x2 – x1 =0, the slope is undefined

a)

38

2135

m Answer:

b) Answer:

c) Answer:

18. Write in slope-intercept form the equation of the line through:

a. (-4,-2) and (0,-3)b. (-3,2) and (4,5)c. (5,-1) and (2,-1)

a) Find the slope:

Find b:

.

Answer:

b) Find the slope:

Find b:

.

7


Answer:

c) Find the slope:

Find b: Answer:

8


19. Determine the slope for:a. the line b. the line c. the line

Write each equation in slope-intercept form: , if possible.a) , Answer: Slope is 0.

b)

Answer: Slope is

c) x = 8 cannot be written in slope-intercept form. The slope is undefined Answer: Slope is undefined

20. Write the equation of the line graphed below

The x-intercept is (-1,0); the y-intercept is (0,-2).

The slope is

Ans: The equation of the line is 21. Determine (a) the domain and (b) the range of the

function graphed below 22. Graph the line

Let x = 0; then 0 – 4y = -12 and y = 3Let y = 0; then 3x – 0 = -12 and x = -4

9

6

6-6

6

-6


The domain of the function f is the set of all input values for which the function is defined. The range of a function is the set of all output values for the given function. Looking at the graph we see that the input values, x, for this function are and the out put values, y, are Ans: Domain: Range:

10

-6 6

-6


23. Determine the distance between the points (-5,2) and (1,-5). Round your answer to the hundredths place.

So,

Answer: 9.22

24. State which of the following relations are functions (there may be more than one correct answer):

A function is a relation in which each x-coordinate is paired with one and only one y-coordinate.For the relations given, only c and d are FUNCTIONS since they are the only sets in which every x is paired with a unique y-value.a) is NOT a function because -2 is paired with three different values of y. b) is NOT a function because 5 is paired with two different values of y.Answer: c) and d) are functions

25. Let . Determine (a) , (b) , (c) a) Answer:

b) Answer:

c) Answer:

26. Let Determine (a) , (b) , (c) a) Answer:

b) Answer:

c) Answer:

27. Solve for x by factoring: a. b. c. a) Put equation in form:

To factor , you must find two numbers whose sum is -9 [b] and whose product is -10 [ac = 2(-5)]. The numbers, -10 and 1, are used as coefficients of x and substituted for -9x to get , a polynomial with four terms. Now, we factor 2x from the first two terms and 1 from the third and fourth terms to get:

To solve , set each factor equal to 0 and solve for x: and

Answer: 5 and

b) To factor , you must find two numbers whose sum is -6 and whose product is +9. The numbers are -3 and -3.

Answer: x=3

c) is a special product—the difference of two squares. Its factors are (3x+2) and (3x-2)

and

28. Solve for x using the quadratic formula: a. b. c.

The quadratic formula gives solution for equations in the form .

Quadratic Formula

a) cannot be simplified.

Answer:

b)

can be simplified to

Answer:

c) can be simplified to .

11


Answer: Answer:

12


29. Let , represent the number of rabbits in a barn after t weeks. How many rabbits are there after (a) 1 week? (b) 3 weeks?

a) Answer: There are 16 rabbits after 1 week.

b) Answer: There are 64 rabbits after 3 weeks.

30. Simplify each of the following. Express each answer using positive exponents only.

a)

Answer:

b) Answer:

c)

Answer:

31. Compute

Ans: 27

32. Multiply, simplifying as much as possible:

Ans:

33. Divide, simplifying as much as possible:

Ans:

34. Add, simplifying as much as possible:

LCD =

13

Intermediate Algebra Appeals Practice Test 6/0735. Subtract, simplifying as much as possible:

LCD =

36. Draw a graph of . In your graph, clearly label and give both coordinates of the x-intercepts, the y-intercept, and the vertex

Vertex” (1,-16); y-int: (0,-15); x-int: (-3,0) and (5,0)

37. Compute

is equivalent to the exponential equation . Since

Ans:

38. Compute .

is equivalent to the exponential equation

. Since

Ans:

39. Determine the domain of the function

.

The domain of function is the set of values of x for which the function is defined. Since this is a rational function, you must look at the denominator and determine the values for which the denominator is zero. These are the values that must be excluded from the domain of the function. The function is not defined for these values since they make the denominator zero.

Ans: Domain:

40. Solve for x: .

LCD = , So multiply both sides by the LCD.

Check:

Ans: x = 2

41. Solve for x: LCD =

So multiply both sides (all terms) by the LCD:

Check:

14

(0,-15) (1,-16)

(5,0)(-3,0)


Ans:

15

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