# Math 0950 Practice Problems for Test 3

1. Use the distributive property to rewrite this expression:-2(x-1)

2. Subtract 4(2x+1) from 2(3x-1)

3. –[-2-(1-x)] can be written more simply as ?

4. 4x-3y-(x+2y-z) equals:

5. Subtract x^{2}-3x+1 from the sum of 2x^{2}+x+3 and 5x-8

6. (6x^{3}-5x^{2}-2)-(x^{3}+2x^{2}-3x+4) equals:

7. Carry out the multiplication (3x^{2}+2x+1)(7x^{2}-2x)

8. (2w-9)^{2} or (2w-9)(2w-9)** **when multiplied out equals?

9. Factor 15x^{2}-25x completely. Check your work using multiplication.

10. Factor a^{2}b+a^{2} completely and then check your work using multiplication.

11. The perimeter of a triangle is the distance you would walk to travel around the edge of the triangle. The shortest side of the triangle is 3 feet less than the length of the middle side. The longest side is 5 feet longer than the middle side. Let the length of the middle side be represented by m. What expressions will represent the length of the shortest side and the length of the longest side? What expression will represent the length of the perimeter?

12. Suppose this year’s revenue of the airline industry is 8 billion dollars less than last year’s revenue. Define the variable expressions for this year’s and last year’s revenue.

13. Solve:5(2-3x)=3-5x

14. Solve:2(3x-5)=-8-4(x+3)

15. Solve:

16. Solve:

17. A plumber charges $55 for the first hour of work and $40 for each additional hour or part of an hour. How much would this plumber earn for working h hours? Write an expression describing his/her earnings.

18. Which of the following operations on the equation 2x-3=4 is done incorrectly?

a) Multiply both sides by :

b) Add 3 to both sides:2x=7

c) Add to both sides:2x-7=0

d) Add to both sides:x-3=2

19. Find the GCF for the following: 12, 16, 20

20. The length of a rectangle is 3 meters more than the width. If the perimeter is 50 meters, find the length and width of the rectangle.

21. The longest side of a triangle is 10 centimeters less than twice the length of the middle side. The short side is 7 cm less than the length of the middle side. If the perimeter is 55 cm, find the length of each side of the triangle.

22. Find the value of , if the measures of a pair of supplementary angles are 3x-1degrees and 5x-3 degrees. What are the angle measures?

23. Find the value of in a rectangle if the width is 2x inches, length is 15 inches, and area is 90 square inches. What is the length and width?

24. The total driving time for two trips is 15 hours. The driving time for the
first trip is half the second. How long is each trip?

a) Define the variable expressions.

b) Write an equation.

c) Solve the equation and determine the values asked for.

d) Check your answer.

Math 0950 Practice Problems for Test 3 Key

11. shortest side = m-3 ft.; longest side = m+5 ft.; perimeter = 3m+2 ft

12. last year’s revenue = r billion dollars; this year’s revenue =
r-8 billion dollars

13.x=7/10

14.x=-1

15.x=3/2

16.x=6

17.55+(h-1)40 dollars

18.d

19. GCF is 4

20. length 14 m; width 11m

21. Sides are 26 cm, 18 cm, 11 cm

22. x=23; angles are 68 degrees, 112 degrees

23. x= 3; width is 6 inches, length is 15 inches

24.

a) s = time for second trip; ½ s = time for first trip

b)

c) time for second trip: 10 hrs.; time for first trip: 5 hrs.

d)