Math 4-8 115
Reflection over x-axis
(-x,-y)
Associative Property of Addition
(a + b) + c = a + (b + c)
Associative Property of Multiplication
(a x b) x c = a(b x c)
Distributive Property of Multiplication over Addition
(a) x (b + c) = (a x b) + (a x c)
slope
(y₂- y₁) / (x₂- x₁) Slope = 0, horizontal line Slope is 1/0 = vertical line Slope is negative = line is downward Slope is positive = line is upward
function
1. A relationship from one set (called the domain) to another set (called the range) that assigns to each element of the domain exactly one element of the range. 2. The action or actions that an item is designed to perform.
Surface area of a sphere
4πr²
linear function
A function whose graph is a straight line. concepts include slope, domain, range and intercepts
vertex
A point where two or more straight lines meet.
Parallelogram
A quadrilateral with two pairs of parallel sides
Proportion
A relationship between two quantities that dictates how one changes when the other changes
horizontal shift
A rigid transformation of a graph in a horizontal direction, either left or right. f (x-b)
recursive formula
A rule for a sequence in which one or more previous terms are used to generate the next term
Prism
A solid figure that has two congruent, parallel polygons as its bases. Its sides are parallelograms
rectangular prism
A solid shape that has: 6 faces (4 rectangles & 2 squares), 8 vertices (corners), and 12 equal edges.
sphere
A solid shape that is perfectly round like a ball. No faces, edges, or vertices.
pyramid
A solid shape with a polygon as a base and triangular faces that come to a point (vertex or apex)
vertical line test
A test used to determine whether a relation is a function by checking if a vertical line touches 2 or more points on the graph of a relation
cube
A three-dimensional shape with six square faces, or sides, with three meeting at each vertex
isosceles triangle
A triangle that has 2 equal sides.
acute triangle
A triangle with 3 acute angles
Outlier
A value much greater or much less than the others in a data set
prime number
A whole number that has exactly two factors, 1 and itself.
Area of a triangle
A=1/2bh
Area of a rectangle
A=bh
Area of a circle
A=πr²
vertical translation
An up or down slide; the y-coordinate changes.
standard form of a linear equation
Ax + By = C, where A,B, and C are real numbers, and A and B are not both zero.
VLT
Example 1 - y = x2 a. Choose values of x: -2, -1, 0, 1, and 2b. Substitute these values into the equation, y = x2c. The corresponding y-values: 4, 1, 0, 1, 4d. Graph the points (-2, 4), (-1, 1) , (0, 0), (1, 1), and (2, 4)
Hypotenuse Leg
If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.
Rational numbers
Includes all integers, decimals, and fractions. Any terminating or repeating decimal is a rational number.
irrational numbers
Numbers that cannot be expressed as a ratio of two integers. Their decimal expansions are nonending and nonrepeating.
Substitution method
Replacing one variable with an equivalent expression containing the other variable
Surface Area of a Cylinder
SA=2πr²+2πrh
Quadratic Function Equation
Solve for x: x^2 - 25 = 0 a. Isolate x, we have x^2 = 25 b. Take the square root of both sides, x = + or - 5 c. The quadratic function y = x^2 crosses the x-axis at +5 and -5 d. Therefore, +5 and -5 are the solutions
circle
The set of all points in a plane that are the same distance from a given point called the center
Domain
The set of the first numbers of the ordered pairs in a relation
least common multiple (LCM)
The smallest multiple (other than zero) that two or more numbers have in common.
complex conjugate
Two complex numbers of the form a + bi and a - bi
Multiplicative Inverse
Two numbers with a product of 1
Volume of a cube or Prism:
V= L x W x H or S^3
Volume of a sphere
V=4/3πr³
Volume of a cylinder/prism
V=Bh
Volume of a rectangle
V=lwh
Volume of a rectangular prism
V=lwh
Volume of a cylinder
V=πr²h
Constant by proportionality
When two quantities have a proportional relationship,
Commutative Property of Addition
a + b = b + a
inscribed circle
a circle in which each side of the polygon is tangent to the circle
Discriminant
a function of the coefficients of a polynomial equation whose value gives information about the roots of the polynomial.
exponential form
a function of the form in which the input variable x occurs as an exponent
nonlinear function
a function whose graph is not a line or part of a line
Population
a group of organisms of the same species populating a given area
Asymptote
a line such that the distance between the curve and the line approaches zero as they tend to infinity
z-score
a measure of how many standard deviations you are away from the norm (average or mean)
complex number
a number of the form a + bi where a and b are real numbers and i is the square root of -1
The decimal, or base 10, system
a number system that uses ten different digits
imaginary number
a number that can be written as a real number multiplied by the imaginary unit i, which is defined by its property i2 = -1
Parabola
a plane curve formed by the intersection of a right circular cone and a plane parallel to an element of the curve
quadrilateral
a polygon with four edges and four vertices or corners
rectangle
a quadrilateral with four right angles
square
a quadrilateral with four right angles and four congruent sides
inverse proportion
a relationship in which an increase in one quantity is accompanied by a decrease in another quantity.
arithmetic series
a sequence of numbers such that the difference between the consecutive terms is constant
system of equations
a set of two or more equations containing the same variables
scalene triangle
a triangle with no congruent sides
scientific notation
a way of writing numbers using exponents
Commutative Property of Multiplication
a x b = b x a
Solve for x: 2x^2 + 5x - 3 = 0
a. Use the factoring method b. By expressing 2x^2 + 5x - 3 = 0 as a product of two binomials, we get (2x -1) (x + 3)2x -1 = 0 and x + 3 = 0 c. The two solutions are x = 1/2 and x = -3 d. the function y = 2x^2 + 5x - 3 crosses the x-axis at 1/2 and -3, which are two solution
Percent to Decimal
a. move the decimal point two places to the left b. remove the percent sign Ex: 325% = 3.25
decimal to percent
a. move the decimal point two places to the right b. add a percent sign Ex: 0.7 = 70%
Fraction to Percent
a. multiply by 100 b. add the percent sign Ex: 3/8 = (3/8 x 100%) = 37.5%
percent to fraction
a. remove the percent sign b. place number over 100 c. reduce answer to its simplest form Ex. 1.5% = 1.5/100 = 15/1000 = 3/200
vertical stretch/shrink
af(x)
Integer
any of the natural numbers (positive or negative) or zero
relation
any set of ordered pairs (x, y)
quadratic equation in standard form
ax^2+bx+c=0
Geometric Series Formula
a↓n = a↓1 • r^(n-1), r = common ratio a series with a constant ratio between successive terms
Congruent Triangles/Polygons
corresponding parts of congruent triangles (polygons) are congruent
Another form of a quadratic function
f(x) = a(x - h)^2 + k where a, h and k are constants The vertex of the parabola is given by the point (h, k)
graph of a quadratic function
f(x) = ax^2 + bx + c creates a curve called a parabola
Graphing method
graph the equation and the solution is the x-intercept, where the parabola meets or crosses the x-axis
triangle
is a polygon with three edges and three vertices
Elimination method
solving systems by adding or subtracting equations to eliminate a variable
mean
the arithmetic average of a distribution, obtained by adding the scores and then dividing by the number of scores
greatest comon factor
the largest number that is a factor of two or more numbers
Median
the middle score in a distribution; half the scores are above it and half are below it
Real Numbers
the set of all rational and irrational numbers
range
the set of second numbers of the ordered pairs in a relation
vertical line
undefined slope
Binary, or base 2
uses only the numbers 0 and 1
slope-intercept form
y = mx + b
horizontal line
y=b where b is the y-intercept of the line slope = 0
horizontal stretch/shrink
y=f(ax)