TREADWELL 8 REVIEW

Functions

100

Does the relation represent a function?

(1,4), (2,5), (3,6), (1,7)

Not a function

200

A relation is shown by the rule:

y=x

Is this a function? Explain why.

Yes 

300

A mapping diagram shows the following relationships: 

• 2 → 5
• 3 → 7
• 4 → 9
• 2 → 5

Is this relation a function

Yes it is a function

400

A relation is defined by the equation:

y=2x−3

If the relation includes the points
(1,−1),(2,1),(3,3),(4,5)

Does this represent a function?

Yes, it is a function

500

A relation is shown by the equation:

x²+y²=25

Does this equation represent a function? Why?

No, because it will appear a square root in the equation.

Exponents and squares

100

Simplify:

a³⋅a⁴

a⁷

200

(k³)⁴

k¹²

300

Simplify

a³ ⋅ a² / a⁴

a

400

Simplify

(j⁵)² ⋅ j³ / j⁴

j⁹

500

Simplify

(a³b^-2)² ⋅ a^-1b⁴  /  a²b^-3

a³b³

Transformations

100

I was in quadrant 1 and rotated to quadrant 2. Which direction and degree did I go?

270 degrees clockwise or 90 degrees counterclockwise

200

The order pair (30,75) was dilated by a scale factor of 1/5. What is the new ordered pair?

(6,15)

300

The figure was translated, then rotated, then dilated. What type of transformation is the entire sequence: rigid or non-rigid? Explain why.” 

It is non-rigid, because the size changed. 

400

A triangle has vertices at
A(2, 3), B(5, 3), and C(4, 6).

1. The triangle is reflected over the y-axis.
2. Then it is translated up 2 units and left 1 unit.

What are the coordinates of the final image A″, B″, and C″?

• A″ = (-3, 5)
• B″ = (-6, 5)
• C″ = (-5, 8) 

500

Triangle △ABC\triangle ABC△ABC has vertices
A(1, 2), B(4, 2), and C(3, 5).

The triangle undergoes the following transformations in order:

1. Rotate 90° clockwise about the origin
2. Reflect over the line y=x
3. Dilate by a scale factor of 2 centered at the origin

• A‴ = (-2, 4)
• B‴ = (-8, 4)
• C‴ = (-6, 10) 

Linear equations

100

3x+7=19 

What is the value of x?

x=4

200

4x−5=2x+9 

What is the value of x?

x = 7

300

5(x−2)=3x+14 

Solve for x

x=12

400

2(3x−4)+5=4(x+1)+9

Solve for x

x=8

500

4(2x+3)−5=8x+9

 How many solutions does this equation have? Explain your answer.

no solution

Angle Relations

100

We are inside the two parallel lines, on the opposite side of the transversal. Who are we?

Alternate Interior Angles

200

Two lines intersect, forming four angles.

One angle measures 65°. 

What is the measure of the vertical angle?

65°

300

Two parallel lines are cut by a transversal.

Angle 1 measures 110°. What is the measure of the same-side interior angle next to it? 

70° 

 Same-side interior angles are supplementary, so they add to 180°

110∘+70∘=180 

400

Two parallel lines are cut by a transversal.

Angle 1 measures (3x + 10)°
Angle 2 measures (5x − 30)°

Angle 1 and Angle 2 are alternate interior angles. What is the value of x, and what is the measure of each angle? 

• x = 20
• Angle 1 = 3(20)+10=70∘3(20) + 10 = 70
• Angle 2 = 5(20)−30=70∘5(20) - 30 = 70

500

Two lines intersect, creating four angles.

• One angle measures (4x + 10)°
• The adjacent angle measures (2x + 50)°
• What is the value of x, and what is the measure of each angle?

x = 20 

(4x+10)+(2x+50)=180