# Math Placement Test Review

Below you will find helpful information regarding the placement test. We wish you the best of luck!

- The Placement Test is a computer generated test. You must answer each question in the order given. You will not be able to return to previous questions.
- A calculator on the computer will be provided for use. You may not use your own. It is a basic four function calculator that becomes active for select questions.
- Scrap paper will be provided.
- Algebraic and Geometric formulas will not be provided on the test.

A review for the placement test is provided. This is meant to only be a review and NOT a tutorial on subject matter. To view the solutions to the practice problems, click on the link to the right of each problem. You must have Adobe X or higher installed on your computer to view the solutions.

**Please Note: (To view the answered demonstrations below you must use Internet Explorer (IE).**

## Fractions and Decimals

**Problem**

1. Round 0.0827149 to the nearest thousandth

2. Simplify 4 ^{2/5} +3 ^{1/3}

3. Find the circumference of the circle below. Use *π *= 3.14

4. A satellite is located 34,160,000,000,000 km from earth. Write this amount in scientific notation.

5. You are travelling from City A to City B, which are located 2,448 miles apart. If you have to stop for gas 2/9 of the trip, how many miles have you traveled?

6. Write 4 ^{7/8} as a decimal

7. Simplify: (-2/3)^{4}

8. Simplify: 4 ^{1/5} ÷ 2 ^{7/10}

9. Simplify: -2.31^{2}

10. Find the area of a right triangle with legs measuring 4 ^{4/5} cm and 3 ^{3/4} cm.

11. Plot the following numbers on the number line: 2/3, 1 ^{1/3}, and 10/3

12. The names of sixteen states of the United States begin with the letters “M” or “N”?

13. Simplify: 6 ^{3/4} – 2 ^{1/8}

14. Simplify: -1.283 – 5.6

## Graphs and Equations of Lines

**Problem**

1. The pictograph shows the number of visitors to the Lost Land of Dinosaurs exhibit at the Southern National Museum during its one week showing this summer. What two days combined total the same number of people as those who visited on Thursday?

2. The bar graph shows the number of cars sold at a local dealership during a five month sales challenge. Approximately how many more cars were sold in July than September?

3. The line graph shows the number of races won by Team Samson for the years 2009 – 2013. Between what two consecutive years did the greatest increase in races won occur?

4. The circle graph shows the results for the Favorite Movie Genre survey of the Senior Class at Wellington High School. If 500 students participated in this survey, how many students voted Comedy as their favorite genre?

5. Complete each ordered pair so that it is a solution of the given linear equation.

3x – 7y = 20

a. ( ,-2)

b. (5, )

6. Determine (8, -1) is a solution of the given linear equation.

y = 1/2x – 3

7. Write the equation of the line in slope-intercept form, given the slope, m, and y-intercept (0, b).

m= 4, b = 1/2

8. Find the slope of each of the following lines.

a) 3x – 2y = 6

b) x = 5y

c) x = 3

9. Write the equation of the line with the given slope and passes through the given point. Write the equation in standard form (Ax + By = C).

m= -3/2, (1,-4)

10. Determine whether the pair of lines are parallel, perpendicular, or neither.

3y = 2x + 21

6x + 2y = -16

11. Translate and graph the statement below. Three times the x-value subtract six times the y-value is six.

The statement is:** ______________________ **

## Linear Equations & Inequalities

**Problem**

1. Evaluate the expression for x = 2 and y = 3.

(xy + 2)

^{2}

2. Write the following phrase as a variable expression.

Use x to represent “a number”.

A number subtracted from eight.

3.Write the following phrase as a variable expression.

Use x to represent “a number”.

Thirteen decreased by six times a number.

4. Simplify the expression.

-6x^{2 }– 7x^{2} + 5x^{2}

5. Simplify the expression.

3h^{2} – 2h^{2} + 5

6. Simplify the expression. First use the distributive property to remove any parentheses.

-(-5*x* – 2y +3)

7. Solve for n.

6(*n* + 7) = 7*n* – 4

8. Solve for c.

9*c* – 18 – 2*c* + 4 = 0

9. Solve for x.

6(2x – 1) – 2(3*x)* = 9

10. Solve for y.

2(*y *+ 2))/3 = 4*y *– 1

11. Solve for n.

15(*n *+ 9) = 3(45 + 5*n*)

12. Find the number described.

The number 76.8 is what percent of 96?

13. A manufacturing company announced that next year the price of their product would increase by 3.5%. This year their product is priced at $17,716.

Find the increase in the price of the product.

Find the new price of the product. (Round to the nearest cent as needed.)

14. Solve and graph the inequality.

*x *– 6 ≥ – 7

15. Solve and graph the inequality.

-7b < 14

16. Translate and solve the inequality. Use x as the variable.

Nine more than twice a number is greater than negative nineteen.

**Answer**

## Operations With Integers

**Problem**

1. A 10m ladder is leaning against a building. The base of the ladder is 5 m from the base of the building. How high up the wall of the building is the ladder leaning?

a) Give the answer in radical form. (Do not simplify).

b) Approximate the answer to 3 decimal spaces.

2. Find the average of the list of number: -14, -28, -10, -12

3. Find the quotient for the following problems:

a. 3/(0)

b. 0/3

c. (-24)/6

4. Find the circumference and area of a circle with diameter = 4 cm. Round answers to the nearest hundredth as needed. (use pi = 3.14)

5. Simplify: (27-3)/(2^{4}– 2^{3} )

6. Simplify: 4^{2} – ( √36- 2^{3})

7. Subtract -9 from 5.

8. Evaluate the following:

a. -6^{2}

b. – | -6 |

c. – ( -6)

9. Simplify: 8 – (-12) + (-7)

10. Evaluate 3 x^{2} – y for x=7 and y = -5

11. Multiply: (-2)(-5)(-3)

12. Graph each integer on the same number line. 0, -4, 3, -5

13. Find the difference of -7 and -3

14. A fence is being put around a rectangular garden that is 12 ft. by 10 ft. If the fencing costs $5 per foot, find the total cost of the fencing.

15. Find the area of the geometric figure:

16. Write using exponential notation: 5•5•8•8•8

17. Find the area of the geometric figure:

18. Simplify: 12 + (-10) ÷ 5

**Answer**

*Solution #1*

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## Polynomials & Quadratic Equations

**Polynomials and Quadratic Equations**

**Problem**

1. Simplify the expression. Write the result using positive exponents only.

((a^(-6) b)/(ab^2 ))^(-2)

2. Subtract.

(6x^2+7)-(-3y^2+7)

3. Find the following product.

〖(6y+8)〗^2

4. Divide.

(-6x^7+8x^5-8)/(2x^3 )

5. Factor the trinomial completely.

5x^2+40x-45

6. Factor the trinomial.

2c^2-11c+5

7. Factor the following binomial completely.

36x^2+1

8. Solve the equation.

x^2-32=-4x

9. An object is thrown upward from the top of a 96-foot building with an initial velocity of 80 feet per second. The height h of the object after t seconds is given by the quadratic equation

h=-16t^2+80t+96. When will the object hit the ground?

10. Find the domain and range of the following relation. Also determine whether the relation is a function.

{(7,7),(-7,-4),(-3,-6),(-7,1)}

11. Use the vertical line test to determine whether the graph is the graph of a function. Yes or no?

12. Find f(-1) if f(x)=(8x+21)/(9x-3)

13. Find the domain and range of the relation using interval notation.

14. Using the following graph of the quadratic function, h(x)=x^2+2, state the vertex and give the equation for the axis of symmetry.

**Answer**

## Ratio, Proportions, Percents

**Problem**

1. A family paid $29,600 as a down payment for a home. If this represents 20% of the price the home, find the price of the home.

2. On an architect’s blueprint, 1 inch corresponds to 4 feet. How long is a wall represented by a 15 inch line on the blueprint?

3. What percent of 150 is 90?

4. 15% of what number is 9?

5. Convert 9.9 kilometers to millimeters.

6. How many cups are in 3 quarts?

7. Susan went shopping and bought a pair of boots for $54, a blouse for $31, and sunglasses for $45. The tax in Susan’s city is 8%. Find the total sales tax and the final cost of the purchases (including sales tax).

8. Triangles R and S are similar triangles. Find the value of y.

9. If the original amount was 24 and the new amount is 6, find the amount of decrease and the percent decrease.

10. Rewrite 3.2 as a Percent.

11. Rewrite 16% as a Fraction.

12. Rewrite 4/5 as a Percent.