Survivor Mode Math 8 Review- Pythagorean T, Volume and Systems

Survivor Mode Math 8 Review #3

​ Pythagorean Theorem, Volume, and Solving Systems

By Brittany Siergiej

Multiple Choice

Level 1

The Pythagorean Theorem works on which triangle?

• obtuse

• scalene

• isosceles

• right

• all triangles

Pythagorean Theorem Basics

Hypotenuse

The hypotenuse of a right triangle is the largest side of the right triangle, and is always located across from the right angle.
The letter c is used to represent the hypotenuse.

The Pythagorean Theorem can be used to determine the length of a missing side of a right triangle.

Finding the Hypotenuse

Multiple Choice

What is the value of x? Round to the nearest tenth.

• 15.1 feet
• 14.9 feet
• 17.0 feet
• 5.8 feet

Multiple Choice

A baseball "diamond" is actually a square with sides of 90 feet. If a runner tries to steal second base, how far must the catcher, at home plate, throw to get the runner "out"? (Distance across the diagonal)

• 180 feet

• 90 feet

• 13.4 feet

• 127.3 feet

The Pythagorean Theorem can be used to determine the length of a missing side of a right triangle.

Finding a Leg

Multiple Choice

Level 2

Solve for the value of y

• 13

• 5

• 23

• 10

Multiple Choice

Your family wants to purchase a new laptop with a 17" widescreen. Since the 17 inches represents the diagonal measurement of the screen (upper corner to lower corner), you want to find out the actual dimensions of the laptop. When you measured the laptop at the store, the height was 10 inches, but you don't remember the width. Calculate the width of the laptop to the nearest tenth of an inch.

• 7 inches

• 10 inches

• 19.7 inches

• 13.7 inches

Multiple Choice

The bottom of a 13-foot straight ladder is set into the ground 5 feet away from a wall. When the top of the ladder is leaned against the wall, what is the distance above the ground it will reach?

• 12 feet

• 13.9 feet

• 169 feet

• 18 feet

Volume 101

Take a look at the example to remind yourself how to find the area of a cylinder.

Example:

Multiple Choice

Is the red line a radius or diameter of the circle?

• Radius
• Diameter

Multiple Choice

Is the red line a radius or diameter of the circle?

• Radius
• Diameter

Multiple Choice

What is the radius?

• 18
• 72
• 38
• 14

Multiple Choice

What is the diameter?

• 8
• 16
• 10
• 4

Math Response

Determine the volume of a cylinder with a radius of 4 cm and a height of 9 cm. Express your answer in terms of $$\pi$$ .

$$V=\pi r^2h$$

Type answer here

Correct Answer: 144\pi

Deg^°

Rad

Math Response

Determine the volume of a cylinder with a diameter of 12 cm and a height of 15 cm. Express your answer in terms of $$\pi$$ .

$$V=\pi r^2h$$

Type answer here

Correct Answer: 540\pi

Deg^°

Rad

Math Response

Determine the height of a cylinder with a radius of 3 cm and a volume of $$126\pi\ cm^3$$ cm. Express your answer in terms of $$\pi$$ .

$$V=\pi r^2h$$

Type answer here

Correct Answer: 14

Deg^°

Rad

Multiple Choice

What is the radius in the cylinder?

• $$3\ in$$

• $$6\ in\$$

• $$12\ in$$

• $$24\ in$$

​Systems 101

Solving Systems of Equations by Graphing

One Solution

When you graph both equations they will cross in exactly ONE POINT. The INTERSECTION POINT is the ANSWER to the system.

No Solution

When you graph both equations they NEVER intersect. No intersection point means no solution.

Infinite Solutions

When you graph both equations and they overlap. When the lines overlap at every point it means they have infinite solutions. They are actually the same line.

Multiple Choice

These two lines intersect at _____.

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

Multiple Choice

The solution to this system of equations is:

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

Multiple Choice

Buzz graphed two lines in order to find the solution to a given system of equations.
What is the solution?

• (-1, 4)
• (1, -4)
• (-4, 1)
• (4, -1)

Multiple Choice

Parallel Lines never intersect because...

• they have the same slopes. 
• they have the same y-intercept.
• they have different slopes.
• they have different y-intercepts. 

Multiple Choice

This system has _____ solutions

• no
• 1
• 2
• Infinitely many

Solving Systems by Elimination

​System of Equations: a collection of two or more equations with the same set of unknowns (variables).

​Example:

​4x - y = -6

​5x + y = -21

2x + 2y = 13

x - 2y = 11​

EXAMPLE

Find the solution to the system.

Solve the system.

(on the graph its where the lines cross)​

Multiple Choice

What would be the first step in finding the solution with elimination?

4x + 3y = 1

x - 3y = -11

• cross out the 3y and -3y

• cross out the 4x and x

• change all the signs of the second equation

• add 1 and -11

Multiple Choice

Which variable will be eliminated?

• x

• y

Multiple Choice

What is the resulting combined equation to the following system of equations when using the Elimination Method?

5x - 4y = 11

5x + 4y = 4

• 8y = 15

• 10y = 15

• 10x = 15

• 25x = 15

Multiple Choice

Which equation is the result of adding these two equations together?  $$2x-y=-15$$    

   2x + 2y =  15

 - 2x + 3y = 30

•  - 3y = - 45

• 6y = 45

• 3y = 15

•  5y = 45

Multiple Choice

$$3x-2y=12$$  

$$2x+2y=-2$$  

What variable will eliminate in the system? 

• x

• y

• both

• neither