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Semester 2 Final Exam Review #2

Unit 7 – Systems of Equations

1. For the given system, what is the value of x?

3 4 6

9 4 12

x y

x y

− − =

+ =

2. Solve the system by elimination. 2 3 7

4 5 8

x y

x y

+ =− + =

3. The sum of the real numbers x and y is 22. Their difference is 12. What is the value of xy?

4. Donna has 16 coins. Some of the coins are quarters and some are dimes. The total value of all of the coins is $3.40. How many of the coins were quarters?

5. A fast food restaurant sells hamburgers and hotdogs. In one night, 117 items were sold for a total revenue of $137.70. Hamburgers cost $1.30 and hotdogs cost $1.10. How many hamburgers did they sell?

Unit 8 – Rules of Exponents

6. Simplify: 5 10 8a a a• • 7. Simplify: ( )

84y

8. Simplify: ( ) ( )22 465x y xy

9. Simplify: 2

5

3xy

10. Simplify: 10

7

5

5

11. Simplify: 7 7 mm− −•

12. Write 0 310 10−• using positive exponents. 13. Simplify: ( )( )5 8 112 8x y x y

14. Simplify: 2 8 2(5 )x y

15. Simplify:

10

5

x

x−

16. Simplify: 8 10 4

3 3 2

45

9

x y z

x y z

− 17. Simplify:

7 4 3

3 8 24

x y z

y z

−

− − −

Unit 9 – Polynomials

1. Find the sum: ( ) ( )2 5 6 10 7x xx − + + +− 2. Find the difference:

( ) ( )3 2 316 10 5 102 3x xx x+ − − + −− −

3. Categorize by degree and number of terms (circle

two below): 5x Degree: Constant Linear Quadratic Cubic # of Terms: Monomial Binomial Trinomial Polynomial

4. What polynomial must be added to 3 24 10 6x x x+ −

so that the sum is 210 9 4x x+ − ?

5. Find the product: ( )( )2 7 7x x+ +

6. Find the product: ( )( )2 4 2 4x x− − − +

7. Find the product: ( )( )2 5 114 2 xx x − +− 8. A rectangle has a length of 6x + and a width of

2 1x + . Write an equation that describes the area, A, of the rectangle in terms of x.

9. Find the product: ( )1 (3 1)3 xx + − 10. 2(5 4) ?x + =

11. Factor the polynomial: 2 21 80x x+ + 12. Factor: 5 24 16 8x x x+ −

13. Factor: 24 7 2x x− − 14. Which is not factorable?

2 10 16x x− + OR 2 6 16x x+ +

15. Factor: 2121 16x −

Unit 10 – Quadratic Equations and Functions

1. Graph: 22 4y x x= −

x y

2. Graph: 2 6 5y x x= − +

x y

3. Which of the functions below, when graphed, would have a minimum (open up)?

A. 2 8 12y x x= − + +

B. 2 6 4y x x= − + −

C. 2 4 1y x x= − + −

D. 22 2 7y x x= + +

4. What is the vertex of the graph of the function2 6 8y x x= − + −

?

5. What is the equation of the axis of symmetry for

the function 22 16 15y x x= − + − ?

6. Solve the equation: ( )23 0x + =

7. Solve: ( ) ( )2 5 0x x+ − + = 8. Solve: 2 5 0x x− =

9. Solve: 2 4 53x + = 10. Solve: 22 98x− = −

11. Solve: 29 16 0x − = 12. Solve: 21

12 232x− − =

13. How many solutions (roots) does the following

equation have? 23 2 2 0x x+ + =

14.

Find the SUM of the solutions: 2 10 24 0x x− − =

Unit 11 - Radicals

1. Write 48 in simplified square root form. 2. Simplify: 24 75•

3. Simplify: 9 121 4. Simplify:

100

81

5. Simplify: 5 5 13 7 18 5+ − 6. Simplify: 27 48−

7. Solve: 4 8 20x + = 8. Solve: 11 9 3x + − =

9. Solve: 3 5x − = − 10. Solve for x: 42x x+ =

Unit 12 – Rational Expressions

1. Simplify: 8

13 2

48 ( 7)

16 ( 7)

w m

w m

−−

2. Simplify: 3

2

2 8

4 4

x x

x x

−− +

3. Simplify: 2 2

10 11

8 64m m m

m m

− −÷ 4. Simplify:

2 2

2

25 4 12

2 15 8

y y y

y y y

− −•

+ −

5. Simplify: 2 36

3 27 12 108

2 12

m m

m x−− −÷

+

Unit 13 – Probability

1. In a bag of skittles there are 10 red, 5 green , 8 blue and 7 purple. Without looking, you draw out a skittle, replace it and then draw out a second skittle. What is the probability that the first and second skittle are both green?

2. A duffel bag contains 2 sweatshirts, 3 pairs of running shorts, and 5 tank tops. Without looking, you draw out an article of clothing and throw it back in. Then you draw out a second article of clothing. What is the probability that the first clothing item and the second are both a pair of shorts?

3. A die is rolled one time. What is the probability of rolling a number that begins with the letter “f” or a 3?

4. So far in algebra class, a student's quiz scores are 68%, 88%, 77%, 73% and 42%. What is the mean average of the quiz scores?

5. For the following information determine the mode: 5, 7, 2, 8, 6, 4, 7, 3

6. A survey was conducted to see who preferred University of Illinois (U of I) over Illinois State University (ISU). Of those who participated, 32 said they preferred the U of I, 27 preferred ISU, and 22 did not care. What is the probability that a person in this survey, chosen at random, preferred ISU?

7. On a warm-up there was one True/False question and one multiple choice question (A-D). What is the probability that the person chose false and the letter “a”?

8. At a swim meet there are 5 swimmers competing. If there are no ties, in how many ways can the first and second place finishers be arranged?

9. On a hockey team there are 13 players. How many ways could you arrange the 6 people on the ice?