Due Date:

4/15/2018
Subject:

8th Pre-Algebra
absolute value the distance a value is from zero

natural numbers counting numbers - 1,2,3, . . .

whole numbers natural numbers and zero - 0,1,2,3, . . .

integers positive and negative whole numbers - ...,-2,-1,0,1,2,…

rational number decimal can be written as a fraction (terminates or repeats)

irrational number decimal can not be written as a fraction

sum The result of an addition expression

difference The result of a subtraction problem

product The result of a multiplication problem

quotient The result of a division problem

Pos / Neg: Add / Sub Signs same: add, keep sign

Signs different: sub, keep sign of one that has more

Pos / Neg: Mult / Div Signs same: positive

Signs different: negative

coefficient the number in front of a variable telling how many

constant a number without a variable that has a fixed value

independent variable the variable in which you choose the value

dependent variable the variable whose value is based on other variables

estimation educated guess

like terms terms with same variables and exponents, can be combined

variable a symbol which represents an unknown value

distributive property a(b + c) = ab + ac, a form of multiplication

commutative property a+b=b+a, ab=ba, if add or mult can be rearranged

associative property a+(b+c)=(a+b)+c, a(bc)=(ab)c, if add or mult can be rearranged

order of operations ( ), nx, * /, + -, l to r

exponents multipling a value by itself

n^{x} power

**n**^{x} base

n^{x} exponent

scientific notation example: 435000 = 4.35 * 10^{5}

Exponent Rules: bases same and multiplication, add exponents

bases same and division, subtract exponents

power to a power, multiply exponents

move a power in a fraction, change the sign of the exponent

square root √, √25 = 5 and -5, multiplied by itself

Pythagorean theorem a2 + b2 = c2, relationship between the sides of a right ∆

hypotenuse the longest side of a right triangle

coordinate plane graph

axis the vertical and horizontal number lines

x-axis horizontal (right-left) number line

y-axis vertical (up-down) number line

coordinate pair ordered pair, (x,y) values

quadrant the four sections of a graph

origin (0,0), where the x-axis and y-axis meet

transformations changing the position, shape, or size of an object

translation sliding an object to a new position (x+value,y+value)

rotation turning a shape; need fixed pointt and degrees

reflection flipping an object over a line; need axis of symmetry

axis of symmetry a line that divides an object in half into mirror images

dilation changing the size of an object

prime an integer with exactly 2 factors, one and itself

composite an integer with more than 2 factors

factor a value that divides without a remainder

fraction a comparison of two values, a partial, compared to a whole

ratio a comparison of two quantities, a:b or a/b

unit rate ratio / rate, amount per 1

proportion two equivalent ratios, solved by cross multiplying

similar same shape, different size / same angles, diff sides

Divisibility rules: 2 - value is even

3 - the sum of the digits is a multiple of 3

4 - divisible by 2, twice

5 - ends in 0 or 5

6 - divisible by 2 and 3

7 - not one

8 - divisible by 2, three times

9 - divisible by 3, twice

10 - ends in 0

percent a ratio out of 100

discount decrease of a price

tax increase of a price by the government

interest charge for use of money (to borrow or invest)

principal amount deposited or borrowed

percent change (new-old)/old, comparing amount of change to original

Solving equations: Goal - to determine the value of 1 of the unkown

Order of operations to simplify distributive, etc.

variables on left, constants on right

underline what needs to be moved to other side

move terms to other side and change sign

combine like terms

mult / div on both sides to get only 1 of the variable

if inequality - if mult / div by negative, reverse sign

equality An equation with an equal sign.

inequality An equation with a greater than or less than sign.

additive inverse opposite, 2 values added together to get 0; 5 + (-5) = 0

multiplicative inverse reciprocal, multiplied together to get 1, 3/5(5/3) = 1

point a dot / specific location on a number line or coordinate plane

line is straight, goes on forever in both directions

ray is straight, goes on forever in one directions and ends in one direction

line segment is straight, ends at a point in both directions

angle (vertex) point of intersection of two lines

side line that makes an angle or 2-D shape

height from the highest point, straight down, forms 90° angle to base

radius distance from midpoint to the circle

degrees units of an angle

protractor tool used to measure an angle

acute angle angle between 0 and 90 degrees

right angle angle that is 90 degrees

obtuse angle angle between 90 and 180 degrees

straight angle angle that is 180 degrees

adjacent angles two angles with a common side

complementary sum of two angles is 90°

supplementary sum of two angles is 180°

vertical angles opposite angles, are congruent

exterior angles the angle formed when a side is extended

parallel lines two lines in the same plane that never meet

perpendicular lines two lines that intersect at a 90° angle

transversal a line that intersects two parallel lines

congruent equal, same

congruent objects same size and shape, same angles and lengths

area number of squares in a 2-D object, units u^{2}

lateral area sum of the areas of only side surfaces, units u^{2}

surface area sum of the areas of all surfaces, units u^{2}

volume amount of cubes in a 3-D object, units u^{3}

acute triangle triangle with all angles between 0 and 90 degrees

right triangle triangle with one angle that is 90 degrees

obtuse triangle triangle with one angle between 90 and 180 degrees

equilateral triangle triangle with three congruent sides

isosceles triangle triangle with two congruent sides

scalene triangle triangle with no congruent sides

quadrilateral polygon with four sides

trapezoid quad with one pair of parallel sides

parallelogram quad with two pairs of parallel sides

rhombus quad with four congruent sides

rectangle quad with four right angles

square quad with four right angles and four congruent sides

kite quad with two pair of adjacent congruent sides

deltoid quad that is concave

Advantages of:

chart organizes data

line graph shows trends, and large amounts of data at a glance

bar graph shows differences, comparisons

equation precise data at any point

words describes, explains

continuous a graph where every data point is valid

discrete a graph where only specific points are valid

slope the steepness of a line between two points

y-intercept where the line intersects the y-axis

linear equation greatest exponent is 1, graph is a straight line

standard form ax + by = c, variables left, constant right, no frac, no dec

slope-intercept form y = mx + b

point-slope form y = m(x - x1) + y1

direct variation linear equation that goes through the origin

quadratic greatest exponent is 2, graph is a parabola

parabola graph of a quadratic equation