End of Year 8th Grade Math Lesson

8th Grade Math EOG Review

Equation of Lines

• y=mx+b

• Find slope by doing  $\frac{rise}{run}$  

• find y-intercept where graph crosses the y-axis

Finding Slope-Intercept

• Find slope

• Plug in an ordered pair (x,y) and solve for b

• Put into y=mx+b

Multiple Choice

• A

• B

• C

• D

Multiple Choice

Which equation best represents the line on the graph?

• y= 1/2x
• y= -1/2x
• y = 2x
• y = -2x

Multiple Choice

What is the y-intercept of the line graphed below?

• 3
• 4
• -3
• 4/3

Multiple Choice

Write the equation of a line with a slope of -3 and y intercept of 8

• x = 8
• y = -3
• y = 8x -3
• y = -3x + 8

Multiple Choice

• A

• B

Multiple Choice

Which is the graph of the linear equation y = -x?

Multiple Choice

Paula and Julia went walking. The equation y = 3x models the distance Paula walked in x hours. Julia walked at a pace one mile per hour faster than Paula. Which graph correctly models Julia’s walking distance as a function of time?

Scatter Plots and Association

• Positive Association: x increases and y increases

• Negative association: x increases and y decreases

• No association: x and y have no effect on each other

Multiple Choice

• A

• B

• C

• D

Multiple Choice

Which best describes the association?

• positive

• negative

• irrational

• almost none

Multiple Choice

What type of association does this graph have?

• positive
• negative
• none
• all of the above

Multiple Choice

The age of a kitten and its weight.

• positive association
• negative association
• no association

Multiple Choice

What type of correlation does this graph show?

• Positive
• negative
• none
• all of the above

Multiple Choice

What type of correlation does this scatter plot show?

• positive linear association
• negative linear association
• no association
• nonlinear association

Multiple Choice

Which statement best describes the linear model?

• A

• B

• C

• D

Multiple Choice

Which equation best models the scatter plot?

• A

• B

• C

• D

Rational vs Irrational

• Rational: can be a fraction, repeating decimal, terminating decimal, perfect square roots

• Irrational: non-repeating, non-terminating decimal, non-perfect squares roots,  $\pi$  

Multiple Choice

Which choice is an irrational number?

• A

• B

• C

• D

Multiple Choice

What kind of number is -3?

• rational
• irrational
• whole
• natural

Multiple Choice

Which of the following number is rational?

• $$\sqrt{127}$$

• $$\pi$$

• $$2.5$$

• $$8.98763...$$

Multiple Choice

Determine which of the following examples is irrational.

• A fraction whose denominator is larger than its numerator

• A decimal that never ends but repeats

• A perfect cube root

• A decimal that never ends and never repeats

Multiple Choice

Which of the following is an irrational number?

• $$\sqrt{0}$$

• $$\sqrt{3}$$

• $$1\overline{.36}$$

• $$-0.19$$

Multiple Choice

Which of the following numbers is rational?

• $$\sqrt{7}$$

• $$\frac{2}{3}$$

• 3.1456289...

• $$\pi$$

BRAIN BREAK

https://youtu.be/lCTVccHc5hA

Function vs Not a Function

• Must pass vertical line test

• X can only be with one y... no cheaters!!

• only one arrow coming from each x-value in a mapping

Multiple Choice

In which choice is y a function of x?

• A

• B

• C

• D

Multiple Choice

In which sets of points is y a function of x?

• A

• B

• C

• D

Linear vs Nonlinear Functions

• Linear means STRAIGHT LINE on a graph

• Constant Rate of Change on Tables and Ordered Pairs

• "Plain x" in equation- x can't be attached to an exponent or on the bottom of a fraction

Multiple Choice

Is the graph pictured a linear or nonlinear function?

• Linear
• Nonlinear

Multiple Choice

Is this function linear or nonlinear?

• Linear function

• Nonlinear function

Multiple Choice

Is this function linear or nonlinear?

• linear function
• nonlinear function

Multiple Choice

Is this function linear or nonlinear?

• linear
• nonlinear

Multiple Choice

• A

• B

• C

• D

Multiple Choice

• A

• B

• C

• D

Multiple Choice

• A

• B

• C

• D

Distance vs Time

• x-axis = home

• steeper the line = faster the speed

Multiple Choice

Which graph best represents the distance Carly went?

• A

• B

• C

• D

Squares, Cubes, and Roots

• Squaring a number= multiplying same number by itself

• Cubing a number= multiplying the same number times itself 3 times

• Square root ( $\sqrt{ }$  ) "What number times itself equals..." 

• Cube Root (  $∛$ ) "What number times itself three times equals..."

• SQUARING A NUMBER AND TAKING THE SQUARE ROOT ARE INVERSE OPERATIONS; SO ARE CUBING AND THE CUBE ROOT

Multiple Choice

√25

• 5

• 50

• 15

• 3

Multiple Choice

√64 = ?

• 2
• 8
• 16
• 6

Multiple Choice

∛27

• 3
• 9
• 17
• 7

Multiple Choice

∛8 = ?

• 2
• 24
• 3.14
• 64

Multiple Choice

13² = ?

• 169
• 26
• 132
• 266

Multiple Choice

4^{2 = ?}

• 8
• 6
• 16
• 32

Multiple Choice

2^{3 = ?}

• 5
• 8
• 6
• 9

Multiple Choice

Which choice is both the square of an integer and the cube of an integer?

• 121

• 100

• 64

• 16

Fill in the Blank

The area of a square...

Fill in the Blank

What is the value of x?

Y-Intercept

• b in slope-intercept form

• b = BEGINNING

• words like "start," "initial," "at birth," "in the beginning," etc.

• never attached to x

Multiple Choice

• A

• B

• C

• D

Multiple Choice

What is the meaning of the y-intercept of the function?

• A

• B

• C

• D

Slope

• m in y=mx+b

• "slope words"- per, each, every, a

• slope is always attached to x

Meaning of Slope

•  $\frac{rise}{run}=\frac{y}{x}$  

• Find slope first!

• Find y measurement and x measurement- match it up with your slope 

Multiple Choice

What is the number of miles...

• A

• B

• C

• D

Multiple Choice

What is the meaning of the slope...

• A

• B

• C

• D

Slope Between Two Points

•  $\frac{change\ in\ y}{change\ in\ x}\ or\ \frac{\Delta y}{\Delta x}$  

• Remember that "change" means subtract! 

• Simplify! 

Fill in the Blank

Fill in the Blank

Slope from a Table

• Pick 2 ordered pairs

•  $\frac{change\ in\ y\ }{change\ in\ x}$  

Multiple Choice

Which statement...

• A

• B

• C

• D

Multiple Choice

Find the slope:
(2, -7) and (-1, 6)

• -13/3
• 3/13
• -1/3
• 1/3

Multiple Choice

Find the slope:

(-1,-9) and (5, -6)

• -15/4

• 1/2

• -3/6

• 11/3

Estimating Non-Perfect Square Roots

• Draw a little number line

• Find perfect square that your number is close to. Mark it above or below your number along with its square root

• Mark the next number (above or below)

• Mark whichever number your non-perfect square is closer to

Fill in the Blank

What positive integer...

Multiple Select

$$\sqrt{19}$$ is between which two perfect squares?

• 4

• 5

• 6

• 7

Multiple Select

$$\sqrt{160}$$ is between which two perfect squares?

• 11

• 12

• 13

• 14

Parallel Lines and Transversals

• Redraw lines on your paper and label angles

• Label Big/Little

• Little = Little

• Big = Big

• Big + Little = 180

Fill in the Blank

A square is drawn below...

Fill in the Blank

What is the value of x?

Multi-Step Equations

• Draw your equation bars ( $\parallel$  )

• Goal is to get variable by itself 

• Use inverse operations

• Addition "undoes" subtraction 

• Multiplication "undoes" division

Fill in the Blank

What is the value of x?

Fill in the Blank

What value of x satisfies the equation below?

Scientific Notation

• Convert to Standard: Move decimal the number of spaces according to exponent

• Convert to Scientific: move decimal until it is behind only one number greater than 0. Count number of spaces for exponent

• Original number greater than 1: positive exponent

• Original number is a decimal: negative exponent

Multiplying/Dividing Sci Not

• Multiply main numbers times each other; add exponents

• Divide main numbers; subtract exponents

• Don't forget to move decimal if needed

• Left Add Right Subtract

• "How many times larger" = divide

Multiple Choice

A light year...

• A

• B

• C

• D

Multiple Choice

What is the value of y?

• A

• B

• C

• D

Pythagorean Theorem

•  $a^2+b^2=c^2$  

• Distance: count the sides lengths

• USE GRAPH PAPER

Multiple Choice

What is the distance from J to M?

• A

• B

• C

• D

Multiple Choice

What is the length of the dotted line?

• A

• B

• C

• D

Multiple Choice

What is the approximate length of side RQ?

• A

• B

• C

• D

Multiple Choice

Which could be the coordinates of the third vertex...?

• A

• B

• C

• D

Multiple Choice

What is the approximate perimeter of the shaded triangle?

• A

• B

• C

• D

Volume

• Cylinder: V= $\pi r^2h$  

• Cone: V=  $\frac{1}{3}\pi r^2h$  

• Sphere: V=  $\frac{4}{3}\pi r^3$  

• If they give you diameter, divide by 2 to find radius!!!!! 

Multiple Choice

What is the approximate volume of the can?

• A

• B

• C

• D

Multiple Choice

What is the approx. volume of the barrel?

• A

• B

• C

• D

Multiple Choice

What is the volume of the sphere?

• A

• B

• C

• D

Transformations

• Translation- L/R affects x and U/D affects y

• Reflection- if x flips, y changes; y flips, x changes

• Rotation- TURN YOUR COMPUTER

• Dilation- multiply points by scale factor

Multiple Choice

What will be the coordinates...

• A

• B

• C

• D

Multiple Choice

What will be the coordinates of Y'?

• A

• B

• C

• D