Free Printable Units 8, 6, & 7 Potpourri Exam

1.

1. Consider the triangle shown. Explain how you know the given triangle is a 45°, 45°, 90° triangle.

a)

The triangle has two equal sides and one right angle.

b)

The triangle has three equal sides.

c)

The hypotenuse is equal to the leg times the square root of 2 (about 1.41)

d)

The triangle has one right angle and two different angles.

2.

Consider the triangle shown. Find the missing length.

a)

6

b)

5

c)

7

d)

8

3.

Consider the triangle shown. Which of the following explains how you know the given triangle is a 45°, 45°, 90° triangle?

a)

The triangle has two equal sides, and thus two equal angles.

b)

The triangle has three equal sides.

c)

The triangle has two right angles.

d)

The triangle has one angle greater than 90°.

4.

Consider the triangle shown. b. Find the length of the hypotenuse.

a)

3√2

b)

2√2

c)

4

d)

5

5.

The hypotenuse of a 45°, 45°, 90° triangle has a length of 20 centimeters. Find the length of a leg of the triangle.

a)

10√2 or 20/√2

b)

10

c)

20

d)

5√2

6.

The hypotenuse of a 45°, 45°, 90° triangle has a length of 68 centimeters. Find the length of a leg of the triangle.

a)

34√2 or 68/√2

b)

34

c)

68

d)

68√2

7.

Find the value of x.

a)

17√2

b)

17

c)

34

d)

Not enough information.

8.

Find the value of x.

a)

22

b)

22√2

c)

11√2 or 22/√2

d)

11

9.

Which is equivalent to: √48?

a)

4√3

b)

2√12

c)

3√6

d)

9√3

10.

Which is equivalent to 32/√2?

a)

16√2

b)

8√2

c)

32√2

d)

4√2

11.

11. △CAR is shown. a. Find m∠C.

a)

m∠C = 66

b)

m∠C = 45°

c)

m∠C = 90°

d)

m∠C = 30°

12.

Find CA.

a)

CA = 24√2

b)

CA = 30

c)

CA = 20

d)

CA = 15

13.

In △HOG, m∠H = 60°, m∠O = 90°, and m∠G = 30°. Find $\frac{OH}{GH}$ .

a)

$\frac{OH}{GH} = \sqrt{3}$

b)

$\frac{OH}{GH} = 1$

c)

$\frac{OH}{GH} = \frac{1}{2}$

d)

$\frac{OH}{GH} = 2$

14.

In a 30°, 60°, 90° right triangle TOP, side TO is opposite the 30° angle and side OP is the hypotenuse. How many times greater is OP than TO?

a)

OP is 2 times greater than TO

b)

OP is 1.5 times greater than TO

c)

OP is 3 times greater than TO

d)

OP is 4 times greater than TO

15.

In right triangle LET, the ratio $\frac{ET}{LE} = \frac{1}{2}$ . What is the measure of ∠L if LE is the hypotenuse of the triangle?

a)

∠L = 60°

b)

∠L = 45°

c)

∠L = 30°

d)

∠L = 90°

16.

△ABC is shown (not drawn to scale). Which of the following statements is true?

a)

△ABC is a 30°, 60°, 90° triangle.

b)

△ABC is a 45°, 45°, 90° triangle.

c)

△ABC is a equilateral triangle.

d)

The side lengths given for △ABC do not make a right triangle.

17.

Is the following statement always, sometimes, or never true?

"Two triangles with different side lengths are similar figures"

a)

Always

b)

Sometimes

c)

Never

18.

Are the following statements always, sometimes, or never true? b. Two triangles with different side lengths are congruent figures.

a)

Always

b)

Sometimes

c)

Never

19.

Is the following statements always, sometimes, or never true?

"Two circles with different radii are similar figures"

a)

Always

b)

Sometimes

c)

Never

20.

The image of a basketball (shown to the left) was scaled to produce the image in Figure 2 (to the right). This scaling represents:

a)

an enlargement

b)

a reduction

21.

If triangle ABC is dilated about point A with a scale factor of $\frac{1}{2}$ , what is the slope of line segment B'C'?

a)

The slope of line segment B'C' is the same as the slope of BC, which is $\frac{2}{-3}$ .

b)

The slope of line segment B'C' is undefined.

c)

The slope of line segment B'C' is 0.

d)

The slope of line segment B'C' is 1.

22.

If triangle ABC is dilated about point B with a scale factor of 2, what is the slope of line segment A'B'?

a)

0

b)

-2/3

c)

3/-2

d)

undefined

23.

Lindsey was dilating a rectangle by a scale factor of 2. In the original rectangle, the sum of the 4 angles was 360°. She predicted that the sum of the 4 angles would be twice as large or 720°. Is Lindsey’s prediction correct?

a)

Yes, the sum of the angles will be 720°.

b)

No, the sum of the angles will remain 360°.

c)

Yes, because the scale factor affects the angles.

d)

No, the sum becomes 180 because the figure becomes a triangle.

24.

Write the equation of the circle shown.

a)

$(x-3)^2+(y+2)^2=25$

b)

$(x + 3)^2 + (y - 2)^2 = 16$

c)

$(x+3)^2+(y+2)^2=25$

d)

$(x + 3)^2 + (y + 2)^2 = 16$

25.

Write the equation of the circle shown.

a)

$(x-3)^2+(y+2)^2=20$

b)

$(x + 3)^2 + (y - 2)^2 = 16$

c)

$(x-3)^2+(y+4)^2=20$

d)

$(x + 3)^2 + (y + 2)^2 = 16$

26.

Write an equation of a circle that is centered at the origin and has a diameter of 18.

a)

$x^2 + y^2 = 81$

b)

$x^2 + y^2 = 36$

c)

$x^2 + y^2 = 18$

d)

$x^2 + y^2 = 9$

27.

Consider the circle given by $(x - 3)^2 + (y + 4)^2 = 16$ . In which quadrant is the center of the circle?

a)

Quadrant I

b)

Quadrant II

c)

Quadrant III

d)

Quadrant IV

28.

Consider the circle given by $(x - 3)^2 + (y + 4)^2 = 16$ . What is the radius of the circle?

a)

2

b)

3

c)

4

d)

5

29.

Is (-1, -4) a point inside, on, or outside the circle given by $(x + 3)^2 + (y - 1)^2 = 25$ ?

a)

Inside the circle

b)

On the circle

c)

Outside the circle

30.

Is (0, 0) a point inside, on, or outside the circle given by $(x - 2)^2 + (y - 3)^2 = 16$ ?

a)

Inside the circle

b)

On the circle

c)

Outside the circle

31.

A circle has an area of 84 square inches. Find the radius of the circle, to the nearest hundredth.

a)

4.61 inches

b)

5.17 inches

c)

5.18 inches

d)

5.19 inches

32.

A circle has an area of 100 square centimeters. Find the radius of the circle, to the nearest hundredth.

a)

5.64 cm

b)

5.65 cm

c)

5.66 cm

d)

5.67 cm

33.

A circle has a circumference of 44 mm. Find the radius of the circle, to the nearest hundredth.

a)

6.99 mm

b)

7.00 mm

c)

7.01 mm

d)

7.02 mm

34.

A circle has a circumference of 18 inches. Find the radius of the circle, to the nearest hundredth.

a)

2.87 inches

b)

2.86 inches

c)

2.85 inches

d)

2.84 inches

35.

A semicircle is cut out of a larger semicircle with a radius of 12 in. The resulting shape is shown. Find the area of the shape.

a)

113.04 in²

b)

169.65 in²

c)

339.12 in²

d)

452.16 in²

36.

A semicircle is added to the side of a quarter circle, as shown in the image. The radius of the quarter circle is 50 cm. Find the area of the shape.

a)

7850 cm²

b)

3925.76 cm²

c)

2945.24 cm²

d)

3140.92 cm²

37.

The shape shown is made up of three semicircles, centered at A, B, and C, respectively. If B is the midpoint of AC and AC = 12 m, find the area of the shape.

a)

72π m²

b)

54π m²

c)

36π m²

d)

18π m²

38.

JL is a diameter of the circle centered at K. JK and LK are diameters of the semicircles shown in the figure. The length of JL is 36 inches. What is the area of the shaded region?

a)

324π square inches

b)

162π square inches

c)

648π square inches

d)

81π square inches

39.

The circumference of a circle is 22π cm. Find the area of the circle.

a)

121π cm²

b)

44π cm²

c)

77π cm²

d)

154π cm²

40.

The circumference of a circle is 30π cm. Find the area of the circle.

a)

225π cm²

b)

150π cm²

c)

75π cm²

d)

100π cm²

41.

Find the value of y.

42.

What is the measure of x?

a)

12

b)

15

c)

6

d)

9

43.

To measure the distance across a pond, a surveyor locates points A, B, C, D, and E as shown. What is AB to the nearest meter?

a)

10

b)

12

c)

15

d)

18

44.

Determine whether the triangles are similar by AA~, SSS~, SAS~, or not similar.

a)

AA

b)

SSS

c)

SAS

d)

Not similar

45.

Determine whether the triangles are similar by AA~, SSS~, SAS~, or not similar.

a)

AA

b)

SSS

c)

SAS

d)

no similar

46.

Determine whether the triangles are similar by AA~, SSS~, SAS~, or not similar.

a)

SSS

b)

AA

c)

SAS

d)

not similar

47.

Are the following similar? Why or why not?

a)

Yes, because the corresponding angles are congruent.

b)

No, the numbers are even

c)

No, the sides are 2 times larger, but the width is the same.

48.

The scale drawing car length is 3 cm. If the scale is 1 cm:4 ft, what is the actual car length?

a)

12 feet

b)

16 feet

c)

10 feet

d)

4 feet

49.

The distance between two cities on a map is 4.125 inches. Find the actual distance if the scale on the map is 2 inches = 40 miles.

a)

165 miles

b)

50 miles

c)

82.5 miles

d)

41.25 miles

50.

What is the Scale Factor from ΔDEF (original) to ΔABC (new)?

a)

1/2

b)

7/3

c)

2

d)

10/3

51.

What is the Scale Factor from ABCD (original) to MNOP (new)?

a)

2/3

b)

3/2

c)

2

d)

3

52.

Find x.

a)

10

b)

$10\sqrt{3}$

c)

$10\sqrt{2}$

d)

20

53.

Find a.

a)

12

b)

24

c)

$24\sqrt{3}$

d)

16

Units 8, 6, & 7 Potpourri Exam

Total questions: 53

Worksheet time: 53mins

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