1. Review: Final Math Exam Tom Steward

2. Chapter. 1

3. The problem solving plan 1.read and understand 2.make a plan 3.solve the problem 4.look back

4. Frequency table - a table that organizes data into intervals Histogram-a graph where data is broken into interval Numerical expression-a mathematical statement using numbers and operations Evaluate-find the answer Order of operations-tells the order in which we should evaluate a numerical expression

5. Ex: 5 *(18-2)+(14 + 4) / 6+3 -2 *4 +9 Algebra- an area of math in which we use letters to represent numbers Variable- a letter that represents a number Variable Expression- an expression that contains number variables, and at least 1 operation Exponent- how many of the base to multiply Power- when a product is written as a base with an exponent Cubed-3 Equation-a math sentence that has an equal sign Squared-2

6. Solution- a number that makes a equation true Formula- an equation that relates two or more quantities Perimeter-the sum of all sides of a shape Area- the space inside of a shape

7. Chapter.2

8. Absolute value – This is the number of places from the number line Ordered pair- this tells where the point on the graph is supposed to go.

9. Coordinate system Coordinate system: a coordinate system is 2 intersecting number lines used to graph things. The x axis is the horizontal line in the coordinate plane. The y axis is the vertical line in the coordinate plane. The origin is where the 2 axis meet. A coordinate plane is broken into 4 sections called quadrants

10. Integer rules When you add two positive integers your outcome will always be positive When you add 2 negative integers the outcome will be negative 2 integers with different signs will always be the number with the higher absolute power’s sign. When you subtract 2 integers remember this, change the subtraction sign to an addition sign, and change the numbers after it to an addition sign

11. The product of two 2 integers with the same sign will always be positive The product of 2 integers with different sign will always be negative The quotient of 2 integers with the same sign will always be positive The quotient of 2 integers with different signs will always be negative Integer rules 2

12. Properties Commutative - Order does not matter Identity - doesn’t change anything Distributive - giving out to everything equally Associative - doesn’t matter where grouping symbols are placed Multiplicative inverse( Reciprocal) - Flip the fraction

13. Examples 4+5= 9 8- (-6)= 14 7+ (-8)= -1 5+ (-2)= 3 5 * 5= 25 -3 * -3 = 9 -4*8 = -32

14. Chapter.3

15. To Solve an equation To solve an equation we always do the same on both sides of the equation

16. 2 step equation To solve a 2 step equation we know to undo the equation backwards on the order of operations

17. Words that tell us to- Add- plus, and, increase Subtract- minus, decrease, difference, Multiply- of, times, Divide- each,

18. Inequality An Inequality is when an equation is not equal on both sides of the problem. The solution of an inequality is just using – more than (>), less than (<) or equal to (=) The symbols only get reversed when both sides are multiplied or divided by a negative.

19. Examples X + 24 = 31 = 14 -3a = 81c – 12 =26 2x + 10 = 46X – 14 < 35 -6y > -96

20. Chapter.4

21. GCF(Greatest Common Factor) The largest number that divides evenly into all of the given numbers. EX: 8: 1, 2, 4, 8, 6:1, 2, 3, 6 So 2 would be the GCF

22. LCM( Least Common Multiple) Smallest of all common multiples Common Multiples are a multiple that 2 numbers share Multiple- is a multiple of B if B divides into A evenly. Ex: 12: 12, 24, 36, 48, 60 10: 10, 20, 30, 40, 50, 60 So 60 would be the LCM

23. Scientific Notation A shorter way to write very large or very small numbers. Ex: 1.24* 10^7 is written in scientific notation we can change this into standard form. Ex: 1.56*10^7 Since the exponent is 7 we would move the decimal 7 places to the left. 15600000. If the exponent is negative you move the decimal to the right

24. Prime and Composite numbers A prime number is a number that is divisible by 1. Ex: 3 is only divisible by 1 nothing goes into it. A composite number is divisible by more than 2 numbers.Ex:10:1,2,5,10 Relatively prime is when a number has no common divisors greater than 1.

25. Rules for Exponents When you have two powers with the same base you have to add them. Ex: X^3*X^9= X^6 When you divide in scientific notation you subtract the exponents instead of adding them You change a negative exponent to a positive exponent by putting it over 1 Any thing to the zero power is 1

26. Prime Factorization and Factor tree’s Prime Factorization- writing a composite number as a product of prime numbers Factor Tree- what we use to find the prime factorization Ex: 36= 6*6= 3*2 & 3*2 Then I stop because there all prime numbers

27. Chapter.6

28. Solving multi step equations First thing you have to do is your order of operations. First you do parenthesis, then you do exponents, multiply, divide, add, subtract. You know when you have to distribute when there are parenthesis and a number outside of the parenthesis. You know when to move variable to the same side when you have the same kind of variable on opposite sides.

29. Examples 5(x + 6) = 45 6y + 12 – 3y + 15 = 51 2x + 14 = 4x – 10 3(x + 4) + 9x = 48 6(x – 7) + 8x = 7(x + 4)

30. Chapter 7

31. Ratio A ratio is a proportional relationship between different numbers. rate- a ratio that compares quantities with different units Unit rate – when the denominator is one

32. To change a rate to a unit rate you must make proportion. 4/5 = p/1 A scale drawing is comparing 2 objects one drew smaller and one drew larger. a scale is the actual size and length of an object

33. Examples A map has a scale of 1in = 150 miles. If two cities are 400 miles apart, how many inches apart are they on the map? Using the same scale as above, if two towns are 4.5 inches apart on the map, how far apart are they in real life?

34. Relation – a property of association meaning at times greater or less than between numbers Input the input is what you put into an equation to find the output Output The output is what comes out of the equation Function Domain Range

35. Scatter plot