Skip to ContentGo to accessibility page
Algebra and Trigonometry 2e

# Practice Test

### Practice 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 $xx$: $3( 2x−5 )−3( x−7 )=2x−9. 3( 2x−5 )−3( x−7 )=2x−9.$

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 .

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

$x 2 3 −x=- 1 2 x 2 3 −x=- 1 2$

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 .

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

Citation/Attribution

Want to cite, share, or modify this book? This book is CC BY and you must attribute OpenStax.

Attribution information
• If you are redistributing all or part of this book in a print format, then you must include on every physical page the following attribution:
Access for free at https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-introduction-to-prerequisites
• If you are redistributing all or part of this book in a digital format, then you must include on every digital page view the following attribution:
Access for free at https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-introduction-to-prerequisites
Citation information

© Dec 13, 2021 OpenStax. Textbook content produced by OpenStax is licensed under a CC BY license. The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.