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Sat index cards
 

Sat index cards

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    Sat index cards Sat index cards Presentation Transcript

    • Numbers and Divisibility
    • Rational Numbers
    • Real numbers/fractions that can repeator terminate. Examples: 33, 1/3
    • Irrational Numbers
    • Real numbers/fractions that do not repeator terminate. Example: π
    • Integers
    • Positive or negative whole numbers. 0is also considered an integer. Example: 4, -2
    • Non-Integers
    • Positive or negative numbers that are infraction form. Ex: 25/7
    • Imaginary Numbers
    • Numbers that are not real, have an i inthem. Ex:
    • Divisible by 2
    • Even #’sEnd in 0,2,4,6 or 8
    • Divisible by 5
    • Ends in a Zero or Five
    • Divisible by 10
    • Ends in Zero
    • Divisible by 3
    • Sum digits togetherSum must be divisible by 3
    • Divisible by 9
    • Add digits togetherSum of the digits must bedivisible by 9
    • Divisible by 4
    • If the last two digits aredivisible by 4 than the wholenumber is
    • Divisible by 6
    • If its divisible by 2 and 3
    • Consecutive
    • • One right after another, the next possible one.
    • Distinct
    • • =Different
    • Factors
    • • Any group of numbers or variables that when multiplied give the original number/variable
    • Multiple
    • • The result of multiplying a number by an integer.• EX: Multiples of 4:…,-8,-4,0,4,8,12…
    • • Union• Combining sets without writing the repeats
    • • Intersection• The overlap of sets
    • Percent Increase or Decrease
    • current − original ×100% original
    • Exponent and Root Rules!
    • How to multiply two powers with same base?
    • a *a =a3 5 3+5 =a 8
    • How to divide two powers with the same base?
    • a /a =a =a5 3 5-3 2
    • Multiplying exponents
    • (a2)3= a2*3= a6
    • Zero as an exponent
    • a0=1ANYTHING TO THE ZERO POWER EQUALS 1
    • Exponent of 1
    • X =X 1Anything to the exponent of 1, is THAT number
    • Negative Exponents
    • a-1= 1/a
    • Simplifying Radicals with multiplication
    • Can be written as a b
    • Simplifying Radicals with division
    • aa/b b
    • Alternate form of square root
    • a = a1/2
    • Alternate form of cube root
    • 3 a = a 1/33 2 a = a 2/3 = ( a) 3 2
    • Graphing/ Writing Equations of Lines
    • Coordinate Plane
    • Y-axisQuadrant 2 Quadrant I X-axis Quadrant 4Quadrant 3 Origin
    • Slope Formula
    • y2 − y1 risem= = x2 − x1 run
    • Distance Formula
    • d = ( y2 − y1 ) + ( x2 − x1 ) 2 2
    • Midpoint Formula
    •  x1 + x2 y1 + y2 = , ÷  2 2 
    • Vertical Lines
    • •Think vertebra to help with visual•Undefined Slope! (cannot walk upwalls)•Form x=#
    • Horizontal Lines
    • •Think horizon to help with visual•Slope = Zero (walking across leftto right there is no incline ordecline)•Form y=#
    • Slope-Intercept Form
    • y = mx + b
    • Parallel Lines
    • •Do not intersect•Have the same slopes•Symbol: ||
    • Perpendicular Lines
    • •Intersect at a right angle/90⁰•Have slopes that are opposite,reciprocals of each other (flip it andswitch it)•Symbol: ⊥
    • X-intercepts
    • •Also known as roots and zeros•Where the graph crosses the x-axis•Plug 0 in for y and solve for x•Answer: (#,0) as an ordered pair
    • y-intercepts
    • •Where the graph crosses the y-axis•Plug 0 in for x and solve for y•Answer: (0,#) as an ordered pair
    • Directly Proportional
    • y = kxAs x increases, y increases ORAs x decreases, y decreases
    • Inversely Proportional
    • k y= xAs x increases, y decreases ORAs x decreases, y increases
    • Function Notation and Variables
    • Function
    • • Equation where every input has exactly one output – For each x-value there is one y-value• F(x)=y – F(x)=mx + b • Plug in x to find F(x) or y
    • F(x)=2x+4 F(-3)
    • F(-3)=2(-3)+4 F(-3)=(-6)+4 F(-3)=-2
    • F(x)=4x+5 F(x)=25
    • 25=4x+525-5=4x 20=4x 4 X=5
    • F(x) + G(x)F of x added to G of x
    • • Add the two functions together
    • F(x) – G(x)F of x subtracted from G of x
    • • Subtract the two functions
    • F(G(x))F of G of x
    • • Plug the function of G(x) into the x-variables in the function F(x)
    • F(x) ● G(x)F of x multiplied by G of x
    • • Multiply the two functions together
    • F(x) / G(x)F of x divided by G of x
    • • Divide the two notations
    • Graph Shiftsf(x)
    • f(x) + 3
    • • The f(x) graph moves up 3 places
    • f(x) - 5
    • • The f(x) graph moves down 5 places f(x)
    • -f(x)
    • • The f(x) graph is reflected over x-axis
    • f(-x)
    • • The graph of f(x) is reflected over the y-axis
    • f(x + 2)
    • • The f(x) graph moves LEFT 2
    • f(x – 4)
    • • The f(x) graph moves RIGHT 4
    • Geometry
    • Sum of Interior Angles of a Triangle? B A C
    • m∠A + m∠B + m∠C = 180 0
    • Perimeter of Triangle
    • a + b + c = perimeter a b c
    • Exterior Angle Theorem
    • m∠A + m∠B = m∠D BA C D
    • Pythagorean Theorem
    • a +b = c 2 2 2 C=hypotenusea b
    • Area of a Triangle
    • Area Formula: ½ x base x height
    • 30⁰-60⁰-90⁰ Right Triangles
    • 60⁰ 2nn 30⁰ n 3
    • 45⁰-45⁰-90⁰ Right Triangles
    • 45⁰ n 2n 45⁰ n
    • Congruent Triangles
    • Scalene Triangle
    • Triangle with no equal sides.
    • Isosceles Triangle
    • Triangle with two equal sides. The corresponding angles are congruent as well.
    • Equilateral & Equiangular Triangle (If equilateral  equiangular and vice versa)
    • Triangle that has three equalsides and three equal angles that are 60⁰.
    • Right Triangle
    • HypotenuseLeg Leg
    • Obtuse Triangle
    • Triangle that has one obtuse angle.
    • Acute Triangle
    • Triangle that has three acute angles.
    • Quadrilateral
    • Four sided Figure
    • Area of a Quadrilateral
    • A=base X height
    • Parallelogram
    • • Quadrilateral with the following properties: 1. Opposite sides are parallel 2. Opposite sides are congruent 3. Diagonals bisect each other 4. Opposite angles are congruent
    • Rectangle
    • • Parallelogram that has all of those properties plus the following: 1. All angles are 90⁰ 2. Diagonals are congruent
    • Rhombus
    • • Parallelogram that has all of those properties plus the following: 1. All sides are congruent 2. Diagonals are perpendicular 3. Diagonals bisect corner angles
    • Square
    • • Parallelogram that has all of those properties plus combines the properties of a rectangle and a rhombus
    • Sum of Interior Angles of a Polygon
    • (n − 2)180 0
    • Sum of Exterior Angles of a Polygon
    • 0360
    • C i R c Le S
    • Diameter of a circle
    • d=2rDiameter Radius
    • Circumference of a circle
    • C= 2 r RadiusCircumference
    • Area of a circle
    • A= r 2Area Radius
    • Central Angle
    • Central AngleO
    • Arc of a Circle
    • ArcO
    • Sector
    • • A sector is a region that is formed between two radii and the arc joining their end points
    • To find the area of a sector…..
    • r2360 Area of a Circle
    • Length of Arc
    • 2 r360 Circumference of a Circle
    • Sum of all angles in a circle
    • 360 o
    • Tangent to a Circle
    • • Tangent line is perpendicular to the radius at the point of tangency
    • Probability
    • Number of favorable outcomeTotal number of outcomes
    • Statistics Terms
    • Average=Mean
    • the sum of a set of valuesthe total number of values in the set
    • Median
    • Middle number in a set of numbers arranged in numerical order
    • Mean
    • average of the middle two numbers
    • Mode
    • Values that appear the most often in a set of numbers.
    • Acute Angles
    • • Angle whose measure is between 0 and 90 degrees.
    • Obtuse Angles
    • • Angle whose measure is between 90 and 180 degrees.
    • Complementary Angles
    • • Two angles that sum to 90 degrees.
    • Right Angle
    • An angle that is 90 degrees
    • Supplementary Angles
    • • Two angles that sum to 180 degrees.
    • Straight Angle
    • • An angle that’s measure is 180 degrees
    • Vertical Angles
    • • Angles that are opposite of each other when two lines cross• Vertical angles are congruent, so angles a and b are congruent in the image.
    • Transversal
    • • A line that crosses two lines (they do not have to be parallel) creating special types of angles
    • Corresponding Angles
    • • Angles in matching corners are corresponding.• In this image, a and e, b and f, d and h, d and g are corresponding.• If the transversal crosses two parallel lines, corresponding angles are then congruent.
    • Alternate Interior Angles
    • • The pairs of angles that are on opposite sides of the transversal but inside the other two lines are alternating interior angles• In this image, c and f, and d and e are alternating interior.• If the transversal crosses two parallel lines, AI angles are then congruent.
    • Alternate Exterior Angles
    • • The pairs of angles that are on opposite sides of the transversal but outside the other two lines are alternate exterior angles• In this image, a and h, and b and g are alternating interior.• If the transversal crosses two parallel lines, AE angles are then congruent.
    • Same Side Interior Angles
    • • Angles that are on the same side of the transversal and on the interior of the other two lines are same side interior.• In this image, 3 and 6, and 4 and 5 are SSI angles.• If the transversal crosses two parallel lines, SSI angles are supplementary.
    • Same Side Exterior Angles
    • • Angles that are on the same side of the transversal and on the exterior of the other two lines are same side exterior.• In this image, 2 and 7, and 1 and 8 are SSE angles.• If the transversal crosses two parallel lines, SSE angles are supplementary.