Math Midterm 2

• ​Can be expressed as a fraction

• Represent an exact amount

• Include terminating and repeating decimals

• Include roots of perfect squares and perfect cubes

​Characteristics of Rational numbers:

​Characteristics of Irrational numbers:

• ​Cannot be expressed as a fraction

• Represents an approximation

• Decimal form is always non-repeating and non-terminating

• Includes roots of non-perfect square and cube roots

Multiple Choice

Classify the following number as rational or irrational:

0.141414141414...

• Rational

• Irrational

Multiple Choice

Classify the following number as rational or irrational:

$$\sqrt[]{2}$$

• Rational

• Irrational

Multiple Choice

Which number is a rational number? (Select all that apply)

• $$\frac{1}{4}$$

• $$\pi$$

• $$\sqrt[]{3}$$

Multiple Choice

What type of number is a non-repeating, non-terminating decimal?

• Irrational

• Prime

• Rational

• Imaginary

Multiple Choice

$$\sqrt[]{196}=$$

• 14

• 14²

• 15

• 15²

Multiple Choice

The area of the square pool on Mr. Carr's vacation was 256 ft². How long was one side of the pool?

• 17 feet

• 18 feet

• 16 feet

• 15 feet

​PERFECT CUBE

​A number that can be written as the cube of an integer.

Ex: 64 = 4 x 4 x 4

Multiple Choice

What does it mean to cube a number?

• Add the number to itself three times

• Divide the number by three

• Multiply the number by itself three times

• Multiply the number by itself twice

Multiple Choice

$$\sqrt[3]{125}=$$

• 5

• -5

• 25

• -25

Multiple Choice

A cube with side length s has a volume of 64 cubic units. What is the length of the side of the cube?

• 32 units

• 16 units

• 8 units

• 4 units

Multiple Choice

Solve: $$x^2=36$$

• 6

• 18

• $$\pm6$$

• $$\pm18$$

Multiple Choice

Solve: $$r^3=216$$

• 6

• -6

• 72

• -72

​Rule # 1: Multiplying with exponents

Multiple Choice

Solve: $$x^3\cdot x^6=$$

• $$x^9$$

• $$x^{18}$$

• $$x^3$$

• $$x^{36}$$

Multiple Choice

Solve: $$c^{-2}\cdot c^7=$$

• $$c^4$$

• $$c^9$$

• $$c^{-5}$$

• $$c^5$$

Multiple Choice

According to exponent rules, when we multiply powers we _______ the exponents.

• Add

• Subtract

• Multiply

• Divide

​Rule #2: Dividing with exponents

Multiple Choice

$$\frac{y^{10}}{y^{-5}}=$$

• $$y^{15}$$

• $$y^5$$

• $$y^2$$

Multiple Choice

According to exponent rules, when we divide powers we _______ the exponents.

• Add

• Subtract

• Multiply

• Divide

​Rule #3: Raising a power to a power

Multiple Choice

$$\left(x^{14}\right)^3=$$

• $$x^{17}$$

• $$x^{42}$$

• $$x^{11}$$

Multiple Choice

According to exponent rules, when we raise a power to a power we _______ the exponents.

• Add

• Subtract

• Multiply

• Divide

Multiple Choice

$$\left(2x^2y^4\right)^3=$$

• $$2x^6y^{12}$$

• $$2x^5y^7$$

• $$8x^6y^{12}$$

• $$8x^5y^7$$

​Rule #4: Power of Zero

Multiple Choice

$$9^0=$$

• 1

• -1

• 9

• -9

​Rule #5: Negative exponents

Multiple Choice

Simplify: $$x^{-7}$$

• -7

• $$\frac{1}{x^7}$$

• $$\frac{x}{7}$$

Multiple Choice

$$\frac{8^2}{8^7}=$$

• $$8^{-5}$$

• $$8^9$$

• $$\frac{1}{8^5}$$

Match

Match the following:

• Add the exponents

• Subtract the exponents

• Multiply the exponents

• $$x^3\cdot x^6$$

• $$\frac{z^8}{z^4}$$

• $$\left(y^2\right)^4$$

​Example 1:

• ​Convert: 9,270,000​ ​

• Move decimal behind the "9"

• Moved 6 places

• Setup as 9.27⋅​10⁶

** Remember
If the number is bigger than 1 - it is a positive exponent
If the number is smaller than 1 - it is a negative exponent

Multiple Choice

Convert to scientific notation: $$27,000$$

• $$2.7\times10^4$$

• $$2.7\times10^3$$

• $$0.27\times10^5$$

• $$2.7\times10^{-4}$$

Multiple Choice

Convert to scientific notation: $$0.000368$$

• $$3.68\times10^3$$

• $$3.68\times10^{-3}$$

• $$3.68\times10^{-6}$$

• $$3.68\times10^{-4}$$

Multiple Choice

Solve:

$$\left(7\times10^{12}\right)\left(2\times10^{10}\right)$$

• $$1.4\times10^{22}$$

• $$1.4\times10^{23}$$

• $$1.4\times10^{21}$$

Multiple Choice

Solve:

$$\left(5\times10^6\right)\left(5\times10^7\right)$$

• $$2.5\times10^{12}$$

• $$2.5\times10^{14}$$

• $$25\times10^{12}$$

• $$25\times10^{13}$$

Multiple Choice

Solve:

$$\frac{1.05\times10^{12}}{5\times10^4}$$

• $$0.21\times10^3$$

• $$2.1\times10^7$$

• $$0.21\times10^8$$

• $$2.1\times10^9$$

Multiple Choice

Solve:

$$\frac{1.4\ \times\ 10^9}{7\ \times\ 10^2}$$

• $$7\times\ 10^7$$

• $$0.2\ \times\ 10^7$$

• $$2\times10^8$$

• $$2\times10^6$$

Multiple Choice

How many total people were surveyed about what ice cream flavor they would pick?

• 107

• 92

• 70

• 269

Multiple Choice

What number should go in the blue box?

• 21

• 135

• 19

• 22

Multiple Choice

How many total have no cell phone?

• 13

• 9

• 22

• 100

Multiple Choice

How many females were surveyed?

• 10

• 16

• 26

• 14

Multiple Choice

How many chemical engineers chose Science as their favorite subject?

• 80

• 91

• 171

• 262

​Reminders

​***Association and Correlation are the same thing!!!

Multiple Choice

What type of correlation does this scatter plot show?

• Postive

• Negative

• No Correlation

Multiple Choice

Which sentence describes the relationship shown on this scatter plot?

• As the temperature decreases, the visitors increase.

• As the visitors increase, the temperature decreases.

• As the temperature increases, the number of visitors increases.

• No Association

Multiple Choice

What is the correlation?

• Negative

• Positive

• No Association

Multiple Choice

Determine the association of the situation below:

The number of siblings you have and your weight. 

• Positive

• Negative

• No Association

​Outlier

• A data point that is too high or low for the data​
  
  Notice how the point at (30, 6000) is an outlier and does not fit with the data

Multiple Choice

A point far away from the other data points is considered a(n) ____?

• Cluster

• Outlier

• Scatter Plot

Multiple Choice

What data points are outliers in the scatter plot? (Select all that apply.)

• A

• B

• C

• D

Multiple Choice

The scatter plot shows the relationship between the number of chapters and the total number of pages for several books.  Use the trend line to predict how many chapters would be in a book with 140 pages. 

• 12 Chapters

• 19 Chapters

• 14 Chapters

• 21 Chapters

​Linear Association vs Non-Linear

• ​Linear - The data shows a line or forms a line

• Non-Linear - the data does not form a line

Multiple Choice

What type of association does this scatter plot represent?

• Positive

• Negative

• No Association

• Nonlinear

Multiple Choice

In the scatter plot, does the image shows a "Line of Best Fit"?

• Yes

• No

​These are all functions

Every input has EXACTLY one output

Multiple Choice

What is the definition of function?

• Has inputs and outputs

• Every input has only ONE output

• x-values and y-values

Multiple Choice

Is the relation a function? Why.

• Yes, because the x-value 11 has two y-values paired with it.

• Yes, because each x-value has only one y-value paired with it.

• No, because the x-value 11 has two y-values paired with it.

• No, because each x-value has only one y-value paired with it.

Multiple Choice

Is this set of ordered pairs a function or not a function?

• Function

• Not a Function

​The Vertical Line Test

• ​To tell if a graph is a function, draw a vertical line anywhere on the graph.

• If any vertical line touches the graph in more than one location it is NOT a function

Multiple Choice

Is this graph a function or not a function?

• Function

• Not a Function

Multiple Choice

Is this graph linear?

• Yes

• No

​Linear Functions...

• ​have a constant rate of change

Multiple Choice

Is this function linear or nonlinear?

• Linear

• Nonlinear

Multiple Choice

Compare the initial values of each function.

• The initial value of item I is greater than the initial value of item II.

• The initial value of item I is equal to the initial value of item II.

• The initial value of item II is greater than the initial value of item I.

Multiple Choice

Which company shows a greater rate of change?

• Water's Edge Rafts

• Ryan's Rafts

Multiple Choice

Solve:

$$8x-10=-34$$

• 4

• -3

• 3

• -24

Multiple Choice

Solve:

$$3\left(x-2\right)=18$$

• 6.7

• 8

• 4

• -4

Multiple Choice

What would be the first step in solving this equation?

$$4x+6=30$$

• Add 6 to both sides.

• Divide by 4 on both sides.

• Subtract 6 from both sides

• Multiply by 4 on both sides.

Multiple Choice

Find the slope of the line:

• $$\frac{3}{4}$$

• $$-\frac{3}{4}$$

• $$\frac{4}{3}$$

• $$-\frac{4}{3}$$

Match

Match the graph with its slope.

Negative

Positive

Zero

Undefined

• Negative

• Positive

• Zero

• Undefined

Multiple Choice

John spent $36 to buy 4 basketballs. What was the price per basketball?

• $9/Basketball

• $8/Basketball

• $144/Basketball

• $12/Basketball

Multiple Choice

Write the equation of the line in slope intercept form.

• $$y=-1x+3$$

• $$y=\frac{1}{4}x+3$$

• $$y=4x+3$$

• $$y=-4x+3$$

Multiple Choice

In order to join an online learning community, there is a $20 startup fee and a $5 monthly fee.

Write an equation in slope-intercept form that models this situation.

• $$y=20x+5$$

• $$y=-5x+20$$

• $$y=5x+20$$

• $$y=5x-20$$

Multiple Choice

Graph the equation of the line:

$$y=-\frac{2}{3}x+4$$