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Practice Test

1.

Graph the following: 2y=3x+4. 2y=3x+4.

2.

Find the x- and y-intercepts for the following: 2x5y=6 2x5y=6

3.

Find the x- and y-intercepts of this equation, and sketch the graph of the line using just the intercepts plotted.

3x4y=12 3x4y=12

4.

Find the exact distance between ( 5,−3 ) ( 5,−3 ) and ( 2,8 ). ( 2,8 ). Find the coordinates of the midpoint of the line segment joining the two points.

5.

Write the interval notation for the set of numbers represented by { x| x9 }. { x| x9 }.

6.

Solve for x: 5x+8=3x10. 5x+8=3x10.

7.

Solve for xx: 3( 2x5 )3( x7 )=2x9. 3( 2x5 )3( x7 )=2x9.

8.

Solve for x: x 2 +1= 4 x x 2 +1= 4 x

9.

Solve for x: 5 x+4 =4+ 3 x2 . 5 x+4 =4+ 3 x2 .

10.

The perimeter of a triangle is 30 in. The longest side is 2 less than 3 times the shortest side and the other side is 2 more than twice the shortest side. Find the length of each side.

11.

Solve for x. Write the answer in simplest radical form.

x 2 3 x=- 1 2 x 2 3 x=- 1 2

12.

Solve: 3x84. 3x84.

13.

Solve: | 2x+3 |<5. | 2x+3 |<5.

14.

Solve: | 3x2 |4. | 3x2 |4.

For the following exercises, find the equation of the line with the given information.

15.

Passes through the points ( 4,2 ) ( 4,2 ) and ( 5,−3 ). ( 5,−3 ).

16.

Has an undefined slope and passes through the point ( 4,3 ). ( 4,3 ).

17.

Passes through the point ( 2,1 ) ( 2,1 ) and is perpendicular to y= 2 5 x+3. y= 2 5 x+3.

18.

Add these complex numbers: (32i)+(4i). (32i)+(4i).

19.

Simplify: −4 +3 −16 . −4 +3 −16 .

20.

Multiply: 5i( 53i ). 5i( 53i ).

21.

Divide: 4i 2+3i . 4i 2+3i .

22.

Solve this quadratic equation and write the two complex roots in a+bi a+bi form: x 2 4x+7=0. x 2 4x+7=0.

23.

Solve: ( 3x1 ) 2 1=24. ( 3x1 ) 2 1=24.

24.

Solve: x 2 6x=13. x 2 6x=13.

25.

Solve: 4 x 2 4x1=0 4 x 2 4x1=0

26.

Solve: x7 =x7 x7 =x7

27.

Solve: 2+ 122x =x 2+ 122x =x

28.

Solve: ( x1 ) 2 3 =9 ( x1 ) 2 3 =9

For the following exercises, find the real solutions of each equation by factoring.

29.

2 x 3 x 2 8x+4=0 2 x 3 x 2 8x+4=0

30.

( x+5 ) 2 3( x+5 )4=0 ( x+5 ) 2 3( x+5 )4=0

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