Math Semester 2 Final Flashcards

1
Q

Standard Equation of a Circle

A

(x - h)² + (y - k)² = r²

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1
Q

Density

A

D = mass/volume

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2
Q

Arc Area

A

(Area of sector / πr²) = (measure of arc / 360)

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3
Q

Arc Length

A

(Arc length / 2πr) = (measure of arc / 360)

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4
Q

Circumference

A

C = 2πr

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5
Q

Area of a Circle

A

A = πr²

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6
Q

Prism Volume

A

V = Bh
(B = area of base)

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7
Q

Cylinder Volume

A

V= πr²h

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8
Q

Cone Volume

A

V =1/3 x πr²h

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9
Q

Pyramid Volume

A

V = 1/3 x Bh

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10
Q

Sphere

A

V = 4/3 x πr³

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11
Q

Special Right Triangles

A

45-45-90: legs = x. hypotenuse = x√2

30-60-90:
Leg next to 60 = x
Leg next to 30 = x√3
Hypotenuse = 2x

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12
Q

Geometric Mean: Altitude

A

CD² = AD x BD
Altitude = part x part of hypotenuse

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13
Q

Geometric Mean: Leg

A

CB² = DB x AB
Leg = corresponding part x whole

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14
Q

Sine

A

Sin = opposite/hypotenuse

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15
Q

Cosine

A

Cos = adjacent/hypotenuse

16
Q

Tangent

A

Tan = opposite/adjacent

17
Q

Two Secants Outside a Circle

A

m∠1 = 1/2 (mBD - mAC)
EA x EB = EC x ED

18
Q

Secant and Tangent Outside

A

mm∠1 = 1/2 (mAD - mAC)
EA² = EC x ED

19
Q

Intersecting Chords Inside

A

m∠1 = 1/2 (mAC + mDB)
EA x EB = EC x ED

20
Q

Volume of a Regular Polygon

A

V = 1/2a x (n x s)

21
Q

Trapezoid Area

A

A = 1/2 (b1 + b2) x h

22
Q

Sine and cosine add up to _____ degrees.

A

90

23
Q

What are the similarity theorems?

A

SSS and AA

24
Q

In a quadrilateral inscribed in a circle, opposite angles are…

A

Supplementary

25
Q

Measure of an Inscribed Angle Theorem

A

The measure of an inscribed angle is half the measure of its intercepted arc. Intercepted arc = central angle.

26
Q

Convert degrees to radians

A

degree/180 x π = rad

27
Q

Convert radians to degrees

A

rad x 180 = degree

28
Q

To complete the square you add _____ to both sides.

A

c = (b/2)²

29
Q

Tangent and Intersected Chord Theorem

A

If a tangent intersects a circle, the measure of each angle formed is half that of the intercepted arc.

30
Q

Tangents are perpendicular to the ______ of a circle

A

Radius/Diameter

31
Q

Circumscribed Angle Theorem

A

The measure of a circumscribed angle is equal to 180 minus the central angle.

32
Q

External Tangent Congruence Theorem

A

Tangent segments from a common external point are congruent.