Free Printable Semester 2 Final Review 2020-2021

1.

What is the longest side of a right triangle called?

a)

Leg A

b)

Leg B

c)

Hypotenuse

d)

Pythagoras' Big Buddy

2.

Determine if the following set of numbers are Pythagorean Triples.
15, 20, 25

a)

Yes

b)

No

3.

The Pythagorean Theorem ONLY works on which triangle?

a)

obtuse

b)

scalene

c)

isosceles

d)

right

4.

In a right triangle, if a = 8 and c = 17, what is the correct setup to find the value of b?

a)

$17^2+8^2=b^2$

b)

$8^2+b^2=17^2$

c)

$17^2+b^2=8^2$

d)

$\frac{8^2}{b^2}=\frac{17^2}{100}$

5.

The longest side of a right triangle is DIRECTLY ACROSS from the...

a)

right angle.

b)

acute angle.

c)

obtuse angle.

6.

Find the length of the missing side.

a)

17 cm

b)

22 cm

c)

15 cm

d)

13 cm

7.

Sides a and b are called legs.

a)

true

b)

false

8.

State if the 3 sides form an acute, obtuse, or right triangle.

9, 14, 15

a)

acute

b)

right

c)

obtuse

9.

State if the 3 sides form an acute, obtuse, or right triangle.

3, 12, 13

a)

acute

b)

right

c)

obtuse

10.

Which side is the long leg in this 30-60-90 triangle? (not the hypotenuse)

a)

4

b)

u

c)

v

11.

Which side is the short leg of this 30-60-90 triangle?

a)

6

b)

m

c)

n

12.

What is the length of u and v in this 30-60-90 triangle?

a)

u = 8 v = 4√3

b)

u = 4√2 v = 8

c)

u = 16 v = 8

d)

u = 4√3 v = 8

13.

Find y.

a)

6

b)

24

c)

12√3

d)

6√3

14.

If you are given the SHORT LEG of a 30-60-90 triangle, how do you find the HYPOTENUSE?

a)

Multiply by 2

b)

Divide by 2

c)

Multiply by √3

d)

Divide by √3

15.

If you are given the SHORT LEG of a 30-60-90 triangle, how do you find the LONG LEG?

a)

Multiply by 2

b)

Divide by 2

c)

Multiply by √3

d)

Divide by √3

16.

Find a.

a)

9

b)

$9\sqrt{3}$

c)

$\frac{9}{2}$

d)

$6\sqrt{3}$

17.

What is the length of y in this picture?

a)

45

b)

5√2

c)

90

d)

5

18.

What is the length of x in this 45-45-90 triangle?

a)

4√2

b)

4

c)

8

d)

4√3

19.

Solve for a and b in the special right triangle.

a)

a = 5, b = 5

b)

a = 10, b = 10√2

c)

a = 10√2, b = 10√2

d)

a = 5√2, b = 5√2

20.

Give the Ratio for SIN X

a)

opp/adj

b)

Adj/hyp

c)

Opp/hyp

d)

adj/opp

21.

Give the Ratio for COS X

a)

Adj/Hyp

b)

Opp/Adj

c)

Adj/Opp

d)

Opp/Hyp

22.

Give the Ratio for TAN X

a)

Adj/Opp

b)

Opp/Adj

c)

Adj/Hyp

d)

Opp/Hyp

23.

Susan is flying a kite, which gets caught in the top of a tree. Use the diagram to estimate the height of the tree.

a)

63 ft

b)

65 ft

c)

74 ft

d)

87 ft

24.

Which one is the easy way to remember trigonometric ratios?

a)

Sah Coh Toa

b)

Soh Cah Toa

c)

Soh Cah Tao

d)

Soh Ceh Toa

25.

Choose the correct ratio.

a)

cos(33)=x/14

b)

sin(33)=x/14

c)

cos(33)=14/x

d)

sin(33)=14/x

26.

Choose the correct ratio.

a)

sin(37)=x/14

b)

cos(37)=x/14

c)

tan(37)=x/14

d)

sin(37)=14/x

27.

What is the cosine of angle P?

a)

p/q

b)

q/r

c)

p/r

d)

r/q

28.

Which trig function would you use to solve for x?

a)

$\sin37=\frac{11}{x}$

b)

$\cos37=\frac{11}{x}$

c)

$\tan37=\frac{11}{x}$

29.

Which trig function would you use to solve for x?

a)

$\sin40=\frac{x}{19}$

b)

$\cos40=\frac{x}{19}$

c)

$\tan40=\frac{x}{19}$

30.

a)

9/41

b)

40/41

c)

9/40

d)

3/10

31.

a)

7/24

b)

14/50

c)

48/41

d)

48/50

32.

Use inverse trig ratios (SOH CAH TOA) to solve for the missing angle

a)

33°

b)

49°

c)

39°

d)

41°

33.

A 10 ft. tree creates a shadow that is 15 ft. long. Find the angle of elevation of the sun.

a)

34 degrees

b)

56 degrees

c)

72 degrees

d)

15 degrees

34.

To the nearest whole degree.

a)

66^°

b)

24^°

c)

22^°

d)

^37°

35.

Round your answer to the nearest tenth.

a)

36.9^°

b)

31.0^°

c)

59.0^°

d)

53.1^°

36.

Which trigonometric function would you use to find "h", the height of the tree?

a)

sine

b)

cosine

c)

tangent

d)

none of these

37.

A 10 ft. tree creates a shadow that is 15 ft. long. Find the angle of elevation of the sun.

a)

34 degrees

b)

56 degrees

c)

72 degrees

d)

15 degrees

38.

Find the mistake

a)

tan 68 should be cos 68

b)

there is no mistake

c)

they should have divided

d)

x/14 should be 14/x

39.

From the top of a tower, a man finds that the angle of depression of a car on the ground is 30°. If the car is at a distance 40 meters from the base of the tower, how would you find the height of the tower?

a)

$\tan30\degree=\frac{x}{40}$

b)

$\tan30\degree=\frac{40}{x}$

c)

$\tan60\degree=\frac{x}{40}$

d)

$\sin30\degree=\frac{40}{x}$

40.

B represents...

a)

Area of Base

b)

Base

c)

Bottom

d)

Area of Bridge

41.

What does the "B" in the volume formula V = B x h stand for?

a)

Bottom of the object

b)

Box

c)

Between

d)

Area of the base

42.

Volume is the amount of space an object takes up.

a)

True

b)

False

43.

What is this formula used to find?
V=πr²h

a)

The volume of a cylinder

b)

The volume of a cone

c)

The volume of a sphere

d)

The area of a circle

44.

What formula do you need to find the area of the base of a cone and cylinder?

a)

A= bh

b)

A= 1/2bh

c)

A=πr²

d)

V= Bh

45.

Find the volume.

a)

13680 m³

b)

684 m³

c)

1140 m³

d)

228 m³

46.

Find the volume of the cone. Round your answers to the nearest tenth.

a)

320.4 in³

b)

314 in³

c)

205.5 in³

d)

267.4 in³

47.

Find the volume of a HEMIsphere with a radius of 4.

a)

85.3π

b)

62.67π

c)

42.67π

d)

8π

48.

Find the volume of the figure.

a)

126 cm³

b)

907.5 cm³

c)

605 cm³

d)

55 cm³

49.

Find the volume of the solid shown in the figure?

a)

7230

b)

6621

c)

1130

d)

907

50.

What is the formula for the volume of a prism?

a)

V = P*h

b)

V = B*h

c)

V = (1/3)P*h

d)

V = (1/3)B*h

51.

What is the formula for volume of a CONE?

a)

V = π r²

b)

V = π r² h

c)

V = ⅓ π r² h

d)

V = ⅓ L W H

52.

What is the formula for the volume of a pyramid?

a)

V = P*h

b)

V = B*h

c)

V = (1/3)P*h

d)

V = (1/3)B*h

53.

What is the volume formula for a sphere?

a)

V = (4 ∕ 3)πr³

b)

V = (1 ∕ 3)πr²h

c)

V = πr²h

d)

V = (1 ∕ 3)Bh

54.

What is the formula for volume of a CYLINDER?

a)

V = π r²

b)

V = π r² h

c)

V = ⅓ π r² h

d)

V = ⅓ L W H

55.

Find the slant height of the pyramid.

a)

28 cm

b)

25 cm

c)

21 cm

d)

24 cm

56.

Find the volume of the hemisphere.

a)

36 km³

b)

18 km³

c)

56.52 km³

d)

113.04 km³

57.

Find the volume of this square pyramid.

a)

214.8 m³

b)

586.7 m³

c)

1818.2 m³

d)

not enough information

58.

Write the equation of a circle with center (h,k) and radius r.

a)

x² + y² = r²

b)

(x + h)² + (y + h)² = r²

c)

(x - h)² + (y - k)² = r²

d)

(x - h)² - (h - k)² = r

59.

Write the equation at the origin with radius 6.

a)

x² + y² = 6

b)

x² + y² = 36

c)

x + y = 6

d)

x + y = 36

60.

What is the center of a circle with equation (x-4)² + y² = 5?

a)

(-4, 0)

b)

(4, 0)

c)

(4, 1)

d)

(-4, 1)

61.

Which of the following is the equation of a circle with a center at (-1,3) and a radius of 4?

a)

(x-1)²+(y+3)²=4

b)

(x-1)²+(y+3)²=16

c)

(x+1)²+(y-3)²=4

d)

(x+1)²+(y-3)²=16

62.

Determine the values of a, b, and c for the quadratic equation:

4x² – 8x = 3

a)

a = 4, b = -8, c = 3

b)

a = 4, b =-8, c =-3

c)

a = 4, b = 8, c = 3

d)

a = 4, b = 8, c = -3

63.

What is this formula?

a)

This is the standard formula.

b)

This is the quadratic formula.

c)

This is the square root formula.

d)

This is the Pythagorean formula

64.

Use the quadratic formula to find the solutions for

y = -x² - 5x + 12

a)

No Real Solution

b)

c)

d)

65.

Solve using the quadratic formula...

9x² = 4 + 7x

a)

b)

c)

d)

No solution

66.

$3x^2-10x+1=0$

Solve using the quadratic formula. Leave your answer in exact form.

a)

$x=\frac{-10\pm\sqrt{88}}{6}$

b)

$x=\frac{-5\pm2\sqrt{22}}{3}$

c)

$x=\frac{10\pm\sqrt{112}}{6}$

d)

$x=\frac{5\pm\sqrt{22}}{3}$

67.

3a + 9 + 4a = 2

a)

-1

b)

1

c)

no solution

d)

-7

68.

4(a + 3) = -32

a)

-11

b)

-44

c)

-20

d)

-8

69.

Solve. 9x - 12 = 33

a)

45

b)

-5

c)

5

d)

-9

70.

Solve 3x - 7 = 32

a)

13

b)

3

c)

12

d)

7

71.

Solve. 2x + 10 = 16

a)

6

b)

3

c)

26

d)

13

72.

If the coefficient of the variable is a fraction, dividing both sides by a fraction is the same as...

a)

dividing by a whole number

b)

subtracting the fraction

c)

using order of operations

d)

multiplying by the reciprocal

73.

Solve:

\frac{3}{4}b=24

a)

32

b)

36

c)

24

d)

18

74.

Solve the equation. Check your solution.

a)

-90

b)

90

c)

-40

d)

-180

75.

$\frac{2}{9}w=24$

a)

$w=801$

b)

$w=10$

c)

$w=108$

d)

$w=110$

76.

Factor Completely:

x²- 7x - 8

a)

(x + 1)(x - 8)

b)

(x + 1)(x + 8)

c)

5(x + 4)(x + 5)

d)

(x - 1)(x + 8)

77.

Factor Completely: 5x²- 11x + 6

a)

(5x + 6)(x - 1)

b)

(5x - 6)(x - 1)

c)

(2x - 7)(x - 3)

d)

(5x - 6)(x + 1)

78.

Factor Completely:

x² - 17x + 72

a)

(x - 9)(x + 8)

b)

(x - 9)(x - 8)

c)

x(x - 3)

d)

(x + 9)(x + 8)

79.

Factor Completely: 5x²-11x+6

a)

(5x+6)(x-1)

b)

(5x-6)(x-1)

c)

(2x-7)(x-3)

d)

(5x-6)(x+1)

80.

Factor:
2x² + 13x + 15

a)

(2x + 1)(x + 15)

b)

(x + 3)(x + 5)

c)

(2x - 3)(x - 5)

d)

(2x + 3)(x + 5)

Semester 2 Final Review 2020-2021

Total questions: 80

Worksheet time: 3hrs 29mins

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