Math 2 Final Review

Similar Triangles & Trig

Quadratics

Transformations & Congruence

Functions
(Inverse, Radical, etc.)

Probability

100

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: k² - 31 -2k = -6 -3k² -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 3x²

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 = x² – 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 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

You choose a card from a standard deck, without replacing it. Your friend chooses another card. The probability that you will both draw diamonds.

What is 1/17?

(13/52)(12/51)

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 – w² = –w² + 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: Corresponding, Vertical, Alternate interior, Alternate exterior

Supplementary: Same side interior, Same side exterior, Linear pair

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

The probability of drawing a queen or drawing a diamond.

What is 16/52?

(13/52) + (4/52) - [(13/52)(4/52)]

400

A ladder is leaning up against the wall of a building. The angle of depression is 60 degrees. If we know the bottom of the ladder is 15 feet away from 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) = 2t² -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

A 10side die numbered 1-10is tossed. Which of the following represents mutually exclusive events? (can not occur at the same time)

A. Roll a 2 or a number > 5

B. Roll an odd or prime number

C. Roll an odd number or a number > 5

D. Roll a number > 3 or a number > 7

What is A. Roll a 2 of a number > 5?

500

A building is 54 feet high. The diagonal distance from the top of the building to the end of the shadow that it casts is 62 feet long. What is the angle of elevation? *HINT*- use trig identities and draw a picture.

What is sin^-1(54/62) = 61 degrees

500

Solve the following equation and identify all possible solutions: 8x² -4x + 5 = 0

What is (1 + - 3i) / 4

500

See file Jeopardy Transformations and Congruence for 500

What is

1. Given

2. QS is congruent to TS

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?

What is 1. .665 2. .985