Geometry Mock Test 4

Probability Intro part 1

Subject | Subject

Some text here about the topic of discussion

Probability intro Part 2

Some text here about the topic of discussion

Probability Number Line

When coming up with the probability of an outcome, divide the outcome you're looking for by the total number of possible outcomes. In a coin toss, the probability of either side is 1 ⁄ 2, as there are two total outcomes. With dice, which have six sides, the probability of one of the numbers landing on top is 1 divided by 6, or 1 ⁄ 6.

The probability of an outcome

Multiple Choice

Stephen has three sweaters: one is blue, one is red and one is green. He pulls a sweater out of his dresser at random. What is the probability that it is his green sweater?

• 1/3

• 3

• 1/4

And when I see the word "or"

"Or" in Probability means to add all possible events together !​

Multiple Choice

What is the probability of rolling an even number on a die?

• 3/6

• 1/2

• 3

​Compound Events

Subject | Subject

Some text here about the topic of discussion

More about compound events

The occurrence of the first event ​changes the outcome of the second event.

Ex. You pick a marble without replacing it​

Dependent

The occurrence of the first event does not ​change the outcome of the second event.

Ex. You pick a marble and replace it​

​Independent

Independent Vs. Dependent Events

Multiple Choice

Jamal, Gary, Charlie and Brian are going to stand in line, one behind the other. In how many different ways can they stand in the line?

• 24

• 16

• 10

• 4

Multiple Choice

There are 14 tiles with one letter from the word MATHEMATICIANS on each. You are now going to choose a letter, put it back and then choose another letter. Find the probability of choosing the letter M, and then the letter A.

• 3/98

• 3/196

• 2/7

• 3/14

Multiple Choice

A bag has 2 yellow marbles and 8 brown marbles. Nancy takes out two marbles without replacing the marbles. What is the probability that they will both be yellow?

• 2/19

• 1/10

• 1/25

• 1/45

Multiple Choice

How many ways can you arrange 7 books on a shelf?

• 7

• 49

• 343

• 5,040

Multiple Choice

There are 18 people running in a cross country race. How many possible ways are there to place the runners in first, second, and third?

• 324

• 4,896

• 816

• 54

Take a moment to familiarize yourself with the formula if you got the previous question wrong.

Multiple Choice

P(A) = ?

• (5)/27

• (5+9)/27

• (5+7)/27

• (5+7+9)/27

Multiple Choice

P(B) =?

• (5)/27

• (5+9)/27

• (5+7)/27

• (5+7+9)/27

Multiple Choice

P(A $$\cap$$  B) =?

• (5)/27

• (5+9)/27

• (5+7)/27

• (5+7+9)/27

Multiple Choice

P(A $$\cup$$  B) =?

• (5)/27

• (5+9)/27

• (5+7)/27

• (5+7+9)/27

Vocabulary

• Frequency - the number of times an even occurred

• Relative Frequency - frequency expressed as a percentage of the total

Multiple Choice

How many male students studied French?

• 18

• 13

• 24

• 17

Multiple Choice

What percent of people who bought no food purchased water?

• 14.3%
• 33.3%
• 5%
• 41.1%

Multiple Choice

What percent of people who play an instrument do not play a team sport?

• 80%
• 27.2%
• 40%
• 90.1%

Multiple Choice

What percent of the total population surveyed were electrical engineers that like math?

• 33.9%
• 48.6%
• 16.5%
• 21.7%

For most 3d objects, the volume is found by finding the area of the base and multiplying that by the height.

Some exceptions are pyramids, cones, and spheres.

Multiple Choice

What is the Volume of this shape: (Go Back to Slide 2 or 7 for Formulas or look them up in a separate tab)

• 2,201.5 m ³

• 1,995.7 m³

• 1,300. 7 m³

Multiple Choice

What is the volume of this shape?

• 125.5 in³

• 260.8 in³

• 290.8 in³

• 586.7 in³

Multiple Choice

What is the volume of this shape?

• 1436.76 in³

• 1523.8 in³

• 1602.45 in³

• 1804.7 in³

Multiple Choice

What is the surface area of this shape? (Right Rectangular Prism= 2(lh)+2(hw)+2(lh)

• 600 cm³

• 624 cm³

• 648 cm³

• 728 cm³

Multiple Choice

What is the surface area of this shape? (Right Square Pyramid: s²+ 2sl

(s=side l=slant height)

• 1503 m³

• 2021.6 m³

• 3023 m³

• 4242 m³

On this problem, we isolated for H, by multiplying by 3 to remove the 1/3 to start.

We then had to divide by (pi)r² to undo the multiplication on the right.

Cavalieri's Principle and Cross Sections

Thinks about it.....​

Do the 2 stacks of coins have the same volume?

What is a cross section?

A cross-section is the shape we get when cutting through an object

Multiple Choice

An oblique shape will always have the same volume as a right shape if they have the same base.

• True

• False - an oblique shape and a right shape can never have the same volume

• False - an oblique shape and a right shape can't have the same base

• False - an oblique shape will always have the same volume as a right shape if they have the same base AND height

Multiple Choice

The shapes below have the Base Areas and Heights. Which will have the same volume. Which ones will have the same volumes based on Cavalieri's Principle?

• Rectangular Pyramid and Triangular Prism

• Rectangular Pyramid and Cone

• Triangular Prism and Cone

• All three.

Multiple Choice

Based on Cavalieri's Principle, will the two prisms have the same volume?

• No, they will not be same. Although the heights are the same, the cross-sections are different shapes. 

• Yes, the heights of both prisms are the same and they have the same cross-sectional area. Therefore, they will have the same volume.

Equation of a circle

Multiple Choice

What is the radius of this circle?

• 2

• 6

• 3

• 5

Multiple Choice

What is the equation of the circle?

• (x+1)^2 + (y +1)^2 = 3

• (x+1)^2 + (y -1)^2 = 3

• (x+1)^2 + (y +1)^2 = 9

• (x-1)^2 + (y -1)^2 = 9

Multiple Choice

In the equation (x+2)²+(y-3)²=4, the radius of the circle is...

• 4

• 2

• 3

• 16

Multiple Choice

In the equation (x-3)²+(y-2)²=16, the center of the circle is...

• (3,2)

• (-3, -2)

• (-2, -3)

• (2, 3)

Multiple Choice

Solve for d.

• 8

• 9

• 10

• 12

Arc Length (COPY NOTES)

Arc Length is the length of a portion of the circumference.

To find this we multiply the circumference by the fraction of the circle the arc subtends.

The fraction of the circle is determined by dividing the central angle by 360.

Explanation Slide...

​

Multiple Choice

Find the length of the bolded arc. Leave pi in your answer. #8

• 5688π ft

• 15.8π ft

• 150.4π ft

• 54,150 ft

Multiple Choice

$$USE\ S=\frac{\theta2\pi r}{360\degree}\ to\ find\ \ \theta\ first$$  Find the area of the dark blue sector shown on the left. The radius of the circle is 4 units and the length of the arc (the curved edge of the sector) measures 7.85 units. Express the answer to the nearest tenth of a square unit. #29

• 0.3 square units

• 15.7 square units

• 19.7 square units

• 50.3 square units

Explanation Slide...

​

Multiple Choice

What is the area of the shaded region? #6

• 50.27 units²

• 3015.93 units²

• 8.38 units²

• 4.19 units²

Explanation Slide...

​

Multiple Choice

Find the estimated area of the shaded area. #7 $$Area_{ }=\frac{\theta\pi r^2}{360\degree}$$  

• 10.732 units squared

• 100.53 units squared

• 9.75 units squared

• 3,015.93 units squared

Converting Radians to degrees

Converting 200 degrees to radians

​Converting Radians to Degrees

Using trig to solve for a missing side

• Calculator in degree mode

• Set up trig ratio: SOHCAHTOA

• Solve for missing side

Using trig. to calculate an angle measure

• Calculator in degree mode

• Set up trig. ratio using the inverse function

Multiple Choice

Solve for x.

• 31.2

• 5.6

• 14.6

• 6.2

Multiple Choice

Solve for x.

• 17.2

• 27.1

• 8.3

• 30.9

Multiple Choice

$$\cos\left(\theta\right)=?$$  

• $$\frac{3}{5}$$  

• $$\frac{4}{5}$$  

• $$\frac{3}{4}$$  

• $$\frac{4}{3}$$  

You can use Pythagorean Theorem to calculate the missing side!

Types of Transformation

Multiple Choice

Where will A' be at, if triangle ABC is reflected by
(x,y) --> (-x,y)?

• (2,1)
• (1,-2)
• (-1,2)

Rotations

Multiple Choice

Rotation Rules (clockwise):

90^o rotation: (x, y)→(y, -x)

What are the coordinates for A' after a 90^⁰ rotation clockwise?

• (1, 3)

• (3, 1)

• (3, -1)

• (1, -3)

Multiple Choice

Point M (-3, 5) is translated using this rule.

(x, y) ----> (x - 1, y)

What are the coordinates of M'?

• (-4, 5)

• (-2, 5)

• (-4, 4)

• (-3, 4)

​Dilation

Multiple Choice

State the coordinate of the image of the given point B (4,9) under a dilation with center at the origin with the given scale factor of 2.

• B' (2 , 4.5)

• B' (-8 ,-18)

• B' (8 ,18)

• B' (9 ,4)

Multiple Choice

Warm - up: What are the important properties of dilations?

• Dilations change the sides and angles of the image

• Dilations preserve angle measures and all sides are scaled equally

• Only angles change

• One side can change without changing the others.

Multiple Choice

There are three isometric transformations. Which of the following is NOT an isometric transformation?

• Dilation

• Reflection

• Rotation

• Translation

A dilation is a transformation that ​enlarges or reduces an original figure proportionally.

​

Dilations!

Enlargement = gets bigger​

Reduction = gets smaller​

​

Triangle A is dilated to get Triangle B. What is the scale factor?

Example: Finding the scale factor

​

Is this an enlargement or a reduction?

Which Triangle is the preimage?

Multiple Choice

All angles in similar figures are congruent (the same).  

• True

• False

Multiple Choice

The ratio of two dilated shapes sides compared to the ratio of their perimeter is ...

• The same

• Squared

• Cubed

Multiple Choice

The ratio of two dilated shapes sides compared to the ratio of their areas is ...

• The same

• Squared

• Cubed

Multiple Choice

The ratio of two dilated solids sides compared to the ratio of their volumes is ...

• The same

• Squared

• Cubed

Multiple Choice

Solve for X.

• 2 ft
• 3 ft
• 4 ft
• 6 ft

Multiple Choice

Solve for BE

• 4.5
• 18
• 3.6
• 4

Multiple Choice

How long is the shadow?

• 3 ft

• 1 ft

• 2 ft

• 18 ft

• It cannot be determined

Multiple Choice

Are these triangles similar? If so, what is the similarity condition?

• AA~

• SSS~

• SAS~

• Not Similar

Multiple Select

Which of the following are similarity conditions?

• SSA~

• AA~

• SAS~

• SSS~