Free Printable 24-25 Geometry Concepts & Connections Post Benchmark (YL)

1.

Triangles ABC and DEF are similar. Find the length of segment EF.

a)

5 cm

b)

8.8 cm

c)

12 cm

d)

14 cm

2.

If m∠A = 110 degrees and m∠B = 35 degrees, find m∠1.

a)

35 degrees

b)

55 degrees

c)

75 degrees

d)

145 degrees

3.

What is the probability of flipping a quarter 3 times and getting all heads?

a)

1/2

b)

1/8

c)

3/2

d)

3/8

4.

A rectangular park, with dimensions of 1500 feet by 2000 feet, has a diagonal walking path that goes from the top northeast corner to the bottom southwest corner. How long is the walking path?

a)

2500 feet

b)

2000 feet

c)

1750 feet

d)

3000 feet

5.

The special at a local pizza place says you can choose any 3 toppings from a list of 5. How many possible combinations are there?

a)

8

b)

10

c)

12

d)

15

6.

What is $(3x^4 + 2x^2 - 6)$ subtracted from $(4x^4 + 2x^2 - 6)$ ?

a)

$x^4$

b)

$-x^4$

c)

$x^4 - x^2 - 3$

d)

$7x^4 - x^2 - 9$

e)

$x^4 + 5x^2 - 9$

7.

Tony needs to create a platform shaped like the diagram with the labeled dimensions. How many cubic feet of concrete are required?

a)

60 cubic feet

b)

81 cubic feet

c)

108 cubic feet

d)

135 cubic feet

8.

Determine the area of the green sector in the circle with a radius of 3 in and a yellow sector of 75°.

a)

(5/4)π in²

b)

(57/8)π in²

9.

Find A ∩ B.

a)

{3,5,6,7,8,11,12}

b)

{3,5,6,7,8,12}

c)

{3,7,6,5}

d)

{3,7}

10.

Michelle draws a card from a standard deck of 52 cards. She replaces the card and draws a second card. What is the probability that she draws a heart and then a spade?

a)

1/16

b)

1/26

c)

1/4

d)

1/52

11.

Given: m∠BJE = 170°, m∠DCE = 44° Find m∠DOB.

a)

36.5°

b)

73°

c)

107°

d)

136°

e)

170°

12.

A city planner needs to verify that Main Street and Oak Street are parallel to each other. Which angles must be congruent to prove this?

a)

∠1 and ∠2

b)

∠1 and ∠4

c)

∠1 and ∠3

d)

∠2 and ∠4

13.

Convert $\frac{7\pi}{21}$ to degrees.

a)

30°

b)

60°

c)

90°

d)

120°

14.

In a dice game if you roll a 2, 4, or 6 you get the value of the die. If you roll as 1, 3, or 5 you lose $5. What is the expected value of the game?

a)

-$1.00

b)

-$0.50

c)

$0.50

d)

$1.00

15.

Which basic construction is shown here?

a)

bisect a line segment

b)

construct a parallel line

c)

construct a perpendicular line

d)

construct a perpendicular bisector

16.

Four rectangles are shown in the diagram. For which dilation is the ratio of the side lengths 1:2?

a)

D to C

b)

D to B

c)

C to B

d)

B to A

17.

Given that ΔUVW is similar to ΔXYZ, find the length of ZX.

a)

14

b)

16

c)

18

d)

20

e)

22

18.

The diagram shown here represents

a)

two intersecting lines.

b)

two intersecting planes.

c)

a ling intersecting one point

d)

Two intersection lines

19.

Which trig expression is equal to sin (72° - a)?

a)

cos 18°

b)

sin 18°

c)

cos (90° - (72° - a))

d)

sin (90° - (72° - a))

20.

Identify the center of the circle whose equation is $(x - 2)^2 + (y + 8)^2 = 16$ .

a)

(-2, -8)

b)

(-2, 8)

c)

(2, -8)

d)

(2, 8)

21.

What is the arc length of an angle of π/3 radians formed on the unit circle?

a)

π/6

b)

π/4

c)

π/3

d)

π/2

22.

Fiona interviewed her 30 classmates on whether or not they had a sibling and if they have assigned chores at home. She displayed her results in the two-way table shown. Which category had the highest relative frequency?

a)

Only Child

b)

Have a Sibling

c)

Do Not Have Chores

d)

Have Chores

23.

How many ways can 12 horses in a race come in 1st, 2nd, and 3rd place?

a)

1320

b)

720

c)

1560

d)

990

24.

At a County fair there is a spinner game with 12 sectors: 2 red sectors, 2 green sectors, 2 blue sectors, and 6 yellow sectors. If the spinner lands on a red sector, the player wins 2 tokens. If the spinner lands on a green sector, the player wins 2 tokens. If the spinner lands on a blue sector, the player wins 2 tokens. If the spinner lands on a yellow sector, the player loses 3 tokens. Is this game fair for the player and how much will the player win or lose on an average over time? Explain.

a)

County fair games are never fair.

b)

The expected value is zero, and the game is fair. So the player will break even for a single spin over time.

c)

The expected values is 1/2, and the game is fair. The player will win about 0.55 tokens on a single spin over time.

d)

The expected value is 0.5, and the game is not fair. So the player will lose about 0.5 tokens for a single spin over time.

e)

The expected value is -0.5, and the game is not fair. So the player will lose about 0.5 tokens for a single spin over time.

25.

Amy, Mark, and Hannah are playing a game with the given spinner. If the spinner lands on red, Amy wins $1.\ If\ the\ spinner\ lands\ on\ blue,Mark\ wins$ 2. If the spinner lands on green, Hannah wins $3. Is this a fair game? If not, who has the advantage?

a)

It is a fair game.

b)

It is not a fair game. Amy has the advantage.

c)

It is not a fair game. Mark has the advantage.

d)

It is not a fair game. Hannah has the advantage.

26.

If the line segment shown is reflected over the x-axis, what will be the new coordinates of point B?

a)

(4,-3)

b)

(-4,3)

c)

(-3,-4)

d)

(-3,4)

27.

What is the probability that a student has brown hair? (round to nearest hundredth)

a)

0.42

b)

0.45

c)

0.58

d)

0.82

e)

0.90

28.

Given that the population density of Georgia is 170 people per square mile and 10,100,000 people live in Georgia, what is the area of the state? (to the nearest hundred mi^2)

a)

50,000 mi^2

b)

50,500 mi^2

c)

58,800 mi^2

d)

59,400 mi^2

29.

Which operation is NOT closed for polynomials?

a)

adding binomials

b)

dividing binomials

30.

Estimate the size of a crowd standing along a 1 mile section of a parade route that is 10 feet deep on both sides of the street. Assume that each person occupies 2.5 square feet.

a)

21,120 people

b)

42,240 people

c)

84,480 people

d)

168,960 people

31.

What would be the BEST formula to model the volume of the teepee shown?

a)

V = πr²h/3

b)

V = πr²h

c)

V = 2πrh

d)

V = (4/3)πr³

32.

What would be the BEST formula to model the volume of an apple?

a)

volume of a cone

b)

volume of a sphere

c)

volume of a cylinder

d)

volume of a rectangular prism

33.

What is the probability of drawing a queen from a standard deck of 52 cards?

a)

1/13

b)

1/26

c)

1/52

d)

1/4

34.

Solve for the missing angle

a)

50

b)

0.053

c)

36.9

d)

95

35.

Add the polynomials: $(3x^3 + 2x^2 - x) + (x^3 - 4x^2 + 5)$ .

a)

$4x^3 - 2x^2 - x + 5$

b)

$4x^3 - 2x^2 + 5$

c)

$4x^3 - 2x^2 - x$

d)

$4x^3-2x^2-5x$

36.

Subtract the polynomials: $(6x^2 + 3x - 8) - (4x^2 - 2x + 5)$ .

a)

$2x^2 + 5x - 13$

b)

$2x^2 + 5x - 3$

c)

$2x^2 + x - 13$

d)

$2x^2 + x - 3$

37.

Convert to radians 390 degrees

a)

b)

c)

d)

38.

Which is the correct applied ratio?

a)

A

b)

B

c)

C

d)

D

39.

What is the correct equation to solve for x?

a)

tan (45) = x/13

b)

cos (45) = x/13

c)

sin (45) = 13/x

d)

sin (45) = x/13

40.

sin $\frac{\pi}{2}$

a)

$\frac{\sqrt[]{3}}{2}$

b)

$\frac{\sqrt[]{2}}{2}$

c)

$\frac{1}{2}$

d)

1

41.

sin 30°

a)

$\frac{1}{2}$

b)

$-\frac{1}{2}$

c)

$\frac{\sqrt[]{2}}{2}$

d)

$\frac{\sqrt[]{3}}{2}$

42.

Find the exact value of: sin(-240°)

a)

(√3)/2)

b)

(-1/2)

c)

(√2/2)

d)

(1/2)

24-25 Geometry Concepts & Connections Post Benchmark (YL)

Total questions: 42

Worksheet time: 37mins

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