8th Grade - End of Year

Autobots!

100

Define the following transformations:

-Translation

-Rotation

-Reflection

A translation is a geometric transformation that moves every point of a figure, shape or space by the same distance in a given direction.

A rotation is a motion of a certain space that preserves at least one point.

A reflection is a mirror image of a figure in the axis or plane of reflection. 

200

Define "rigid transformation"

A transformation where the size and shape of a figure does not change

300

What type of transformation keeps the figures' shape but not size?

Dilation

400

Triangle PQR has the following vertices P(-4,4), Q(-2,3), and R(-5,2). The triangle is reflected across the x-axis and rotated 180 degrees clockwise. What are the coordinates of the vertices after the transformations?

P(4,4), Q(2,3) and R(5,2)

500

Name 3 real-world applications of geometric transformations.

Examples include: engineering precision, architectural design, medical imaging analysis, computer graphics, robotics, automation, and navigation systems 

Time to head to the Mountains

100

What are the formulas for calculating slope?

y = mx + b

y = mx

200

When working with slope-intercept form, which variable represents the y-intercept?

b

300

Solve the equation: 6(x+2) = 3(2x+4). How many solutions are there?

Infinitely many solutions

400

When you have the slope as both negative and a fraction, does the negative sign go to both the denominator and numerator, or only one of them?

Only 1; Numerator

500

Graph the following slope-intercept form:

y = -4x + 5

Your line in on the y-intercept at 5 and proceeds going down 4 and 1 to the right. 

Take my place or get out!

100

Use substitution or elimination to solve the following system of linear equations:

4x - 12y = -8

-3x + 12y = 12

(4,2)

200

Use substitution or elimination to solve the following system of linear equations:

6x - 9y = 18

-6x + 2y = 4

(0,2)

300

Use substitution or elimination to solve the following system of linear equations:

7x + 6y = 16

4x - 2y = 1

(1, 3/2)

400

Use substitution or elimination to solve the following system of linear equations:

x + y = 5

6x + 3y = 27

(4,1)

500

Use substitution or elimination to solve the following system of linear equations:

5x + 2y = 10

2x + y = 2

(6,-10)

Theorem Crafting

100

Explain what Pythagorean Theorem is.

Pythagorean's Theorem states that a right triangle the sum of the squares of the legs is equal to the square of the hypotenuse.

aka (a²+ b² = c²)

200

How do you know if 3 length measurements makes a triangle?

If the two smaller measurements when added together are bigger than the 3rd.

300

A firefighter brings a 13-ft ladder to a burning building. He secures the ladder to the ground 5ft away from the wall. How high will the ladder reach?

12ft

400

The perimeter of an equilateral triangle is 48cm. From the base to its height, how tall is the triangle? Round your answer to the nearest whole number.

The square root of 192 is between 13 and 14, but closer to 14.

500

Look at each set of three numbers and determine which are a Pythagorean triple?

2, 3, 4

4, 5, 6

5, 12, 13

6, 8, 10

8, 15, 17

9, 16, 25

5, 12 and 13

6, 8, and 10

8, 15 and 17

I have the power!

100

Rewrite the expression using only positive exponents:

(7/16)^-3

16³ / 7³

200

Write the following expression using only positive exponents:

19^-3 x 19 x 19^-4 x 19³

1/19³

300

Evaluate the expression:

3⁴ x 3^-6 x 9⁰

1/9

400

Evaluate the expression:

( (3^-4 x 3⁶)/(6³ x 6^-1) )^-2

16

500

Evaluate the expression:

18^-4 x 6⁷

8/3