Applied Algebra Review Semester #1

Applied Algebra Review Semester #1

Skills and Pratice to Pass the Final

Skill #1: Order of Operations

PEMDAS

Fill in the Blank

 $3^2-2\left(10-7\right)\div2+5$  

Multiple Choice

40 - 2⁴ + 8

• 40
• 32
• 24
• 42

Multiple Choice

Solve the following:
(2 + 7 - 1) ÷ 2²

• 16
• 2
• 72.25
• 8.75

Skill #2: Simplifying Expressions

Distributing and Combining Like Terms

Multiple Choice

Find the mistake in this problem: 3(x + 2) = 3x + 2.

• Should have added the 3 and the x.

• There is no mistake in this problem.

• Should have multiplied the 3 with the 2.

• Should have added the 3 and the 2.

Multiple Choice

6x + 3(-2 - x) - 4

• 9x - 10

• 3x + 2

• 3x - 10

• 9x + 10

Multiple Choice

3(2 + x) + 6x - 4

• 6x + 5

• 9x + 1

• 9x + 2

• 3x + 8

Multiple Choice

6(7 + x) + 5x

• 6x + 13

• x + 42

• 6x + 42

• 11x + 42

Skill #3 Functions and Their Notation

Multiple Choice

What is the definition of function?

• Has inputs and outputs

• Every input has exactly ONE output

• Inputs have different outputs every time

• x-values and y-values

• All continuous graphs with a range and domain.

Multiple Choice

All of the x values or inputs are called what?

• Domain

• Range

• Relation

• Function

• Dependent Variable

Multiple Choice

All of the y values or outputs are called what?

• Domain

• Range

• Relation

• Function

• Independent Variable

Multiple Choice

Give the domain and range. Tell if it is a function.

• D: {-4, -2, 0, 2}

  R: {-2, -2, 1, 1}

  Function

• D: {-4, -2, 0, 2}

  R: {-2, 1}

  Function

• D: {-4, -2, 0, 2}

  R: {-2, -2, 1, 1}

  Not a Function

• D: {-4, -2, 0, 2}

  R: {-2, 1}

  Not a Function

• Not enough information to determine range and domain.

Multiple Choice

g(x) = 3x + 1
g(10) = ______

• 14
• 31
• 15
• -31

Multiple Choice

What is x if
f(x) = -2?

• 4
• 0
• 3
• 8

Multiple Select

Which of the following could be the graph of a function of x? Check ALL that apply!

Multiple Select

Which of the following tables represent could be a function of x? Check ALL that apply.

• None of the tables have values that could represent a function

Multiple Select

Which of these mappings sets represents a function, choose all that apply?

Skill #4: Solving Equations

Multiple Choice

Solve for x:
4 - 2(x - 3) = 24

• - 7
• 7
• 14
• - 14

Multiple Choice

Solve the equation.

• x = 21

• x = 27

• x = 36

• x = 2.25

Multiple Choice

10(h+1) - 4 = 76

• h=10

• h=4

• h=7

• h=76

Multiple Choice

 $21=3+4n+5n$  

• 9

•  $-7$  

• 6

• 2

Skill #5: Solving and Graphing Inequalities

​

Multiple Choice

-2 (x+2) < 14

• x < - 5
• x > -5
• x < -9
• x > -9

Multiple Choice

Which graph matches the inequality
-2 ≥ n?

• A
• B
• C
• D

Multiple Choice

Which graph matches the inequality
2 > p?

• A
• B
• C
• D

Multiple Choice

-4x + 14 ≤ 54

• x ≥ - 10
• x ≤ -10
• x ≥ 10
• x ≤ 10

Skill #6: Finding Slope

​

Multiple Choice

What is the slope in the picture?

• Positive
• Negative
• Zero
• Undefined

Multiple Choice

What type of slope?

• negative
• steep
• undefined
• zero slope

Multiple Choice

Find the slope

• -5/3
• -3/5
• 5/3
• 3/5

Multiple Choice

Find the slope given the points (3,2) and (4,7).

• 4

• 5

• -5

• 1/5

Multiple Choice

Find the slope of the line.

• Undefined
• 0
• 1
• -1

Skill #7: Graphing in Slope Intercept Form

​

Multiple Choice

What is the equation for this graph?

• y= 4/5 x + 4

• y= 5/4 x + 4

• y= 4x -5

• y= 5x + 4

Multiple Choice

What is the equation of this line?

• y = 2x +2
• y = 2x -2
• y = -x + 2
• Cannot be Determined

Multiple Choice

Write the equation for the line.

• y= -1x+3
• y= 4x+3
• y=1/4x+3
• y= -4x+3

Skill #8: Graphing Linear Inequalities

​

Multiple Choice

Which of the following equations match the given graph?

• y ≤ -3/4 x + 3
• y ≥ -3/4 x + 3
• y < -3/4 x + 3
• y > -3/4 x + 3

Multiple Choice

Select the correct graph for each inequality.

• A
• B
• C
• D

Multiple Select

According to the graph, which point is a solution? Choose all that apply.

• (0, 0)

• (4, 2)

• (-1, -5)

• (-3, 0)

Multiple Choice

Which of the following equations match the given graph?

• x ≥ -1
• x ≤ -1
• x > -1
• x < -1

Multiple Choice

Which graph best represents the following inequality?

Skill #9: Solving Systems of Equations by Graphing

Including Types of Solutions

Multiple Choice

What is the solution?

• No solution
• (0, 2)
• (0, -4)
• (3, -3)

Multiple Choice

When you graph the exact same equation twice,

• you will have no solution. 
• you will have one solution.
• you will have infinite solutions. 
• you will graph a giraffe. 

Multiple Choice

Where do these two lines intersect?

• No solution
• (-2, 3)
• (3, -2)
• (2, 3)

Multiple Choice

Solve by graphing.
y = 2x + 1
y = 4x - 1

• (1,3)
• (-1,-3)
• (-1,3)
• (3,1)

Skill #10: Solving Systems of Equations Algebraically

Substitution

Skill #10: Solving Systems of Equations Algebraically

Elimination

Multiple Choice

Determine if (4, 1) is a solution for the system of equations.
y = -x + 5
y = 2x - 7

• yes
• no

Multiple Choice

Solve the system of equations.

y = 4x+1

3x + 2y = 13

• (1, 5)

• (5, 1)

• (0.25, 2)

• ∅

Multiple Choice

Solve for x and y
3x + 2y = 16
7x + y = 19

• (-2,5)
• (-2,-5)
• (2,-5)
• (2,5)

Multiple Choice

Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes.  Which system of equations represents the situation?

• 3x + 2y = 315
  2x + 4y = 450
• 3x + 2y = 450
  2x + 4y = 315
• 2x + 2y = 315
  3x + 4y = 450

Multiple Choice

Some students want to order shirts with their school logo. One company charges $9.65 per shirt plus a setup fee of $43. Another company charges $8.40 per shirt plus a $58 fee. Which equation represents the number of shirts when both companies charge the same amount? 

• y = 9.65 + x
  y = 8.40 + x
• y = 9.65x + 43
  y = 8.40x + 58
• y =9.65x
  y = 8.40x
• y = 9.65x - 43
  y = 8.40x - 58

Skill #11: Systems of Inequalities

Multiple Choice

Determine the ordered pair that IS a solution.

• (2, 2)
• (2, 4)
• (3, 2)
• (-3, 2)

Multiple Choice

Given the system, determine a solution.

• No solution

• Infinite solutions

• (-5, 5)

• (5, -5)

Multiple Choice

Solve the system of inequalities by graphing.

Multiple Choice

Solve the system of inequalities by graphing.

Multiple Choice

Which system of inequalities is shown?

• y ≥ -x - 1
  y < x + 4
• y < -x - 1
   y ≥ x + 4
• y > -x - 1
  y ≥ x + 4
• y > -x - 1
  y ≥ x + 3

Skill 12: Probability Basics

Multiple Choice

The letters that form the word ALGEBRA are placed in a bowl. What is the probability of choosing a letter other than “A”?

• 2/7

• 5/49

• 5/7

• 10/49

Multiple Choice

If an event has an experimental  probability of .02, which of the following is true? 

• The event is always going to happen
• The event is more likely to happen than it is to not happen
• The event is unlikely to happen but could
• The event will never happen

Multiple Choice

If an event has an experimental  probability of 1, which of the following is true? 

• The event is always going to happen
• The event is more likely to happen than it is to not happen
• The event is unlikely to happen but could
• The event will never happen

Multiple Choice

Andrew picks one marble at a time from a box and replaces it. He repeats this process 25 times and records the results in the table. Based on the table, which color marble has an experimental probability of 1/5?

• Yellow

• Red

• Blue

• Green

Multiple Choice

If a man is chosen at random, what is the probability that he favors sports cars?

• 35%

• 16.25%

• 65%

• 25%

Skill #13: Arithmetic Sequences

Explicit Formula

Skill #13: Arithmetic Sequences

Recursive Formulas

Multiple Choice

Find a₂₀ in the arithmetic sequence: 5, 12, 19, 26...

• 145
• 144
• 142
• 138

Multiple Choice

Find the next three terms in the arithmetic sequence: 25, 34, 43, 52, ...

• 63, 72, 81

• 79, 88, 97

• 70, 79, 88

• 61, 70, 79

Multiple Choice

Given the first five terms, write the recursive formula.
15, 12, 9, 6, 3 ....

• u₁ = 15
  u_n = u_n-1 + 3
• u₀ = 15
  u_n = u_n-1 + 3
• u₁ = 15
  u_n = u_n-1 - 3 
• u₀ = 15
  u_n = u_n-1 - 3

Multiple Choice

Find the first four terms of the sequence.

a_n= a_(n-1) - 18 where a₁=10

• 18, 8, -2, -12

• 28, 46, 64, 82

• -8, -26, -44, -60

• 10, -8, -26, -44

Multiple Choice

Write the explicit formula for the sequence.

9, 5, 1, -3, ...

• $a_n=9+5\left(n-1\right)$

• $a_n=9-4\left(n-1\right)$

• $a_n=4+9\left(n-1\right)$

• $a_n=9\cdot4^{\left(n-1\right)}$