Math 2 Honors Exam Review

The smallest angle of rotation for a heptagon

51.4 degrees

The smallest angle of rotation for a nonagon

40 degrees

The smallest angle of rotation for a octagon

45 degrees

What is the smallest angle of rotation that a regular pentagon and decagon have in common?

72 degrees

Reflection across x-axis

(x,-y)

Reflection across y-axis

(-x,y)

y=x

(y,x)

y=-x

(-y,-x)

Rotation 90 degrees counterclockwise (CCW)

(-y,x)

Rotation 90 degrees clockwise (CW)

(y,-x)

Rotation 180 degrees either direction

(-x,-y)

Rotation 270 degrees counterclockwise (CCW)

(y,-x)

Rotation 270 degrees clockwise (CW)

(-y,x)

The smallest angle of rotation for a pentagon

72 degrees

to find the smallest angle of rotation for a regular polygon…

360/# of sides

The smallest angle of rotation for a hexagon

60 degrees

The smallest angle of rotation for a decagon

36 degrees

To find scale factor:

image / pre image

Domain

pre image

Complementary angles

Two angles that add up to 90 degrees

Supplementary angles

two angles that add up to 180 degrees

Vertical angles

two angles formed when two lines intersect

linear pair

two adjacent angles that add to 180 degrees

corresponding angles

two angles that lie on the same side of the transversal in same relative positions

alternate interior angles

Interior angles that lie on opposite sides of the transversal

alternate exterior angles

exterior angles that lie on opposite sides of the transversal

consecutive interior angles

interior angles that lie on the same side of the transversal.

A + B = 180

consecutive exterior angles

exterior angles that lie on the same side of the transversal

A + B = 180

Scalene triangle

No sides or angles are congruent

Triangle sum theorem

The sum of the interior angles of a triangle adds to 180 degrees

Exterior angle theorem

theorems to prove 2 triangles are congruent

SSS, SAS, ASA, AAS, HL

theorems to determine if two triangles are similar

AA, SSS, SAS

Describe (x,y) → (x-4)(y+2)

The x value will go left 4, and the y value up 2

r x-axis ∘ T 3,4

Do (T 3,4) first, and (r x-axis) second

Dilation rule

f(x,y) → (Kx, Ky)

*k stands for scale factor

x=0

y axis

c² < a² + b²

acute

c² > a² + b²

obtuse

45-45-90 Triangle Theorem

L = H divided by√2

H = L√2

30-60-90 Triangle Theorem

LL = SL√3

SL = H/2 or LL / √3

H = 2 SL

Sine

opposite / hypotenuse

Cosine

adjacent / hypotenuse

Tangent

opposite / adjacent

Vertical stretch

a > 1

Vertical compression

a < 1

Vertex form of a quadratic equation

f(x) = -a (x-h)² + k

Vertex

(h,k)

How to find vertex when it’s standard form

-b / 2a

Quadratic Formula

x=(-b±√(b²-4ac))/(2a)

Direct variation

y = kx

To find k: y/x

Inverse variation

y = k/x

To find k: x * y

Pick a card from a standard deck of cards without replacement, and then select another card

dependent

roll a die and then spin a spinner

independent

Mutually Exclusive Events

Two events cannot occur at the same time

P (A or B) = P (A) + P (B)

Inclusive Events

Two events can occur at the same time

P (A or B) = P (A) + P (B) - P (A and B)

P (B | A) =

P ( A and B) / P (A)