CRCT Review

Transformations:◦ Translation:

slide◦ Rotation:

turn◦ Reflection:

flip/mirror image◦ Dilation:

enlarge / reduce

Types of Transformations

Rules:◦ Rotation

90 around the origin (x, y) -> (y, -x)

180 around the origin (x, y) -> (-x, -y)

270 around the origin(x, y) -> (-y, x)

◦ Reflection Over the x- axis (x, y) ->

(x, -y) Over the y-axis (x, y) ->

(-x, y)

◦ Translation (x, y) -> Up/down add to the Y Left/Right add to the X

◦ Dilation (x, y) -> Multiple to both the x and y

Transformation

Congruent◦ Same Shape, Same Angles, Same Size

Similar◦ Same Shape, Same Angles, DIFFERENT Size

Congruent VS Similar

Opposite / Vertical angles:◦ When 2 angles intersect; share a vertex

Corresponding angles:◦ Same position; same side of transversal

Alternate exterior angles: ◦ Outside of parallel lines, opposite side of transversal

Alternate interior angles: ◦ Inside of parallel lines, opposite side of transversal

Supplementary angles: ◦ Angles that form a straight line

Complementary angles: ◦ Angles that form a right angle

Angles

Anglesa)Opposite / Vertical angles

b)Corresponding angles

c) Alternate exterior angles

d)Alternate interior angles

e)Supplementary angles

f) Complementary angles

Exterior Angles

Example: Angle a = 57Angle b = 68

What is the measure of Angle d?

( x m ) ( x n ) = x( m + n )

Ex: (x3)(x4) =

( xm ) n = x m n

Ex: (x2)4 =

Exponents

Negative Exponents – rewrite as a fraction ex: =

Any base raised to the zero power has a value of 1

Exponents

Very LARGE numbers will have a POSITIVE exponent

Very SMALL numbers will have a NEGATIVE exponent

Scientific Notation

Write in decimal notation: 3.6 × 108

Convert 4.2 × 10–7 to decimal notation.

Convert 93,000,000 to scientific notation.

Scientific Notation

Simplify and express in scientific notation: (2.6 × 105) (9.2 × 10–13)

Simplify and express in scientific notation: (8.2 × 10–3) ÷ (4 × 10–2)

Scientific Notation

Rational #s= fractions, repeating decimals, terminating decimals, whole numbers, perfect square roots

Irrational #s= non-terminating and non-repeating decimals, non-perfect squares, and pi

Rational and Irrational #s

http://www.math-play.com/rational-and-irrational-numbers-game/rational-and-irrational-numbers-game.html

Square Roots

Cube Roots

Non-perfect square roots Find the perfect squares that are closest to

the number. Estimate a value between the square roots

of the two closest perfect squares. EX:

Square Roots

y = mx + b M= slopeb = y-intercept

EX: y = 2x – 6

EX: y = -1/3x + 5

Linear Equations

What is the equation of the line?

Linear Function

http://www.crctlessons.com/Slope-Intercept-Test/slope-intercept-test.html

Linear Equations

To find the x-intercept, set y = 0 To find the y-intercept, set x=0

Example find the x and y-intercepts:3x + 4y = 12

X and Y Intercepts

Pythagorean Theorem

http://www.crctlessons.com/Pythagorean-theorem-game.html

Pythagorean Theorem

Cylinder= πr2h

Cone=1⁄3πr2h

Sphere= 4⁄3πr3

http://www.flocabulary.com/volume-cone-cylinder-sphere/

Volume

Big B = Area of the b

b= base

EX: Volume of a Cone V=1/3Bh◦ What does the “B” stand for?

Big B / Little b

Any function that forms a straight line Has a constant rate of change Can be written in slope intercept form No exponents Does not have a variable in the

denominator Linear or nonlinear?? y = 3x y = + 8 y = - 7

Linear Functions

Tables:◦ The x value cannot repeat

Ordered Pairs◦ The x value cannot repeat

Graphs:◦ Vertical Line Test – only touches in 1 spot

Functions

Examples

Slope

Rate of Change

Slope

2 variables or quantities changing

Bivariate Data

Describe the association between age and height.

Scatter Plots

What is the equation for the line of best fit for each graph?

Graphing

Systems of Equations

Elimination: x + y = 7 4x – y = 3

Systems of Equations

Substitution 3x – 2y = 5 x = 4y - 5

Systems of Equations