Messmer High School                               Name_________________________

 

Algebra, Final exam preview           Date____________ Hour_________

 

 

 

integer

 

1

 

A number that can be expressed as a ratio of two integers

 

 

 

proportion

 

2

 

A(B + C) = AB + AC

 

 

 

Absolute value

 

3

 

A second action that cancels out a first action

 

 

 

Rational number

 

4

Finding the value, or values, for a variable that makes an equation, or an inequality, true

 

 

 

inverse

 

5

 

The multiplicative inverse of a number

 

 

 

Identity property

 

6

 

Whole numbers, both positive and negative, and zero

 

 

 

solving

 

7

Mathematical sentence containing ³greater than², ³less than², ³greater than or equal to², or ³less than or equal to².

 

 

 

inequality

 

8

 

A x B = B x A

 

 

 

reciprocal

 

9

 

A + 0 = A and A x 1 = A

 

 

 

Associative property

 

10

 

Equation stating that two ratios are equal

 

 

 

Commutative property

 

11

 

A + (B + C) = (A + B) + C

 

 

 

Distributive property

 

12

 

The distance on the number line of a point from zero

 

 

 ratio

13

Comparison expressed as a fraction

 

 

Additive inverses

14

 Two numbers whose sum is zero

 

Addition property of inequality

 

15

If a < b then a+ c < b + c or

If a > b then a + c > b + c

 

Addition property of equality

 

16

 

If a = b then a + c = b + c

 

 

Exponential notation

17

 

A way of writing numbers that uses exponents

 

 

Degree of a term

18

 

The sum of the exponents of a term

 

 

binomial

19

 

A polynomial with exactly two terms

 

 

Monomial

20

Either a numeral, a variable, or a product of numerals and variables with a whole number exponent

 

 

trinomial

21

 

A polynomial with exactly three terms.

 

 

Scientific notation

22

 

A way of writing numbers using a mantissa and an exponent

 

 

Polynomial

23

 

A monomial or a sum of monomials

 

 

mantissa

24

 

A number greater than of equal to 1 and less than ten used in scientific notation.

 

 

factorization

25

 

Finding two expressions that, when multiplied together, give a product

 

 

Difference of two squares

26

 

Two terms, both squares, with a minus sign between the terms.

 

 

Factoring completely

27

 

Factoring until further factoring is no longer possible

 

 

Trinomial square

28

 

The square of a binomial

 

What are the three tests for determining if a trinomial is a trinomial square?

 

Test 1.________________________________________________________

 

Test 2._______________________________________________________

 

Test 3._______________________________________________________

 

What are the three tests for determining if a binomial is the difference of two squares?

 

Test1.________________________________________________________

 

Test 2._______________________________________________________

 

Test 3._______________________________________________________

Simplify

92 x 95                                                         a7b4  /  a4b3

 

 

 

 

Simplify by combining the like terms:

10 + 6x2- 10x + 4x2 + 25x - 3  p;                    4 + 4n2 - 13n + 24n2 + 5n - 27

 

 

 

 

Multiply or divide as indicated

4B(2B + 11)                                                         (5A - 7)(5A + 11)

 

 

 

Write using scientific notation

5,230                                                     0.00125

 

 

 

Write using standard notation:

6.78 x 103                                                             5.2 x 10-3  

 

 

 

Factor completely   

 8a2 - 24a &nbbsp;                                                  7x3 - 28x2 + 21x   

 

 

 

 

49x2 - 144                                                   64y4 - 9x2

 

 

 

 

 

9x2 + 6x + 1                                                          16y2 - 24y + 9

 

 

 

 

x2 + 15x + 50                                              x2 + 18x + 72       

 

 

 

 

x2 + 5x - 14                                                 x2 - 3x - 54

 

 

 

 

 

 

 

6x3 + 12x2 + 5x + 10                                   5x3 - 2x2 + 10x - 4>

 

 

 

 

 

 

 

Solve the following equations. Remember to find both values for the variable:

 

x2 - 9x + 14 = 0                                           x2 - 81 = 0

 

 

 

 

 

 

 

 

2x2 - 16 = 0                                                 9x2 - 4 = 0 &                    

 

 

 

Graph

1

A point drawn on a number line or coordinate plane representing a number of ordered pair

 

x-axis

2

The horizontal line where y = 0

 

y-axis

3

The vertical line where x = 0

 

Origin

4

The intersection where the x-axis crosses the y-axes

 

Coordinate plane

5

A plane in which a coordinate system has been set up.

 

x-coordinate

6

The first number in an ordered pair

 

y-coordinate

7

The second number in an ordered pair

 

Coordinate axes

8

The x and y axes used to map the coordinate plane

 

Quadrant

9

One-fourth of the coordinate plane

 

Linear equation

10

Variables are only raised to the first power.

 

Intersect

11

Where two lines cross

 

X Intersect

12

The Y value when X = 0

 

Y Intersect

13

The X value when Y = 0

 

Slope-intercept equation

14

Equation in the form y = mx + b

 

Slope

15

Rise divided by run

 

Find the slope of the line connecting the following two points. Use the formula for slope or graph the points and use the counting method

(0,0) and (6,3)

 

 

 

 

 

(2,4) and (0,6)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Write a T-chart below and find three solutions to 

y = 4 - 2x.

Plot the points and connect them with a line to graph the equation.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Draw a graph for the given equation

based on the intercepts: 6x + 4y = 12. Include a T chart below

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


 

Change the following equations to slope-intercept form:

2y - 6x = 8

4Y + 2X = 12

 

 

 

 

 

 

 

 

 

 

 

Complete the following t-charts and graph each set of points. Connect the lines.:

 

Y = 2X + 1

0

 

 

-3

 

 

3

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Y = (1/2) X - 4

0

 

 

4

 

 

-4

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

                                                                  

Change to slope-intercept form

2y - 5x = 18

 

 

 

 

 

 

Determine whether the given ordered pair is a solution to both equations. Show your work

(3,5) in 4x - 3y = -3

    and   y = 2x - 1

 

 

 

 

 

Solve by substitution: 

 y = 2x + 1

 2x + y = 5

 

Solve by addition:

4x + 2y = 20

3x - 2y =8

 

 

 

 

 

 

 

The sum of two numbers is one hundred twenty. The difference between them is sixteen. What are the numbers?

 

 

 

 

 

 

 

 

 

A jar of dimes and quarters holds  $15.25. There are 103 coins in all. How many of each are there?

 

Let A = { 1, 2, 3, 4, 5 } , B = {-5, -3, -1, 1, 3 } and C = { -2, -1, 0, 1, 2}

Use roster notation for

      A Union C                                                      B Intersect A

 

 

 

 

Graph these conjunctions:  

-2 < x and x < 3                                -3 ²  x + 2  < 0

 

                                               

Graph these disjunctions

x < -3 or x > 1                                   2x < -8 or 3x > 12

 

 

Simplify

x2 + 4x + 4

   x2 - 4

 

 

 

 

 

 

 

6x3y2

3xy

x2+6x - 27

  x2 - 9

x + 6     times                x2 + 5x + 6

x + 3                              x2 + 7x + 6

 

 

 

 

 

14x ­ 21    divided by                  2x - 6  

x + 2                                        x2 - x ­ 6

 

 

 

 

x+2     plus      3x + 10

  4                         8

x-3   minus     2x + 4

 2x                  x ­ 1

 

 

 

 

 

 

 

 

 

Solve

(2/3) + (5/6) = (1/x)

 

 

 

 

x + (4/x) = -5