VIEWS: 5 PAGES: 11 POSTED ON: 11/20/2011 Public Domain
Factor - A factor is a number that divides evenly into another number. 2, 4, 5,20 are all factors of 20. Prime Number - A number that can only be divided by one and itself. Prime Factorization – All the prime factors of a given number. A number can be listed more than once. Examples: 20 100 54 Greatest Common Factor (GCF) - The greatest common factor is the largest factor that can be divided into 2 numbers evenly. To find the GCF, find the prime factorization of both numbers and then line them up. Circle the common factors and then multiply all the circled numbers on the top row. Examples: 12,18 100,225 Try - 250, 500 Least Common Multiple - The smallest multiple that two numbers have in common. To find the LCM, just find the multiples of each number until you have a match. Examples: 12, 8 100,225 8- 8,16, 24 LCM =24 100 – 100,200,300,400,500,…900 12- 12,24 225 – 225,450,675,900 LCM = 900 Try - 10, 18 1 Order of Operations - Pemdas Parenthesis, Exponents, Multiplication or Division, Addition or Subtraction Examples: Try: Integers …-3,-2,-1,0,1,2,3… Absolute Value- The number of spaces a number is away from 0 on the number line. The symbol Examples 5 = 5 -7 = 7 -100 = 100 Adding Integers Same Sign - Add and keep the sign. Example -25 + -5 = -30 20 + 100 = 125 Try- -15 + -20 = 25 + 50 = Different Signs - Take the difference and the use the sign in front of the larger number. Examples: -25 + 5 = -20 -10 + 10 = 0 20 + -8 = 12 Try- 15 + -10 -6 + 10 -12 + 20 40 + -20 Subtracting Integers - Change subtraction to addition. Change the sign of the second number ( subtrahend) to the opposite. Then add using the integer rules. Examples - -25 - -10 -30 - 15 -25 + +10 = -15 -30 + -15 = -45 Try: 1) -20 – 8 2) 12 – 5 3) -15 - -10 4) -20 - 14 Multiplying and Dividing Integers - Multiply or divide as usual. Then count up the number of negative signs. An even number of negative signs is a positive answer and an odd number of negatives is a negative answer. Examples- -10 * -2 = 20 -5 * 4 = -20 -2 * -3* -5 = -30 Try: 1) -2 * -8 * -2 = 2) -15 * 2 = 3) -4 * -5= Exponents with Integers (-2) = (-5) = ( 3) = (5) = Algebra Variable – A variable is a letter that represents a number. Examples x,w,r,b Expression – An expression is a math statement without an = sign. Examples x + 5, 2+3, 5 + n Equation - An equation is a math sentence with an = sign. Examples 2 + 3 = 5, x + 6 = 11, r – 12 = 36 Writing statements in algebraic form – Write a variable for any unknown number and use symbols for the operations. Also change words to numbers (ten to 10). Operation words Adding Subtracting Multiplication Division more than less than product quotient plus minus times divided by sum difference Examples: A number increased by eleven is twenty. N + 11 = 20 Four times a number is forty. 4x=40 Twice Jan’s salary. 2j One-Step Equations Solving 1. Find the operation used with the variable and use the inverse(opposite) operation to solve. Checking 1. Rewrite the original equation. 2. Substitute the number for the letter. 3. Solve to check. Example: Solve Check x + 7 = 14 x + 7 = 14 -7 -7 7 +7 = 14 -------------- 14 =14 x=7 Solve Check N – 5 = 12.5 N – 5 = 12.5 + 5 +5 17.5 -5 = 12.5 ----------------- 12.5 = 12.5 N = 17.5 Try: z + 21.4 = 100 m – 4 = 12 Example: Solve Check 4z = 16 4z= 16 4 4 4*4=16 z= 4 16=16 w =4 w=4 2 2 8=4 W=8 2 4=4 Try: 5x =20 s =12 2 2-Step Equations Solving 1. Use the inverse of addition or subtraction to get rid of a number. 2. Use the inverse of multiplication or division to solve. Check 1. Check the same way that you did for the one –step equations. Example 2x + 7 = 17 r – 5 = 10 - 7 -7 3 ____________ 2x = 10 Try 4x +16 =20 p + 12 = 15 3 Monomials - One term 2x, 4, 10s Coefficient- The number in front of the variable. Like terms – Terms with the same variable. Example -2x,4x or 10w,11w Adding and Subtracting Monomials - 1. Add the coefficients and keep the same variable. Example: 4x + 6x = 10x -3a + 10a = 7a Try 1) 3a + 70a= 2) -10a + 4a 3) 12c – 6c Multiplying Monomials 1. Multiply the coefficients. 2. Add the exponents of like variables. Examples: Try: Dividing Monomials 1. Divide the coeffiencts. 2. Subtract the exponents of like variables. Examples: Try: Simplifying Equations before Solving 1. Simplify 2. Solve Example: 2x + 4x + 12 = 36 Try: 12x -10x + 4 = 24 6x +12 = 36 -12 -12 ---------------- 6x = 24 6 6 x=4 Geometry Point – A particular location. Example . Line Segment – A line segment is a set of points that starts with an endpoint and ends with an endpoint. Example ._________________. A B Ray – A set of points that starts with an endpoint and continues in one direction. Example Line – A line is a continuous set of points. Example Angle- An angle is formed by two intersecting lines, rays, or line segments. Example Degrees – Degrees are used when finding an angle’s measurement. Right Angle- An angle that measures exactly 90 degrees. Example Acute Angle – An angle that measures less than 90 . Example Obtuse Angle – An angle that measures more than 90 less than 180. Example Straight Angle – An angle that measures exactly 180 degrees. Example: Vertical Angles – Angles that are formed by intersecting lines. Opposite angles are congruent. Example: Complementary Angles – Angles that add up to 90 . Example Supplementary Angles – Angles that add up to 180 . Example Parallel lines cut by a Transversal Alternate interior angles - Opposite angles located on the interior. They are congruent. Example: Alternate exterior angles- Opposite angles located on the exterior. They are congruent. Example: Corresponding Angles - Angles that match up from the bottom to the top. They are congruent. Example: Triangle- Polygon- Any enclosed figure that has sides. Triangle- A 3 sided polygon. A triangle has 3 angles that add up to 180 . Example: Right triangle- A triangle with one 90 angle. Example: Acute Triangle- A triangle with all angles less than 90. Example: Obtuse Triangle- A triangle with one obtuse angle. Example: Scalene Triangle – A triangle with 3 different sides and angles. Example: Isosceles Triangle – A triangle with two congruent sides and angles. Example: Equilateral Triangle – A triangle with three congruent sides and angles. Example: Area – The inside of a figure. Perimeter – The distance around the circle. The Area of a Triangle = base x height * The base and height always form a 90 angle. 2 Examples: The Perimeter of a Triangle = Side + Side+Side Examples Hypotenuse – The longest side of a right triangle. Legs – The two shorter sides of a right triangle. Pythagorean Theorem = a2+ b2 = c2 * a and b are the legs, c is the hypotenuse Page 10 Circle – A circle is a set of points equidistant from a center point. There are 360 degrees in a circle. Radius ( radii) - The radius is the distance between the center point and a point on the circle. Diameter - The distance between two points on a circle that also contains the center point. * The diameter is twice the size of the radius since it is made up of 2 radii. Chord – The distance between two points on the circle. Pi ( ) - 3.141592654… is the number used to help find area and perimeter. Circumference - is the distance around the circle. The formula to find the circumference is c = diameter or c = d Area – the area is the inside of the circle. The formula to find the area of a circle is A = where r stands for the radius. Triangle – 3 sided figure Quadrilateral – 4 sided figure Pentagon – 5 sided figure Hexagon – 6 sided figure Heptagon – 7 sided figure Octagon – 8 sided figure Nonagon – 9 sided figure Decagon – 10sided figure