Unit 5 Review

Unit 5 Review

Rational

Values that can be written as a fraction.

Look for: fractions, whole numbers, terminating decimals, repeating decimals, and perfect squares.

Irrational

Values that can NOT be written as a fraction.

Look for: Never-ending non-repeating decimals, pi, and imperfect squares.

Poll

Solving Quadratic Equations, How you feeling right now?

Multiple Choice

Categorize the following:  $$\frac{3}{4}$$   

• Rational

• Irrational

Multiple Choice

Categorize the following:  $$-32$$  

• Rational

• Irrational

Multiple Choice

Categorize the following:  $$5.984732...$$  

• Rational

• Irrational

Rational Numbers

Irrational Numbers

Multiple Choice

$$\sqrt{4}+\sqrt{4}=$$  

Solve:

• $$4;\ rational$$  

• $$\sqrt{8};\ irrational$$  

• $$\sqrt{16};\ rational$$  

• $$2\sqrt{4};\ irrational$$  

Multiple Choice

$$5\sqrt{11}-3\sqrt{11}$$  

Solve:

• $$2\sqrt{11};\ irrational$$  

• $$2\sqrt{22};\ rational$$  

• $$2;\ rational$$  

• $$22;\ rational$$  

Multiple Choice

$$2\sqrt{9}+3\sqrt{4}-\sqrt{5}$$  

Solve:

• $$12-\sqrt{5};\ irrational$$  

• $$4\sqrt{8};\ irrational$$  

• $$2\sqrt{9}+3\sqrt{4}-\sqrt{5};\ irrational$$  

• $$30-\sqrt{5};\ rational$$  

Multiplying rational/irrational number

Multiple Choice

Multiply and simplify if possible.

• ⅝
• ¼
• 2 ⅓
• ⅘

Multiple Choice

Solve:  $$\sqrt{2}\cdot\sqrt{5}=$$  

• $$\sqrt{10};\ irrational$$  

• $$\sqrt{7};\ irrational$$  

• $$\sqrt{3};\ irrational$$  

• $$5;\ rational$$  

Multiple Choice

$$2\sqrt{5}\cdot\sqrt{5}=$$  

Solve:

• 50; rational

• $$3\sqrt{5};\ irrational$$  

• $$2\sqrt{10};\ irrational$$  

• $$10;\ rational$$  

Multiple Choice

HOW is a coordinate pair ordered?

• (big number, small number)

• (small number, big number)

• (y, x)

• (x, y)

Types of Solutions

• One Solution

• No Solution

• Infinite Solutions

Multiple Choice

What is the solution?

• (6, 3)

• (3, 6)

• (-6, 3)

• No solution

Multiple Choice

How many solutions will this system have?

• No solution

• One Solution

• I Don't Know

• Infinitely Many Solutions

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

If a system of linear equations has one solution, what does this mean about the two lines?

• Parallel lines

• the same line

• Intersecting lines

Multiple Choice

HOW is a coordinate pair ordered?

• (big number, small number)

• (small number, big number)

• (y, x)

• (x, y)

Multiple Choice

What is the solution?

• One Solution

• No solution

• Infinitely Many Solutions

• (0, -1.5)

Multiple Choice

What is the solution?

• (1, -1)
• (-1, 1)
• (0, -2)
• (0, 1)

Multiple Choice

How many solutions will this system have?

• one solution

• no solution

• infinitely many solutions

Fill in the Blanks

Multiple Choice

HOW is a coordinate pair ordered?

• (big number, small number)

• (small number, big number)

• (y, x)

• (x, y)

Multiple Choice

The solution (x, y) to a system of equations is the point where they...?

• Run off the graph

• Don't touch

• Intersect

• Exist

​

Substitution

​

• To verify the solution to a system of linear equations, substitute the coordinate point for x and y to determine if the coordinate makes both equations true.

​

Multiple Choice

HOW is a coordinate pair ordered?

• (big number, small number)

• (small number, big number)

• (y, x)

• (x, y)

Multiple Choice

Use Substitution, to solve the system of equations:  $$y=2x+1$$  

$$y=-x+16$$  

• (3,-7)

• No solutions

• Infinitely many solutions

• (5,11)

Multiple Choice

Use Substitution, to solve the system of equations

$$y=x+6$$   $$y=3x$$  

• (3,9)

• (-3,9)

• (3,-9)

• (-3,-9)

Multiple Choice

Use Substitution, to solve the system of equations y = 2x + 1 y = 4x - 1

• (1,3)
• (-1,-3)
• (-1,3)
• (3,1)

​

Substitution

​

• To verify the solution to a system of linear equations, substitute the coordinate point for x and y to determine if the coordinate makes both equations true.

​

Multiple Choice

• (4, -3)

• (-1, -3)

• (-4, -3)

• (-4, 3)

Multiple Choice

• (-1, -6)

• (-6, 1)

• (-3, -6)

• (1, -6)

Multiple Choice

y = -6x + 5
-2x + y = 5

• (-3, -6)
• (-6, 3)
• (0, 5)
• (-3, 5)

Multiple Choice

Use Substitution, to solve the system of equations

y = -2x + 5 y = 2x - 11

• No Solution
• (0, 0)
• (3, -1)
• (4, -3)

​

Substitution

​

• To verify the solution to a system of linear equations, substitute the coordinate point for x and y to determine if the coordinate makes both equations true.

​

Multiple Choice

Solve using the substitution method.

x + y = 12

x = 2y

• (8, 4)

• (4, 8)

• (-8, 4)

• (-4, 8)

Multiple Choice

Using Substitution, solve for the following system of linear equations:  $$y=x+3$$  

$$y=-2x-3$$  

• No solution

• (-3,-3)

• Infinitely many solutions

• (-2,1)

One Solution

• The two lines intersect (touch) at ONE POINT

• Your answer should be an ordered pair (x, y)

No Solution

• The two lines NEVER intersect (touch)

Infinitely Many Solution

• The equations are on SAME LINE

• Your answer should be an ordered pair (x, y)

Multiple Choice

Does the following system have One Solution, No Solution, or Infinite Solutions?

y = 4x + 8

y = -5x + 3

(Hint: Look at the slopes and y-intercepts. You don't have to graph)

• One solution

• No solution

• Infinite solution

Multiple Choice

Does the following system have One Solution, No Solution, or Infinite Solutions?

y = 4x + 8

y = 4x + 8

(Hint: Look at the slopes and y-intercepts. You don't have to graph)

• One solution

• No solution

• Infinite solution

Multiple Choice

Does the following system have One Solution, No Solution, or Infinite Solutions?

y = 4x + 8

y = 4x - 3

(Hint: Look at the slopes and y-intercepts. You don't have to graph)

• One solution

• No solution

• Infinite solution

Multiple Choice

Does the following system have One Solution, No Solution, or Infinite Solutions?

y = 4x + 8

y = 4x - 8

(Hint: Look at the slopes and y-intercepts. You don't have to graph)

• One solution

• No solution

• Infinite solution

Multiple Choice

Does the following system have One Solution, No Solution, or Infinite Solutions?

y = 3x + 9

y = 2x - 10

(Hint: Look at the slopes and y-intercepts. You don't have to graph)

• One solution

• No solution

• Infinite solution

Multiple Choice

Does the following system have One Solution, No Solution, or Infinite Solutions?

y = 3x + 9

y = 3x + 9

(Hint: Look at the slopes and y-intercepts. You don't have to graph)

• One solution

• No solution

• Infinite solution

Multiple Choice

Does the following system have One Solution, No Solution, or Infinite Solutions?

y = 4x + 9

y = 4x + 9

(Hint: Look at the slopes and y-intercepts. You don't have to graph)

• One solution

• No solution

• Infinite solution