Practice Exam II

1. Use the algebraic tests to check for symmetry with respect to both axes and the origin.

y = x3

 

 

 

 

 

2. Find the x- and y- intercepts of the graph of the equation algebraically

2x + 3y = 10

 

 

 

 

 

 

3. Solve the equation

=

 

+

 
_4__ _6__ _15_

x 1 3x + 1 3x + 1

 

 

 

 

 

 

 

 

 

 

Check your answer

 

 

 

 

 

 

 

4. Solve for x

6x + ax = 2x + 5

 

 

 

 

 

 

 

 

 

 

 

5. A rectangular room is 1.5 times as long as it is wide, and its perimeter is 25. Find the dimensions of the room.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6. Solve the quadratic equation using the specified method.

a. 4x2 + 12x + 9 = 0 factoring

 

 

 

 

 

 

 

 

 

b. (4x + 7)2 = 44 extracting square roots

 

 

 

 

 

 

 

 

 

 

 

 

c. 9x2 12x 14 = 0 completing the square

 

 

 

 

 

 

 

d. 5 + 2x2 = 8x Quadratic Formula

 

 

 

 

 

 

 

 

7. Perform the operation and write in standard form.

a.       (4 + 5i )2

 

 

 

 

 

 

 

 

b. (13 2i) (-5 + 6i)

 

 

 

 

 

 

 

 

 

 

 

c. __5__

1 i

 

 

 

 

 

 

 

 

 

_

 
 


d. __2__ _3__

1 + i 1 i

 

 

 

 

8. Find all solutions of (x+2) (2x 3) = -1

 

 

 

 

 

 

 

 

 

 

 

9. Find all solutions

3

 

=

 

 
a. 1 _1_

x x +1

 

 

 

 

 

 

 

 

 

 

 

 

b. |x2 +6x| = 3x + 18

 

 

 

 

 

 

 

 

3 x

2

 
 


10. Determine whether each value of x is a solution to the inequality 1 < 1

a.       x = 0

 

b.      x = -5

 

 

c.       x = 1

 

 

d. x = 5

 

11. Solve the inequality and sketch the solution on the real number line.

a. 1/2 (8x + 1) < 3x + 5/2

 

 

 

 

 

 

 

 

 

 

b. |1 2x| 1

 

 

 

 

 

 

 

 

 

 

 

c. x2 + 2x < 3

 

 

 

 

 

 

 

 

 

 

 

> 4

 
d. _3x 5_

x 5

 

 

 

 

 

 

12. Find the domain of x in the expression

( x2 7x + 12)

 

 

 

 

 

 

13. Find the slope of the line passing through the pair of points.

(-3, -2) and (1, 6)

 

 

 

 

 

 

 

 

 

 

14. Determine whether the lines L1 and L2 passing through the pairs of points are parallel, perpendicular, or neither.

L1 : (4, 8), (-4, 2)

L2 : (3, -5), (-1, 1/3)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

15. Find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope. Sketch the line.

(0, -2) m = 3

 

 

 

 

 

 

 

 

 

 

 

16. Determine whether the equation represents y as a function of x.

x2 + y2 = 4

 

 

 

 

 

 

17. Evaluate the function at each specified value of the independent variable and simplify.

4 5x x -2

f(x) = 0 -2 < x 2

x2 + 1 x > 2

 

a. f(-3)

 

 

b. f(4)

 

c. f(-1)

 

 

18. Find the domain of the function

g(y) = (y 10)

 

 

 

 

 

 

 

 

 

 

 

 

20. Find the zeros of the function.

f(x) = 3x2 + 22x 16

 

 

 

 

 

 

 

 

 

 

 

Also know: given a graph use it to

find the domain and range

perform the vertical line test to determine whether y is a function of x

find the intervals where the function is increasing, decreasing and constant