Math 2 Honors Semester 2 Final Review

Solving Quadratics

Real World Application of Quadratics

Special Right Triangles

Probability

Compare/Contrast Quadratics

100

Solve the equation for x:

x^2 = 225

What is

x=\pm15

100

Ms. Gibala is trying to show her coach how high her vertical leap is. She starts her jump and is in the air for 5 whole seconds. She reached a maximum height of 12.5 feet in the air, like the swoll queen that she is.

What is the vertex of the function?

What is

(2.5, 12.5)?

100

Saul can see Spiderman about to jump off the spire (the pointy thing) on top of the Empire State Building. Saul wonders how tall the spire is. He stands 120 feet away from the base of the empire state building and takes the measurements shown in the diagram below.

What trigonometric ratio (sine, cosine, or tangent) or special right triangle shortcut can be used to solve for the height from the ground to the top of the spire?

What is

Tangent

100

Ms. Whitmer rolls a standard six-sided die. What is the probably that the die lands on a 3 or an even number?

What is

P(even or 3) = \frac{4}{6} = \frac{2}{3} = 0.67 = 67%

100

For the function f(x) below, identify if the vertex is a maximum or a minimum.

What is

Minimum vertex

200

Solve the equation for x:

x^2 + 12x - 15 = 0

What is

x=-6\pm\sqrt51

200

Dylan uses a catapult to launch a watermelon into the air from next to a river. He loads the catapult 3 feet away from the river. His friend times the distance of the watermelon from when it was launched until it lands to be 13 ft. The watermelon reaches a maximum height which is 37.5 ft.

What are the x-intercepts of the function? (In order to get points, you need to include both x-intercepts.)

What is

(3,0) and (16,0)

200

Solve for the height from the ground to the top of the spire.

What is

x=120tan(45) = 120\ feet

200

You go to Subway with your friends at lunch. Their sandwich orders are below.

What is the probability that your friends order a 6 inch sandwich?

What is

P(six) = \frac{6}{9} = \frac{2}{3} = 0.67 = 67%

200

For the function f(x) below, identify the y-intercept

What is

(0, -24)

300

Solve the equation for x:

x^2-10x+9=0

What is

x=9 \ AND \ x=1

300

Ms. Whitmer uses a cannon to shoot a huge marshmallow into the air from next to the Golden Gate Bridge. She loads the cannon 1 ft away from the bridge. Her friend calculated the distance of the marshmallow from when it is launched until it lands to be 12 ft. The marshmallow reaches a maximum height at the lowest part of the bridge which is 30.25 ft.

What is the vertex of the function?

What is

(7, 30.25)

300

What trigonometric ratio (sine, cosine, or tangent) or special right triangle shortcut can be used to solve for the height of the Empire State Building?

What is

Tangent

300

You go to Subway with your friends at lunch. Their sandwich orders are below.

What is the probability of ordering a turkey given it is a 6 inch sandwich?

What is

P(turkey\ given\ 6) = \frac{1}{6} = 0.17 = 17%

300

For the function f(x) below, identify whether the function is a vertical stretch or a vertical shrink.

What is

Vertical stretch by a factor of 2.

400

Solve the equation for m:

d=\frac{1}{2}rm^2

What is

m = \pm\sqrt\frac{3d}{r}

400

Alexis is standing on top of a 48 ft cliff overlooking the ocean. She throws a rock into the air. After three seconds, the rock reaches a maximum height of 75 ft. Five seconds later, the rock enters the ocean.

Write a function to model the situation.

What is

y=-3(x-3)^2+75

400

Solve for the height of the Empire State Building.

What is

x = 120tan(30) = 69.28\ feet

400

You go to Subway with your friends at lunch. Their sandwich orders are below.

What is the probability of ordering a footlong sandwich given it is veggie?

What is

P(foot\ long\ given\ veggie) = \frac{1}{3} = 0.33 = 33%

400

The function f(x) is represented by the graph below.

The function g(x) is represented by the following equation:

g(x) = -4(x-2)^2+25

Compare and contrast the vertex of f(x) and g(x). A comparison of the two functions should include whether the vertex is a maximum or minimum.

What is

The vertex of f(x) is a minimum while the vertex of g(x) is a maximum.

500

Mr. Wolf was trying to impress Ms. Gibala with his knowledge of solving literal equations. He was solving the following equation for d using the steps below.

g=\frac{1}{7}hd^2

Step 1:

g=\frac{1}{7}hd^2

Step 2:

7g = hd^2

Step 3:

\pm\sqrt(7g)=hd

Step 4:

\frac{\pm\sqrt(7g)}{h}=d

Ms. Gibala sees an error in Mr. Wolf's work. Where is the mistake and how would you fix it?

What is

Step 3 is incorrect. Mr. Wolf should have divided both sides by q before taking the square root. So the final answer should have been

d=\pm\sqrt\frac{7g}{h}

500

Mae is training her puppy to jump through hoops. She runs 5 ft from the wall and takes off into a jump! She jumps through a hoop at a height of 13.75 inches and lands on the ground 10 ft after she jumps.

Write a function to model the situation.

What is

y=-\frac{1}{2}(x-10)^2+12.5

500

How tall is JUST the spire?

What is

x=120 - 69.28 = 50.72\ feet

500

You go to Subway with your friends at lunch. Their sandwich orders are below.

P(turkey) =

\frac{3}{9}

P(turkey given 6 inch) =

\frac{1}{6}

Are {turkey} and {6 inch} independent?

What is

No turkey and 6 inch sandwiches are associated.

500

The function f(x) is represented by the graph below.

The function g(x) is represented by the following equation:

g(x) = -4(x-2)^2+25

Compare and contrast f(x) and g(x). A comparison of the two functions should include the vertical stretch/shrink.

What is

Both f(x) and g(x) have a vertical stretch. f(x) is stretched by a factor of 2 while g(x) is stretched by a factor of 4.