Alg 1 Sem 1 FINAL EXAM REVIEW

Learning Intention:
1) To review different topics we've studied this first semester
2) To answer questions that will count as your FINAL EXAM

Algebra 1 Semester 1 Exam

How this ONLINE SEMESTER EXAM will work:

​REVIEW slides, then TEST slides of multiple choice questions.

• I will insert REVIEW SLIDES to show EXAMPLES of problems and things we have done. TAKE YOUR TIME to look at them and then ANSWER the questions!

• You will ANSWER a total of 50 MULTIPLE CHOICE QUESTIONS, which means they will count 2 points each. The percentage of CORRECT responses will be your SEMESTER EXAM GRADE!

​NOTE: Commute means to change locations. So, numbers MOVE!

​Associative refers to who you "associate" with or grouped with in ( )!

​What number can you ADD and keep the same number (same identity)? ..0

​What number can you MULTIPLY and keep the same number (same identity)? 1

​ADDITIVE INVERSE -number to add and =0

​MULTIPLICATIVE INVERSE -number to multiply and = 1 RECIPROCAL (flip it)

​Don't forget...you CAN Always GO BACK and Review the Slides using the <- Back buttons and -> go Forward to the questions.

Multiple Choice

$$4+\left(a+b\right)=\left(4+a\right)+b$$

• Commutative Property of Addition

• Associative Property of Addition

• Identity Property of Addition

• Distributive Property

Multiple Choice

$$2\left(x+9\right)=2\cdot x+2\cdot9$$

• Distributive Property

• Identity Property of Multiplication

• Identity Property of Addition

• Associative Property of Addition

Multiple Choice

$$\left(2x\right)\cdot1=2x$$

• Commutative Property of Multiplication

• Associative Property of Multiplication

• Identity Property of Multiplication

• Distributive Property

Multiple Choice

$$\left(m+n\right)+3=\left(n+m\right)+3$$

• Commutative Property of Addition

• Associative Property of Addition

• Identity Property of Addition

• Distributive Property

Multiple Choice

$$\left(5-k\right)\cdot0=0$$

• Associative Property of Multiplication

• Identity Property of Multiplication

• Inverse Property of Multiplication

• Zero Property

Simplifying Expressions with Like Terms

Objective: Simplify algebraic expressions by combining like terms.

​Like Terms: terms that have the SAME variable(s) and the same EXPONENT

​​Example: 4x and 17x
Example: -x² and 5x²

​

​Unlike Terms: terms that DO NOT have the same variable(s)

​​Example: 4x and 17xy

​Vocabulary

Match

Match the following LIKE TERMS. Which pairs are "alike?"

• 8x

• 12x²

• 4x²y

• 7xy²

• 9y

-x

6x²

-9x²y

2xy²

-12y

• -x

• 6x²

• -9x²y

• 2xy²

• -12y

​Combine Like Terms: take multiple like terms and make them one
ADD the numbers
in front!

​

​Another word used
is SIMPLIFY.

​Vocabulary

Combining Like Terms Examples

Multiple Choice

Simplify the following expression:

6x + 5 - 3x -1

• 9x+6

• 3x+4

• 3x-4

• 6x+4

Multiple Choice

Rewrite the expression by combining like terms.

2x² + 10x + 5x² + 25x

• 3x² + 3xy + 6y

• 6y² + 2xy + 2x

• 7x² + 35x

• 3x² + 6xy + y

Multiple Choice

2a² – 8a²+ 5a³– 11a²

• - 5a² + 5a³
• -17a² + 5a³
• 5a^{2 -} 5a³

Multiple Choice

Evaluate 2r + 1      if   r = 3

• 6
• 5
• 7
• 8

Multiple Choice

Evaluate the expression:

6a - 3d
when a = 1, d = 2

• 3
• 12
• 1
• 0

Multiple Choice

Evaluate the expression:

b² + 4
when b = 3

• 10
• 12
• 13
• 11

Multiple Choice

SOLVE for k:

$$k+19=10$$   

• k = 190

• k = -9

• k = 29

• k = 10/19

Multiple Choice

SOLVE for j:

$$-14\ =\ j\ -\ 20$$  

• j = -7/10

• j = -34

• j = 280

• j = 6

Multiple Choice

SOLVE for m:

$$110\ =\ -11m$$  

• m = 99

• m = -10

• m = 121

• m = -1210

Multiple Choice

Solve: $$\frac{n}{2\ }=\ -6$$  

• n = -12

• n = -4

• n = -3

• n = -8

Multiple Choice

What is the first step to solve this equation?

3k + 5 = 20

• Multiply both sides by 3

• Subtract both sides by 3

• Divide both sides by 3

• Subtract both sides by 5

Multiple Choice

What is the next step in the equation?

3x = 15

• Divide both sides by 3

• Add 3 and 15

• Subtract 3 and 15

• Multiply 3 and 15

Multiple Choice

SOLVE for x:

2x - 8 = 6

• 3

• 8

• 7

Multiple Choice

Distribute first and then Solve:

7(2x - 4) = 42

• x= 5

• x= 8

• x= 2

• x= 9

Multiple Choice

Solve the equation shown

• 51

• 52

• 27

• 21

Translating Algebraic Expressions

Objective: To translate English phrases into algebraic expressions

​Words that mean ADDITION

​Sum

​Add

​Plus

​All together

​​Increased by

​More than

​Total

​ADDITION special case

'more than' - you have to reverse the order

​

​Example: 9 more than 3 ...... = 3 + 9

​

​Example: 1 more than a number..... = n + 1

​Words that mean SUBTRACTION

Minus

​Difference

​Take away

​Less than

​Decreased by

​​Subtract

​Less

​Fewer than

​Subtracted from

​SUBTRACTION special case

'less than' - you have to reverse the order

​

​Example: 9 less than 3...... = 3 - 9

​

​Example: 1 less than a number...... = n - 1

​Words that mean MULTIPLICATION

Product

​Times

​Of

​​Twice

​Double

​Multiplied by

​Words that mean DIVISION

Divided by

​Quotient of

​Half or 1/2

​​Fractions

​Statements like:

​"a fourth of" 1/4

​"a seventh of" 1/7

​QUANTITY OF use (parenthesis)

Writing Algebraic Expressions

​You can translate word phrases into variable expressions.

– Examples:

1. Three more than a number = x + 3

2. The quotient of a number and 8 = y/8

3. Six times a number = 6 • n or 6n

4. 15 less than a number = z – 15

5. The quotient of 30 and a number plus 10 = 30/x + 10.

CCSS.MATH.CONTENT.HSA.SSE.A.1:

Interpret expressions that represent a quantity in terms of its context.

Multiple Choice

In a math problem, "combine 2 and 3" is a clue for ....

• Addition

• Subtraction

• Multiplication

• Division

Multiple Choice

Write an expression to represent "the product of 3 and x"

• 3 + x

• 3x

• 3 - x

• 3 ÷ x

Multiple Choice

In a math problem, "tripled" is a clue for ....

• Addition

• Subtraction

• Multiplication

• Division

Multiple Choice

In a math problem, "decreased by 8" is a clue for ....

• Addition

• Subtraction

• Multiplication

• Division

Multiple Choice

Write an expression to represent "2 more than a number"

• n + 2

• 2 > n

• n > 2

• 2n

Multiple Choice

Eight times a number increased by 9 is the same as 15 more than 7 times the number.  Find the number.

• 6
• -7
• 1
• 2

Multiple Choice

45 more than half of F

• 2F+45
• 45-½F
• 45-2F
• ½F+45

Multiple Choice

Translate: 3 divided by the quantity of x minus 5

• $$\frac{3}{x}-5$$  

• $$3\left(x-5\right)$$  

• $$\frac{\left(x-5\right)}{3}$$  

• $$\frac{3}{\left(x-5\right)}$$  

Multiple Choice

Translate this phrase into an algebraic expression.
8 less than the product of 4 and a number
Use the variable m to represent the unknown number.

• 8 - 4m
• 8m - 4
• 8m + 4
• 4m - 8

Multiple Choice

Ten decreased by four times a number.  

• 10 - 4x
• 4x - 10 
• 10 - x
• 10/4x

Here are the steps in solving a multi-step equation: DCI method

• Distributive Property

• Combine like terms (on the same side of the equation)

• Use Inverse operations to put variables and constants on opposite sides of the equation.

• Isolate the variable

Multiple Choice

Let's Practice using the Distributive Property.

6(x-3)

• x-18

• 6x+18

• 6x-18

• 6x-9

Multiple Choice

Distributive property:

-3 (n - 8) = ?

• 3n-8

• -3n-24

• -3n+24

Remember DCI!

D: Distribute the -4 first

C: Combine like terms on left

I: Inverse Operations - subtract 4 from both sides and then divide by them both by -4

-4y = 12
y = -3

Here is an example of how to solve a Multi-Step equation.

See if you can follow the steps that are written on the side.

EXAMPLES

Multiple Choice

What is the first thing you should do to simplify an equation?

• Isolate the variable

• Distributive Property

• Combine like terms

Multiple Choice

$$-83\ =\ 5\left(1\ +\ 4x\right)\ +\ 2x$$  

• -4

• 4

• 8

• -8

Slope from a graph

Positive: going up the hill, incline

Negative: going down the hill, decline

Undefined: vertical line (up and down)

Zero: horizontal line (side to side)

Multiple Choice

What type of slope does this graph have?

• Positive

• Negative

• Zero

• Undefined

Multiple Choice

What type of slope is shown on the graph?

• Positive

• Negative

• Zero

• Undefined

Multiple Choice

What type of slope does this graph show?

• Positive

• Negative

• Zero

• Undefined

Multiple Choice

Find the slope

• 4/5

• 5/4

• -5/4

• -4/5

Multiple Select

Which graph(s) have a slope of ZERO?

Slope on a Graph

Multiple Choice

What is the slope?

• 4/5

• 5/4

• -4/5

• -5/4

Multiple Choice

What is the slope?

• 5/7

• 7/5

• -7/5

• -5/7

Multiple Choice

Locate at least 2 "perfect points" on the graph.

What is the slope between the points?

• $$-\frac{1}{2}$$

• $$3$$

• $$4$$

• $$-2$$

Slope Formula and Using the Slope Formula
​

​EXAMPLE: Build your frame and plug numbers in!!!

Multiple Choice

• 1/-2

• 5/14

• 1/2

• -1/2

Multiple Choice

• 1/6

• 1

• -1/6

• -1

Multiple Choice

Find the slope of the line that goes through the points

(−11,−5) and (1,−12)

• $$-\frac{5}{8}$$

• $$\frac{16}{11}$$

• $$\frac{1}{6}$$

• $$-\frac{7}{12}$$

Multiple Choice

Find the slope given the points (1,4) and (5,9). 

• 5/4

• 4/5

• -5/4

• 2/3

A Literal equation is easy if you know your basic operations and how to apply them to equations.

By now you know the basics,

but let us review.

A Literal equation contains at least two different variables.

>Use the SAME strategies as for solving any equation!
>Use OPPOSITE operations to solve.
>Isolate the variable indicated!
Solve for b means make it say "b="

~~YOUR SOLUTION will still contain ALL the variables you started with!~~

Multiple Choice

Which operation will we use to solve: C = 2πr, for r?

• Add

• Subtract

• Multiply

• Divide

Multiple Choice

Solve:
C = 2πr, for r

• $$\frac{C}{2\pi}=r$$  

• C + 2π = r
• C - 2π = r
• 2πC = r

Multiple Choice

Solve a = b + c   , for  c

• c = a - b
• c = a + b
• c = ab
• c = a / b

Multiple Choice

$$g\ =\ 6x\ \ \ solve\ for\ x$$  

• $$x\ =\ \frac{g}{6\ }$$  

• $$x\ =\ \frac{6}{g}$$  

• $$x\ =\ g+6$$  

• $$x\ =\ g-6$$  

Multiple Choice

S = 3F - 24  Solve for F

• F = (S + 24)/3
• F = S/3 + 24
• F = 3S + 24
• F = 3(S + 24)

In order to solve proportions, we will use criss-cross multiplication

​

​Solving Proportions

Solving Proportions

• Criss-Cross multiply

• Solve for x.

​Example 1

Multiple Choice

Solve:

• 1

• 4

• 10

• 5

Multiple Choice

Solve:

(Hint: don't forget to distribute the 5 to both parts of "m-7")

• 3

• 4

• -7

• 15

​WORD Problems: 2 numbers Example

Multiple Choice

The highest score on an Algebra test was 40 more than the lowest. What expressions can we use for these 2 scores

• x AND 40x

• x AND y

• x AND x + 40

Multiple Choice

The larger of 2 numbers is 4 more than the smaller number. Write expressions for both numbers

• x and x + 5

• x and 4x

• x and x + 4

Fill in the Blanks

The large number is 4 more than the smaller number. If the sum is 56, what is the smaller number?

x + x + 4 = 56

Solve for what the smaller number is.

Fill in the Blanks

If the two numbers were

X and X + 4

and the smaller number is 26,

what is the larger number?

Multiple Select

One number is 4 times as large as another. Their sum is 45. What are the numbers? Select the two that apply.

• 6

• 9

• 12

• 36

• 27

Multiple Choice

Which of the following setups would be used to find four consecutive integers?

• n

  n+2

  n+4

  n+6

• n

  2n

  4n

  6n

• n+1

  n+2

  n+3

  n+4

• n

  n+1

  n+2

  n+3

​WORD Problems: Perimeter Example

Perimeter = Add all the sides
Perimeter = 2 (length) + 2 (width)

EX:
P = 2(y+1) + 2(y-3)
P = 2y + 2 + 2y - 6
P= 4y - 4

Multiple Select

Which 2 of these represent the perimeter of the rectangle:

• 2(x+7)

• 4x + 14

• 2x + 14

• 2(x) + 2(x+7)

Multiple Choice

If a rectange has length that is 2 more than the width, write an equation for the perimeter

• perimeter = 2(x + 2) + 2(x + 2)

• perimeter = 2(2x) * 2(x)

• perimeter = 2(x + 2) + 2(x)

Multiple Choice

The length of a rectangle is 3 inches more than its width. If the perimeter is 42 inches, find the dimensions of the rectangle.

• 9 in by 12 in

• 3 in by 14 in

• 10 in by 13in

• 8 in by 13 in

Fill in the Blanks

The length of a garden is 10 cm longer than three times the width. The perimeter of the garden is 260 cm. Find the dimensions of the garden.

​WORD Problems: CONSECUTIVE Integers Example

Multiple Choice

The sum of three consecutive integers is 48. What are they?

• 16, 17, 18

• 15, 16, 17

• 17, 18, 19

• 24, 25, 26

Multiple Choice

The sum of three consecutive integers is 147. Which equation can be used to find the first integer? 

• 3x = 147
• x + 3 = 147 
• x + x + 1 + x + 2 = 147 
• x ⋅ x ⋅ x = 147 

Fill in the Blanks

Find two consecutive numbers whose sum is 115.

​WORD Problems: CONSECUTIVE ODD/EVEN Integers Example

Multiple Choice

What two consecutive even integers have a sum of 90?

• 30 and 60

• 43 and 47

• 44 and 46

• 10 and 80

Fill in the Blanks

Find two consecutive odd numbers that add to give you 44.