Exam 1 Review:

Here is a list of topics and some sample questions:

Order of Operations: Simplify the following:

• 9 – 2[6(3-5) + 7]
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• 
• + 5(7 - 13)
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Translate English phrases into mathematical expressions: Don’t forget to label you variable.

• Five less than the product of four and the sum of a number and six.

What is an algebraic expression?

What is an equation?

What is a linear equation?

What are the three types of equations in one variable?

What are equivalent algebraic expressions? What are equivalent equations?

• All linear equations are conditional equations. T F
• All conditional equations are linear equations. T F
• 3(x + 2) = 3x + 6 is an example of a contradiction. T F
• The solution for an identity equation is all real numbers. T F
• If an equation has more than one solution, then it is an identity. T F
• = 0 is an example of a linear equation. T F
• is an example of a linear equation. T F
• is an example of a linear equation. T F

Evaluate algebraic expressions. Evaluate the following for x = -3 and y = 2.

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• 
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Know the Real Number System.

• What are the integers?
• The whole numbers?
• The natural numbers?
• The rational numbers?
• The irrational numbers?
• The real numbers?

List the smallest set that the following numbers belong to.

• 5
• 0
• -12
• .3
• .303303303303…
• 
• 
• 

What is the absolute value of a number?

Operations with real numbers and their order of operations:

What are the properties of real numbers?

Commutative property of addition

Commutative property of multiplication

Associative property of addition

Associative property of multiplication

The distributive property

The additive identity

The multiplicative identity

The additive inverse

The multiplicative inverse

The following are examples of what properties?

(3*4)(5)=5(3*4)

5 + 0 = 5

5 + 0 = 0 + 5

5 + (-5) = 0

[(5 + 0) +3]=5 + 3

[(5 + 0) + 3] = 5 + (0 + 3)

5x + 3x = x(5 + 3)

Simplify expressions: make sure that you add like terms!

• 5(2x + 3) - (6x -7)
• 2 - 4(3x + 6) + 5(8x + 7)
• 4xy + 3x – (6x – 5yx)

Solving equations:

• x + 7 = 9
• x -12 = -3
• -8 = 4x
• 
• 
• 
• .04(.3x + 2) -5( .046x + .03) = -.179

Applications:

Consecutive integers

Five times the largest of 3 consecutive even integers is 4 less than three times the sum of the other two integers. What are the integers?

Complementary angles

Supplementary angles

The sum of an angle and twice its complement is its supplement. What is the supplement of the angle?

Interpret English sentences and change them into algebraic equations.

The number of women in a math 0094 class was 3 more than the number of men. The sum of twice the number men and three times the number of women was 49. How many women were in the class?