8th Grade Course 3 Math
Chapter 1 Vocabulary
1.1
Conjecture- educated guess
1.2
Variable- a symbol, usually a letter to represent a number
Algebraic expression- a variable, a number and one operation
Numerical expression- replaces the variable with a number
Evaluate- solve
Order of Operations- PEMDAS
Powers- repeated multiplication
Equation- a math sentence that contains an equal sign
Property- open sentences that are true for any number
Commutative-The order in which two numbers are added or multiplied does not change their sum or product. For any numbers a and b, a + b = b + a and ab = ba. Example: 2 + 3 = 3 + 2 or 2 x 3 = 3 x 2
Associative-The way in which three numbers are grouped when they are added or multiplied does not change their sum or product. For any numbers a, b, and c,
(a + b) + c = a + (b + c), and (ab)c = a(bc).
Example:: (2 + 3) + 4 = 2 + (3 + 4) or (2 x 3) x 5 = 2 x (3 x 5).
Distributive-To multiply a sum by a number, multiply each addend of the sum by the number outside the parentheses. For any numbers a, b, and c, a(b + c) = ab + ac and
a(b - c) = ab - ac.
Example: 2(5 + 3)=(2 x 5) + (2 x 3) and 2(5 - 3) = (2 x 5) - (2 x 3)
Identity-The sum of an addend and zero is the addend. The product of a factor and one is the factor. Example: 5 + 0 = 5 and 5 x 1 = 5
Counterexample- example that shows that a conjecture is false.
1.3
Negative Number- any number that is less than zero
Integers- The set of whole numbers and their opposites {. . .-2, -1, 0, 1, 2. . .}.
Coordinate- the number that corresponds to a point on a number line.
Inequality- a sentence that compares two different numbers
Absolute Value- The absolute value of a number a is its distance from zero on a number line and is represented by |a|. Example: The absolute value of -2 is 2, or |-2| = 2.
1.4
Opposites- every positive number and its negative pair
Additive Inverses-A number that when added to a given number, results in a sum of zero. Example: The additive inverse of 4 is -4 because 4 + (-4) = 0.
1.7
Defining a Variable- A variable and an unknown quantity for the variable to represent
1.8
Solve- Find Values of the variable that makes the equation true
Solution- Value for the variable that makes an equation true
Inverse Operation- Pairs of operations that undo each other; addition and subtraction are inverse operations. Multiplication and division are inverse operations.
Chapter 2
2.1
Rational Number- the numbers of form a/b, where a and b are integers and b does not equal 0.
Terminating Decimal- a decimal whose digits end. Every terminating decimal can be written as a fraction with a denominator of 10, 100, 1000, and so on.
Repeating Decimal- a decimal whose digits repeat in groups of one or more. Examples are .1818181818 and .833333
Bar Notation- in repeating decimals, the line or bar placed over the digits that repeat. Another way to write 2.63636363 is 2.63
2.3
Dimensional Analysis-the process of including units of measurement when you compute.
2.4
Multiplicative Inverse- a number times its multiplicative inverse is equal to 1. The multiplicative inverse of 2/3 is 3/2.
Reciprocals- the multiplicative inverse of a number. The product of reciprocals is 1.
2.5
Like Fractions- Fractions with like denominators. For example: ⅜+⅝= 8/8
2.6
Unlike Fractions- Fractions with unlike denominators. For example: ⅓+⅜=
2.8
Base- is the number that is multiplied. For example: 4^3= 4*4*4.
Exponent- tells how many times the base is used as a factor. For example: 4^3
Power- the number that is expressed using an exponent.
2.9
Scientific Notation- A number written as the product of a number between 1 and 10 and a power of ten.
3.1
Perfect Square- a rational number whose square root is a whole number. 25 is a perfect square because its square root is 5. √25= 5.
Square Root- One of the two equal factors of a number. √144= 12. Because 12x12= 144.
Radical Sign- The symbol used to indicate a nonnegative root. √
Principal Square Root- A positive square root.
3.3
Irrational Number- a number that cannot be expressed as a/b, where a and b are integers and b does not equal 0.
Real Number- the set of rational numbers together with the set of irrational numbers.
3.4
Right Triangle- an angle that measures 90 degrees.
Legs- the two sides of a right triangle that form the right triangle.
Hypotenuse- the side opposite the right angle in a right triangle.
Pythagorean Theorem- in a right triangle, the square of the length of the hypotenuse c is equal to the sum of the squares of the lengths of the legs a and b. c2= a2 + b2.
Converse- the converse of the Pythagorean theorem can be used to test whether a triangle is a right triangle. If the sides of the triangle have lengths a, b and c, such that c2= a2+b2, then the triangle is a right triangle.
3.5
Pythagorean Triple- a set of three integers that satisfy the Pythagorean theorem.
3.6
Coordinate Plane- formed by two number lines, X-horizontal, Y-vertical
Origin- intersection of X and Y, where X=0 and Y=0
Y-Axis- Vertical Change, vertical number,
X-Axis- horizontal change,
Quadrants- the number line separates into 4 parts.
Ordered Pair- (X, Y)
X-Coordinate- First number, abscissa
Y-Coordinate-second number, ordinate
Abscissa-first number
Ordinate- second number
Chapter 4
4.1
Ratio- a comparison of two numbers by division; 3 to 6, 3:6; 36
Rate- comparison of two quantities with different types of units. Examples: $5 for 2 pounds of cereal
50 miles per 1 hour; 25 miles per 1 gallon
Unit Rate- Simplified denominator 1. $7.50 per hour which means $7.50 per 1 hour.
4.2
Rate of Change- quantity changes in relation to another. Example: distance/time.
4.3
Slope- Rise/Run. Change vertically over change horizontally.
Rise- vertical change. Y-Axis
Run—horizontal change. X- Axis
4.4
Proportion- an equation stating two ratios are equal.
Cross Products- in a proportion two cross products are equal
4.5
Polygon-closed figure; with or more line segments.
Similar- same shape
Corresponding Parts-the parts that match in a similar polygon
Congruent- equal, have the same measure
Scale Factor-two ratios equal to each other.
4.6
Scale Drawing- is used to represent an object that is too small or too large.
Scale Model- same as scale drawing
Scale- determines the measure of an object; mass, distance, capacity
4.7
Indirect Measurement- measuring an object by using other objects
4.8
Dilation- increase or decrease the size of an object.
5.1
Percent- is a ratio that compares a number to 100, example: 1/100, 1 to 100, 1:100, 1%.
5.3
Percent Proportion-the part is being compared to the whole quantity called the base.
5.5
Compatible Numbers- two numbers that are easily divided
5.6
Percent Equation- is/of= %/100
5.7
Percent of Change- subtract/original amount
5.8
Interest- amount earned off of the principal
Principal—amount invested
Lesson 6.1- Geometry
Acute Angles- less than 90 degrees
Right Angles-90 degrees
Obtuse Angles- bigger than 90, less than 180
Straight Angles- 180 degrees
Vertical Angles- across means equal
Adjacent Angles- share a boundary
Complementary Angles- two angles added up to 90.
Supplementary Angles-two angles added up to 180 degrees.
Perpendicular Lines- Lines that intersect at right angles
Parallel Lines- two lines in a plane that never cross or intersect
Transversal- lines that intersect with two or more other lines
Alternate Interior Angles- those on opposite sides of the transversal and inside the other two lines, are congruent.
Alternate Exterior Angles- those on opposite sides of the transversal and outside the other two lines are congruent.
Corresponding Angles- those in the same position on the two lines in relation to the transversal, are congruent
6.2
Triangle- three sided figure
Acute- less than 90
Obtuse- more than 90 and less than 180
Right- 90 degrees
Scalene Triangle- 3 different length sides
Isosceles Triangle- 2 sides are equal
Equilateral Triangle- all sides equal
Equiangular Triangle- all angles equal
6.4
Quadrilateral- 4 sided figure
Trapezoid- one pair of parallel sides
Parallelogram- two pairs of parallel sides
Rectangle- 4 right angles
Rhombus- 4 sides are equal
Square- 4 congruent sides and 4 right angles
6.5
Congruent polygons- the same size and same shape
Example: