CRCT Review

Types of Transformations Translation: slide Rotation: turn Reflection: flip/mirror image Dilation: enlarge / reduce

Transformation Rules: Rotation Reflection Translation (x, y) -> 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

Congruent VS Similar Congruent Similar Same Shape, Same Angles, Same Size Similar Same Shape, Same Angles, DIFFERENT Size

Angles Opposite / Vertical angles: Corresponding 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 Opposite / Vertical angles Corresponding angles Alternate exterior angles Alternate interior angles Supplementary angles Complementary angles

Exterior Angles Example: Angle a = 57 Angle b = 68 What is the measure of Angle d?

Exponents ( 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: 𝑥 −3 = Any base raised to the zero power has a value of 1

Scientific Notation 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)

Rational and Irrational #s 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

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

Square Roots

Cube Roots

Square 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: 80

Linear Equations y = mx + b M= slope b = y-intercept EX: y = 2x – 6

Linear Function What is the equation of the line?

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

X and Y Intercepts 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

Pythagorean Theorem

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

Volume Cylinder= πr2h Cone=1⁄3πr2h Sphere= 4⁄3πr3

Big B / Little b Big B = Area of the b b= base EX: Volume of a Cone V=1/3Bh What does the “B” stand for?

Linear Functions 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 = 6 𝑥 + 8 y = 2𝑥 2 - 7

Functions Tables: Ordered Pairs Graphs: The x value cannot repeat Vertical Line Test – only touches in 1 spot

Examples

Rate of Change Slope 𝑅𝑖𝑠𝑒 𝑅𝑢𝑛 𝑌2−𝑌1 𝑋2−𝑋1

Slope

Bivariate Data 2 variables or quantities changing Describe the association between age and height.

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

Systems of Equations Graphing

Systems of Equations Elimination: x + y = 7 4x – y = 3

Systems of Equations Substitution 3x – 2y = 5 x = 4y - 5