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92 Cards in this Set
- Front
- Back
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(x+y)^2
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x^2 + 2xy +y^2
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(x-y)^2
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x^2 - 2xy+ y^2
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(x+y) (x-y)
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x^2 - y^2
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quadratic formula
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x= -b+ or -
square root of b^2-4ac /2a |
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roots of odd numbres there is only one solution
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negative, positive or 0
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even roots of positive numbers have
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positive root
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square root of number between 0 and 1
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result is greater than original number i.e.
S.R 1/4= 1/2 |
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square root of number greater than 1,
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result will be less than the original number i.e.
SR4= 2 |
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when number between 0 and 1 is squared, the result becomes
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smaller
i.e. 1/2^2=1/4 .4^2=.16 |
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when you square a number that is greater than 1 or is less than 0, the result becomes
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bigger
2^2=4 -(.4)^2=-.16 (-.4)^2=.16 |
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when number is raised to even expononent, the result is always
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positive or 0, but we don't know the sign of the variable
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when numbr is raised to odd exponent, the result is
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positive, negative or 0
the sign of the result determines the sign of the variable |
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(x^a times y^a)=
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x^a times y^a
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(x/y)^2=
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x^2/y^2
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(x^a)^b=
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X^ab
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x^a/x^b=
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X^a-b
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X^a times X^b=
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X^a+b
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x^-a=
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1/x^a
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1/x^-a=
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x^a
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x^1/2=
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square root of x
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|x| is less than y
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-y is less than x is less than y
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|x| is greater than y
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x is greater than y or
x is less than -y |
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Perimeter of triangle
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sum of its sides
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area of triangle
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A=b*h/2
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Two intersecting lines forms
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4 angles with 2 pairs of identical angles on opposing sides of intersection
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Pythagorean Theory
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a^2 + b^2= C^2
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Common Right Triangles
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Any ration of 3-4-5 or 5-12-13
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30-60-90 triangle has sides with lengths of the proportion
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1, Root 3, and 2
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Right isosceles triangle
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45-45-90 triangle
half a square 2 sides and 2 angles are equal |
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45-45-90 triangle has sides with lengths of the proportion
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1-1-root 2
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Equilateral Triangle
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All sides of equal length
All angles of 60 degrees |
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when you halve an Equilateral Triangle you form:
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2 30-60-90 triangles
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when you halve an isoceles triangle you form:
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2 45-45-90 triangles
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Area of Equilateral Triangle
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= (1/4 * s^2 * square root of 3)
where s is the side of the triangle |
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Height of Equilateral Triangle
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square root of 3 divided by 2 * side of triangle
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The third side of a triangle is always
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greater than the difference of the other two sides and less than the sum of the other two sides
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An Exterior Angle is
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----an angle drawn off an interior angle of a triangle
----always equal to sum of the other two interior angles |
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AAA Similarity
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If angle measures in one triangle match the angle measures in other, triangles are similar
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SSS Similarity
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If there is constant ration of corresponding sides, triangles are similar
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SAS Similarity
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If there is a constant ration of corresponding sides for 2 sets of sides And if angle in between those two sides is the same, triangles are similar
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Trapezoid
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only one set of sides is parallel
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area of trapezoid=
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(base 1 + base 2)/2 *height
take averag of bases * height |
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Area of Square
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Side squared
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Perimeter of Square
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4 x side= 4s
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Area of Rectangle
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= width * length
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Perimeter of Rectangle
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2L + 2W
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Area of Parallelogram
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= base * height
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Perimeter of Parellelogram
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2a + 2b
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Perimeter of Trapezoid
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a+b+c+d
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Diagonals of Square
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Equal in Length
Intersect at 90 degrees bisect each other |
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Diagonals of Rhombus
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intersect at 90 degrees
bisect each other Opposite lengths are equal |
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Diagonals of Rectangle
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Equal in length
bisect each other form isoceles triangles |
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Diagonals of paralellogram
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bisect each other (meaning cut exactly in half)
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If all sides of parallelogram are equal the figure is a
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rhombus
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Diagonals
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equal in length, intersect at 90 degrees
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Sides of a square
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equal and opposites sides are parallel
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sides of rectangle
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opposite sides are parallel and equal
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sides of parallelogram
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opposite sides are parallel
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sides of trapezoid
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only one pair of sides are parallel
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angles of square
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all angles are 90 degrees
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angles of rectangle
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all angles are 90 degrees
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angles of parallelogram
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Opposite angles are equal
Adjacent angles equal 180 degrees |
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Angles of Trapezoid
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add up to 360 degrees
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area of parallelogram
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A=base * height
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area of trapezoid
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area= 1/2 (base 1 + base2) * height
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Sum of interior angles of all polygons=
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(number of sides -2) 180
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Regular polygon has
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all sides and angles are exactly the same length and measure
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radius
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distance from center of circle to the circle itself
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Diameter
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2 * radius
the distance from one side of circle to the other side |
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Circumference
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the line that encloses the circle
=Pie *diameter or = 2 *Pie*radius |
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Area of circle
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Pie * r^2
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chord
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line that connects any two points on a circle
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central angle
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has vertex at the center of the circle
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inscribed angle
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has vertex on the circumference of circle
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sector
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portion of a circle defined by two radii
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Tangent
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line that touches the circle only at one point. Tangent is perpendicular to circle
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Minor Arc =
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central angle/ 360 * Circumference (pie * diameter)
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Two inscribed angles that cut out same arc are
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equal
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any inscribed angle that cuts out the sam arc as the central angle is
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half of the measure of central angle
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If two lines are parallel and another line bisects them, then opposite angles are
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equal
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Volume =
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length * width * height
or area of base * height |
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volume of cylinder=
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Pie * r^2 *height
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Volume of triangle solid=
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area of isoceles triangle * height
or s^2 * square root of 3 divided by 4 * height |
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Surface Area=
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2lw + 2lh + 2 wh
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how many faces does a rectangular solid have?
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6 with three unique surfaces
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surface area of cylinder=
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2 * area of circle + height * circumference of circle
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surface area of triangle=
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area of equilateral triange *2 + 3 Length * width
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Greatest possible difference of rectangle box=
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square root of l^2 + w^2 + h^2
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greatest possible difference of cube=
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square root of 3* side^2
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slope
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change in y / change in x
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distance formula to find distance between any two points: (X1,Y1) and (X2,Y2)=
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square root of (x1-x2)^2 + (y1-y2)^2
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Midpoint Formula=
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X1+X2 divided by 2 and Y1+Y2 divided by 2
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