College Algebra

# Practice Test

College AlgebraPractice Test
1.

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

2.

Find the x- and y-intercepts for the following: $2x−5y=6 2x−5y=6$

3.

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

$3x−4y=12 3x−4y=12$

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${ x| x≤9 }. { x| x≤9 }.$

6.

Solve for x:$5x+8=3x−10. 5x+8=3x−10.$

7.

Solve for x:$3( 2x−5 )−3( x−7 )=2x−9. 3( 2x−5 )−3( x−7 )=2x−9.$

8.

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

9.

Solve for x:$5 x+4 =4+ 3 x−2 . 5 x+4 =4+ 3 x−2 .$

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.

$x 2 3 −x=- 1 2 x 2 3 −x=- 1 2$

12.

Solve:$3x−8≤4. 3x−8≤4.$

13.

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

14.

Solve:$| 3x−2 |≥4. | 3x−2 |≥4.$

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:$(3−2i)+(4−i). (3−2i)+(4−i).$

19.

Simplify:$−4 +3 −16 . −4 +3 −16 .$

20.

Multiply:$5i( 5−3i ). 5i( 5−3i ).$

21.

Divide:$4−i 2+3i . 4−i 2+3i .$

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:$( 3x−1 ) 2 −1=24. ( 3x−1 ) 2 −1=24.$

24.

Solve:$x 2 −6x=13. x 2 −6x=13.$

25.

Solve:$4 x 2 −4x−1=0 4 x 2 −4x−1=0$

26.

Solve:

$x−7 =x−7 x−7 =x−7$

27.

Solve:$2+ 12−2x =x 2+ 12−2x =x$

28.

Solve:$( x−1 ) 2 3 =9 ( x−1 ) 2 3 =9$

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.

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