Are the following triangles similar? if so, state the reason and the scale factor:
Triangle ABC is a right triangle: it's legs are 6cm and 8 cm.
Triangle DEF is a right triangle: It's legs are 18cm and 24cm.
What is
Yes. By SAS, since the right angle is between the two legs and the legs of the triangles have a scale factor of 3.
100
Solve the following equation by using the quadratic formula:
k^2 - 31 -2k = -6 -3k^2 -2k
What is
k = 5/2 and k = -5/2
100
Which of the following is NOT a way to prove triangles congruent: *NOTE* it is okay to have more than one choice for your answer.
SSS SSA AA SAS AAS HL
What is
SSA and AA.
100
Convert the following equation between rational and radical form:
(3x)^2/4
What is
The fourth root of 3x^2
100
Assume the population of a school is 1000. If a student is randomly selected, the chance that this randomly selected student is male is .47. what is the number of females enrolled in this school?
What is
530 females
200
What are the only three theorems we can use to argue two triangles being similar?
What is
AA, SSS, SAS
200
Which function is equivalent to y = x^2 – 6x + 10?
A y = (x + 3)2 – 1
B y = (x – 3)2 + 1
C y = (x + 6)2 – 10
D y = (x – 6)2 + 10
What is
What is
B) y = (x-3)^2 +1
200
A square with points A (-3,3), B (-3,6), C (-6,3), D (-6,6) is reflected across the x-axis. What are the points of the image of this square?
What is
A'(-3,-3) B'(-3,-6) C'(-6,-3) D'(-6,-6)
200
The length of a rectangular prism is 4sqrt(3) units. The height is 3sqrt(6) units. If the volume is irrational, which could be the measure of the width of the rectangular
prism?
A 2(sqrt)50
B 4(sqrt)12
C 5(sqrt) 8
D 7(sqrt)18
What is
B) 4(sqrt)12
200
True or false: In probability, "and" means add and "or" means multiply.
What is
False! It's the other way around!
300
A ship is anchored to a seabed. We know that the rope anchoring the boat is 30 m long, and the angle where the rope meets the seabed is 39 degrees. Use the correct trig identity to find out how deep we would need to go to reach the seabed is. *HINT*- draw a picture!
What is
Use sin(39) = x/30
Answer: 18.88 m deep
300
You have a 500-foot roll of fencing and a large field. You want to construct a rectangular playground area. What are the dimensions of the largest such yard? What is the largest area?
What is
A = Lw = (250 – w)w = 250w – w^2 = –w^2 + 250w
The largest area will have dimensions of 125 by 125,
for a total area of 15,625 square feet
300
Separate the following angle relationship pairs into two categories: Those which are congruent and those which are supplementary.
Corresponding Alternate exterior
Vertical Same side interior
Same side exterior Alternate interior
Linear pair
What is
Congruent: Supplementary:
Corresponding Same side exterior
Vertical Same side interior
Alternate exterior Linear pair
Alternate interior
300
The graph of f(x) = 2x2 – 3x + 5 will be translated 8 units down, producing the
graph of q(x). Which equation represents the new function, q(x)?
A q(x) = 2x^2 – 3x – 3
B q(x) = 2x^2 – 11x + 5
C q(x) = 2x^2 – 3x + 13
D q(x) = 2x^2 + 5x + 5
What is
A) q(x) = 2x^2-3x-3
300
A cube number 1-6 is rolled three times. What are the chances that the cube lands on 2 all three times?
What is
.004, less than one percent chance!
400
A ladder is leaning up against the wall of a building. The angle where the ladder meets the ground is 30 degrees. If we know the bottom of the ladder is 15 feet of the wall, what is the length of the ladder? *HINT* - use trig identities and draw a picture
What is
*SPECIAL TRIANGLE* 30-60-90
ladder length = hypotenuse = 30
400
The flight of a rocket launched in the air can be modeled by the function f(t) = 2t^2 -7t -3 where t is time in seconds and f(t) is height (in feet) of the rocket. How many seconds will it take for the rocket to return to the ground?
What is
3.89 seconds
400
A triangle with vertices (2,-2), (-5,3) and (3,6) will be rotated 90 degrees clockwise around the origin and then reflected across the y-axis producing a triangle image. Which additional transformation will map the triangle back to it's original points?
A rotation 270° counterclockwise around the origin
B rotation 180° counterclockwise around the origin
C reflection across the line y = –x
D reflection across the line y = x
What is
D) reflection across the line y = x.
400
Describe the intervals of increasing and intervals of decreasing for the function -x^2 + 10
What is
increasing from (-infinity to 10)
decreasing from (10 to infinity)
400
Suppose you are renting a car. The chance that the car selected for you is a sedan is .48. The chance that this car is red is .30. The chance that your car is both a sedan and red is .12. If you are told ahead of time that your car is a sedan, what is the chance that you also get a red car?
*HINT* probability of a given b.
What is
conditional probability! Probability of both/ probability of b
.12/.30 = .4
There is a forty percent chance of this.
500
A building that is 54 feet high casts a shadow that is 72 feet long. What is the angle where the shadow meets the ground? *HINT*- use trig identities and draw a picture.
What is
arcsin(54/72) = 60 degrees
500
Solve the following equation and identify all possible solutions:
8x^2 -4x + 5 = 0
What is
1 + - 3i / 4
500
Given: Triangle QSR and triangle TSR are right triangles, QS is congruent to TS
Prove: Triangle QSR is congruent to triangle TSR
*HINT*- draw it out!
Statements: Reasons:
1. Triangle QSR and triangle TSR 1.
are right triangles
2. 2. Given
3. 3. Reflexive property
4. Angle QRS is congruent to 4. All right angles are
angle TSR congruent
5. 5. HL
What is
Statements: Reasons:
2. QS is congruent to TS 1. Given
3. SR is congruent to SR
5. Triangle QSR is congruent to
triangle TSR
500
Sketch a graph to demonstrate the following inequality:
-b^2 + 8b - 10 > 0
What is
U shaped graph with zeros at 1.55 and 6.45. Graph should be shaded between the two zeros.
500
Cassie is worried about her upcoming exams. She predicts that there is a 95 percent chance she will pass her Math 2 exam, and a 70 percent chance she will pass her World History Exam.
1. What is the probability Cassie passes both her exams?
2. What is the probability Cassie passes at least one of her exams?