Math 093 Practice Final Exam #1 1

1.) Factor completely: (a) 3x8 + 7x 7  6x 6 (b) 4x 2 16 a 2  9a 20 a 2  4a 2.) Simplify:  a 2  2a 15 3  a x 2  9 3.) For the rational expression: x 2  2x 15 (a) Find the values of x for which the expression is undefined. (b) Simplify completely.

4.) Simplify: (5xy  3y 2  x 2 y)  (5y 2  x 2 y  2xy  4xy 2 )

20y 5 z 8  2y 4 z 2  4y 2 z 4  8y 2 z 5.) Divide: 4y 2 z 4 6.) Multiply and simplify: (a) (x 2  5y) 2 (b) (x 3  2)(x 6  2x3  4)

7.) Solve for x: (x  5) 2  36

8.) Solve for x: 3  x 1  x

3 1 5 9.) Solve for x:   1 x 2 x

10.) Solve for x by using the quadratic formula: x 2  2x  4

11.) A rectangle has a base which is five times as long as its height. Find the base and the height of the rectangle if the perimeter is 240 meters.

y 1 12.) Add and simplify:  y 2  25 y 2  8y 15

13.) Simplify. Write your answers without negative exponents. Assume all variables are positive. 5x 2 y 8 z 3 (a) (5x 5 y 9 )2 (b) 10x 6 y 2 z 5

14.) Perform the indicated operation and simplify, if possible. Assume all variables are positive. 27x5 y 4 (a) ( 2  6)(4 2  6) (b) 3x 2 y11 Math 093 Practice Final Exam #1 2

15.) Perform the indicated operation and simplify, if possible. Assume all variables are positive. 5 (a) Rationalize: (b) 18m5n16 8  3

16.) Consider the equation of the line 5x + 2y = 8: (a) Find the x-intercept. Write your answer as an ordered pair. (b) Find the y-intercept. Write your answer as an ordered pair. (c) Find the slope (d) Graph the line. Label two points.

17.) A straight line passes through the points (-3, 5) and (-2, -6). (a) Find the slope of the line. (b) Find the equation of the line in slope-intercept form.

18.) Graph the inequality: -3x + 2y < 4.

19.) Solve the system. If there is no solution or an infinite number of solutions, state this. (1) 3x – 8y = 14 (2) x + 4y = -2

20.) Solve the system. If there is no solution or an infinite number of solutions, state this. (1) –x + 2y = 4 (2) 2x – 4y = 8

21.) A jar is filled with quarters and dimes. Ken decides to cash them in at the bank. The teller gives him $14.40 and tells him there were 78 coins in all. How many of each were in the jar?

22.) Perform the indicated operations and simplify, if possible. Assume that all variables are positive. 2 50x 5  5x 12x3  3x 2 98x

23.) Graph the parabola: y  2x 2  8x  6 . Clearly state the y-intercept, any x-intercept(s), and the vertex.

24.) If f (x)  3x 2  5x  4 , find f (2) .

25.) Solve the inequality: 4(3  2x)  5 < 31 Math 093 Practice Final Exam #1 3

ANSWERS

1 1a.) x6(3x – 2)(x + 3) 2.) 3a.) x = 5, -3 a x  3 b.) 4(x – 2)(x + 2) b.) x  5

1y 2 2 4.) 3xy-2y2+2x2y-4xy2 5.) 5y 3 z 4  1 6a.) x4-10x2y+25y2 2z 2 z 3 b.) x9 + 8

7.) x = 1, -11 8.) x = 5 9.) x = 4

y 1 10.) no real solution 11.) 20 and 100 12.) (y  5)(y  3)

y18 2 10  15 13a.) 14a.) 2  6 3 15a.) 25x10 5 1z 2 3x xy b.) b.) b.) 3m 2 n8 2m 2x 4 y10 y 4

16a.) ( 8/5, 0) 17a.) -11 18.) y-int (0,2) b.) (0, 4) b.) y = -11x – 28 slope = 3/2 c.) -5/2 dotted line shade below

19.) (2, -1) 20.) no solution 21.) 44Q , 34D

22.) 31x 2 2x 10x 2 3x 23.) y-int (0,-6) 24.) 2 x-int (3,0) and (1,0) vertex (2, 2) opens downward

25.) x > -3