Math 2- Finals review

TOPICS COVERED:
1. Transformation geometry
2. Key features of quadratics
3. Triangle congruence
4. Inverse variations and radicals
5. Solving Quadratics
6. Similiar Triangles
7. Right triangle trigonometry.

​

​MATH 2- FINALS REVIEW

Multiple Choice

A transformation that “turns” a figure about a fixed point at a given angle and a given direction.

• rotation
• translation
• reflection
• dilation

Multiple Choice

Determine how to translate triangle ABC to triangle A'B'C'. 

• right 2, down 5
• right 2, down 9
• left 2, up 9
• left 2, down 9

Multiple Choice

How many degrees was the figure rotated?

• 90 degrees counterclockwise 
• 180 degrees
• 270 counterclockwise 

Multiple Choice

Identify the transformation from ABCD to A'B'C'D'.

• Translation
• Reflection across the x-axis
• Reflection across the y-axis
• 90^o counter clockwise rotation

Multiple Choice

If the quadrilateral is translated 4 units to the left and 5 units down what is the coordinates for Point A'?

• (4,0)
• (0,4)
• (-1,5)
• (5,-1)

Multiple Choice

If ∆CAB≅∆FED , then $$\angle C\cong\angle F$$  

• True

• False

Multiple Choice

If $$\Delta MAN\cong\Delta BOY$$ , which of the following statements are true?

• $$\overline{MA}\cong\overline{BO}$$  

• $$\overline{AN}\cong\overline{BY}$$  

• $$\overline{BO}\cong\overline{NA}$$  

• $$\overline{MN}\cong\overline{BO}$$  

Multiple Choice

Which of the following is not a postulate used to prove triangle congruence?

• SSA

• SAS

• ASA

• SSS

Multiple Choice

Which triangle congruence theorem can be used to prove the triangles are congruent?

• SAS
• SSS
• ASA
• HL

Multiple Choice

Which triangle congruence theorem can be used to prove the triangles are congruent?

• AAS
• SSS
• Not enough information given
• ASA

Multiple Choice

Does this parabola have a minimum or a maximum?

• Minimum

• Maximum

Multiple Choice

Where is the vertex of this parabola?

• (1,3)

• (-1,3)

• (3,1)

• (3, -1)

• What do you notice about the roots of this parabola?

  
  

  *it is where it crosses the x- axis*

• What are the roots of this parabola?

  
  

  x= -3 and x = 5

• Where is the vertex?

  
  

  (1, -4) 

  
  

  
  

Multiple Select

What are the root(s) of this parabola?

• x= 0

• x = 1

• x = 4

• x = -7

Multiple Choice

Does this parabola have a maximum or minimum?

• Maximum

• Minimum

Fill in the Blanks

Multiple Choice

What is the line of symmetry?

• x = 1

• y = 1

• x = -1

• y = - 4

Domain & Range when a<0

• Domain: all the x-values

• What is the domain of this parabola?

  
  

• 
  

  
  

• Range: all the y-values

• What is the range of this parabola?

• 
  

  
  

Domain & Range when a>0

• Domain: all the x-values

• What is the domain of this parabola?

• 
  

• Range: all the y-values

• What is the range of this parabola?

• 
  

  
  

Multiple Choice

What is the domain of this parabola?

• [4, $$\infty$$ )

• $$\left(-\infty,\infty\right)$$

• Does not have a domain

• [-2, 2]

Multiple Choice

What is the range of this parabola?

• [-4 , $$\infty$$ )

• $$\left(-\infty,\ \infty\right)$$

• $$\left[4,\ \infty\right)$$

• [-2, 2]

Multiple Choice

What is the constant of variation of the equation, x = 29/y?

• 0

• 1

• 29

• y

Multiple Choice

y varies inversely with x. If y = 40 when x = 16, find x when y = -5.

• -64

• -128

• -256

• -512

Multiple Choice

12 men can dig a hole in 8 days. How many men can dig it in 6 days?

• 14 men

• 16 men

• 18 men

• 20 men

Multiple Choice

If 32 men can reap a field in 15 days, in how many days can 20 men reap the same field?

• 18 days

• 20 days

• 22 days

• 24 days

Multiple Choice

Solve 2(x-1)² = 32

• x= -3, 5
• x= -4, 4
• x= 3, 5
• x= 2, 6

Multiple Choice

What is the equation for the axis of symmetry?

• y=3
• x=3
• x=5
• x=1

Multiple Choice

Does y = -4x² have a maximum or minimum value?

• maximum
• minimum

Multiple Choice

What is the vertex of the quadratic function:
y = x² - 6x + 11?

• (3,2)
• (-3,-2)
• (-3,2)
• (3,-2)

Multiple Choice

Which of the following is the correct equation for the given graph?

• f(x) = (x - 2)² - 1
• f(x) = (x + 2)² - 1
• f(x) = -(x + 2)² - 1
• f(x) = -(x - 2)² - 1

Multiple Choice

Select the answer that has a, b, and c correctly labeled:

$$y=-x^2+2x-9$$  

• a= 1, b= 2, c= -9

• a= 2, b= -1, c= 9

• a= -9, b= 2, c= -1

• a= -1, b= 2, c= -9

Multiple Choice

What form is this equation written in?

$$y=-x^2+6x+7$$  

• standard form

• vertex form

• factored form

• slope-intercept form

Multiple Choice

Factor completely: x²+16x+64

• (x+4)(x+16)
• (x-8)(x-8)
• (x+2)(x+32)
• (x+8)(x+8)

Multiple Choice

You are cliff diving with some friends. Your path to the water is modeled by h(t) = -16t^2 + 8t +24. How long will it take for you to hit the water? What are you solving for?

• roots

• axis of symmetry

• y-value of the vertex

• y-intercept

Multiple Choice

The height of a ball that is thrown into the air is given by h(t) = -5t² + 40t + 2. From what height was the balloon released?

• 2 meters

• 4 meters

• 5 meters

• 8 meters

Multiple Choice

A ball is thrown vertically into the air. Its height in feet after t seconds is given by the equation h(t) = –5t² + 20t, and is graphed below. How high will the ball be after 3 seconds?

• 20 ft

• 15 ft

• 5 ft

• 10 ft

Solving radicals example

Multiple Choice

Solve the equation $$\sqrt{x}+4\ =\ 10$$  

• x = 36

• x = 196

• x = 100

• x = 84

Multiple Choice

Solve.

$$\sqrt{u-8}=\sqrt{43-2u}$$  

• $$3u=51$$  

• $$u=3$$  

• $$u=17$$  

• No Solution

Multiple Choice

• 1

• 3

• 224

• 226

Multiple Choice

Solve

• 102
• 12
• 98
• 7

Multiple Choice

Which transformation transforms the graph of
f(x) = x² to the graph of
g(x) = (x + 4)²?

• a vertical translation 4 units up
• a vertical translation 4 units down
• a horizontal translation 4 units to the left
• a horizontal translation 4 units to the right

Multiple Choice

How did we transform from f(x) =x²

to

g(x) = -3x²

• reflection in x-axis and vertical shift down

• reflection in x-axis and vertical stretch

• horizontal stretch

• reflection in x-axis and vertical compression

Multiple Choice

If the blue graph is

f(x) = x²

then the red must be...

• g(x) = x² - 5

• g(x) = x² + 5

• g(x) = (x - 5)²

• g(x) = (x + 5)²

Multiple Choice

Solve for n

$$\frac{n}{4}=\frac{8}{7}$$  

• 5

• 32

• 4

• 32/7

Multiple Choice

Find the scale factor going from the small triangle to the larger triangle

• 3

• 1/3

• 2

• 5

Multiple Choice

State the postulate that proves these triangles are similar.

• SSS
• AA
• SAS
• Not similar

Multiple Choice

The triangles are similar by...

• SAS
• AA
• ASA
• SSS

Multiple Choice

Which triangles are similar to triangle A?

• B

• C

• Both

• None

Multiple Choice

What is the length of the altitude, segment CD, of triangle ABC?

• 7√3 square units

• 14√3 square units

• 14√2 square units

• 7√2 square units

Multiple Choice

To the nearest whole degree, what is the angle of elevation of the rope?

• A. 74°

• B. 75°

• C. 77°

• D. 79°

Multiple Choice

Find the value of x. Round to the nearest tenth.

• 32.6

• 38.9

• 25.7

• 19.2

Multiple Choice

The Burj Khalifa, located in Dubai in the United Arab Emirates, is the tallest building in the world as of 2022. Andre visited Dubai over winter break. He stood 700 meters away from the building, looked up at a 48.11 degree angle using a laser rangefinder and spotted the top of the building. How tall is the Burj Khalifa, in meters?

(write down your answer because you will need to use it in the next question)

• 700 meters

• 800 meters

• 780 meters

• 700 * tan(48.11) meters

Multiple Choice

Solve for x.

• -11
• 9
• -9
• 10

Multiple Choice

Find the measure of angle A.

• 21 degrees
• 31 degrees
• 128 degrees
• 24 degrees

Multiple Choice

Find the measure of the indicated angle. 

• 35 degrees
• 40 degrees
• 25 degrees
• 30 degrees

Multiple Choice

Find the measure of the indicated angle. 

• 87 degrees
• 82 degrees
• 83 degrees
• 72 degrees