Chapter 1 Test Review

Chapter 1 Test Review

1-1 Variables and Expressions

• Word phrases or numeric expressions can be used

• Switch words: more than, less than, greater than. When you see a switch word, you switch the order.

• Examples: 3 more than twice a number x= 3+2x

• The quotient of 6 and a number= 6/n

• The product of 4 and a number = 4x

• The difference of 8 and a number c= 8-c

Multiple Choice

What word phrase can be used to represent the algebraic expression n/7?

• The product of a number and 7

• The quotient of a number and 7

• The difference of a number and 7

• The sum of a number and 7

Multiple Choice

What expression represents the product of 5 and the sum of a number and 11

• 5(2+x)

• 5(11)

• 5(n + 11)

• 5n + 11

1-2 Order of Operations

• We follow the order of operations when solving expressions.

• PEM/D A/S Parentheses, Exponents, Multiplication or Division, Addition or Subtraction

• Exponents: 4² the 4 is the base, the 2 is the exponent, the two tells you how many times to multiply the 4 by itself

• 4x4= 16, so 4²= 16

Multiple Choice

Simplify 5³

• 125

• 25

• 15

• 8

Multiple Choice

 $52\ -8^2\ +\ 3\left(4-2\right)^3$  

• -32

• 6

• 37

• 12

Multiple Choice

Evaluate the expression for the given values of the variables.

 $3m^2\ -\ n;\ m=3,\ n=6$  

• 21

• 12

• 9

• 75

1-3 Real Numbers and the Number Line

• When ordering rational numbers, think of the number line

   $3.5,\ -2.1\ \sqrt{9,}\ -\frac{1}{2},\ \sqrt{5}$  

• Order the numbers above from least to greatest- Answer below:

•  $-2.1,\ -\frac{1}{2},\ \sqrt{5},\ \sqrt{9},\ 3.5$  

Multiple Choice

Order the following numbers from least to greatest.

 $-6,\ \sqrt{20},\ 5.3,\ -6.56$  

•  $-6,\ -6.56,\ 5.3,\ \sqrt{20}$  

•  $-6.56,\ -6,\ 5,\ \sqrt{20}$  

•  $-6.56,\ -6,\ \sqrt{20,}5$  

1-4 Properties of Real Numbers

• Commutative Properties of Multiplication and Addition- changing the order of the numbers, remember the number "commute" example: 5+8= 8+8 or 7x5=5x7

• Associative Properties of Multiplication and Addition- who you "associate with" is who you are grouped with. example: 4+ (5+7) = (4+5)+ 7 or 6x(4x2)= (6x4)x2

• Identity property- the original number/variable stays the same, remember it keeps its identity. Example: 5+0=5 1xn= n

Multiple Choice

What property is demonstrated in the equation: 9+0 = 9

• associative property of addition

• commutative property of addition

• identity property

• associative property of multiplication

Multiple Choice

What property is demonstrated in the equation: 8+7=7+8

• associative property of addition

• commutative property of addition

• identity property

• associative property of multiplication

Multiple Choice

What property is demonstrated in the equation: a+ (b+c)= (a+c) +b

• associative property of addition

• commutative property of addition

• identity property

• associative property of multiplication

1-5 Adding and Subtracting Real Numbers

• Song for adding integers: Same signs add and keep, different signs subtract, keep the sign of the larger number then you'll be exact.

• Subtraction problems can be written as addition problems if you add a negative sign to the second number, example -3-7 is the same as -3 + (-7)= -10

Integer chips website if you need practice

https://toytheater.com/two-color-counter-whiteboard/

Multiple Choice

Simplify: -2+ (-7)

• -5

• -9

• 7

• 5

Multiple Choice

Simplify: 36 - (-12)

• -48

• -12

• 24

• 48

Multiple Choice

Simplify: -13-7

• -20

• -6

• 6

• 20

Multiple Choice

Simplify: 5 + (-18)

• 23

• 13

• -23

• -13

Multiplying and Dividing Real Numbers

• Positive x Positive = Positive Pos/Pos = Pos

• Negative x Negative = Positive Neg/Neg = Pos

• Negative x Positive = Negative Neg/Pos= Neg

• Positive x Negative = Negative Pos/Neg= Neg

Multiple Choice

Simplify: -6(-5)

• -30

• 30

• -11

• 11

Multiple Choice

Simplify: 32/-4

• -8

• 8

• 6

• -28

Multiple Choice

Simplify: 7(-3)

• 21

• -21

• 24

• 20

Multiple Choice

Simplify: -9/-3

• -3

• 3

• 6

• -6

The Distributive Property

• You distribute the factor outside the parentheses to each term inside the parentheses.

• Example: 5(2x-3)= 10x-15

• Example -3(-4x-5)= 12x + 15

Distribute Property Table Method

The table method can also be used.

 $-3\left(6x\ +8\right)$  

Multiple Choice

Simplify: (j+2)7

• 7j+2

• 7j+14

• -7j-2

• j+2

Multiple Choice

Simplify -8(x-3)

• -8x -3

• 8x +24

• -8x - 24

• -8x + 24

Multiple Choice

Simplify: -2(x-1)

• -2x+2

• -2x-2

• x-2

• x+2

1-7 Cont. Combining Like Terms

• We can combine variables to the same power and constants. See Examples Below

• Examples: 2n+1 - 4n +3

• Simplified Form: -2n +4

Multiple Choice

 $2x^2\ +9x\ -9x^2$  simplify

•  $7x^2\ +9$  

•  $2x^2$  

• 2x

•  $-7x^2\ +\ 9x$  

Multiple Choice

Simplify: 6(4t-3) + 6(t+3)

• 24t +36

• 24t

• 30t

• 18

Multiple Choice

Simplify: -(n-3)

• -n+3

• -n-3

• n+3

• n

1-8 Introduction to Equations

• An equation is a mathematical sentence that uses an equal sign (=)

• An equation is an open sentence if it contains one or more variables and may be true or false depending on the variables.

• Examples: Is the equation True, False, or Open?

• 3y+ 6 = 5y - 8 Open because depending on the variable's value it could be true or false

• 16-7 = 4+5 9=9 True because both sides of the equation are equal

• 32/8 = 2x3 4=6 False because both sides of the equation are not equal

Multiple Choice

Is the equation true, false or open?

29-34= -5

• true

• false

• open

Multiple Choice

Is the equation true, false or open?

85 + (-8) = 95

• true

• false

• open

Multiple Choice

Is the equation true, false or open?

5x + 7 = 17

• true

• false

• open

Identifying if a number is a solution to an equation

• Example 1 : 18+ d = 24; 6

• Substitute 6 for d, 18+6=24

• 6 is a solution to this equation

• Example 2: 5b+1=16; 2

• Substitute 2 for b, 5(2) +1 =16

• 10+1 =16

• 11=16, 2 is NOT a solution to the equation

Multiple Choice

Is the given number a solution to the equation?

 $9a+\ 72\ =\ 0;\ -8$  

• yes

• no

Multiple Choice

Is the given number a solution to the equation?

 $2=10-4y;\ 2\$  

• yes

• no

Multiple Choice

Is the given number a solution to the equation?

 $\frac{m}{3}=7;\ 28$  

• yes

• no

You are finished!

Good luck on your test!