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My Year’s Math Notes

My Year’s Math Notes. Chapter 1. Problem Solving Plan- 1. Read and Understand 2 . Make a Plan 3. Solve the Problem 4. Look back; Check to make sure your answer is reasonable Frequency Table- a table that organizes data into intervals

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My Year’s Math Notes

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  1. My Year’s Math Notes

  2. Chapter 1 • Problem Solving Plan- 1. Read and Understand2. Make a Plan3. Solve the Problem4. Look back; Check to make sure your answer is reasonable • Frequency Table- a table that organizes data into intervals • Histogram- a graph where data is broke into intervals • Numerical Expression- a mathematical statement using numbers and operations • Evaluate-Find the answer

  3. Continued…. • Order of operations-tells the order in which we should evaluate numerical expression • Exponent-how many of the base to multiply • Squared-to the second powercubed-to the third power • Base-the number being multiplied • Power-When a product is written as a base with an exponent • Squared-to the second power • Cubed-to the third power • Equation-a math sentence that has an equally signSolving an equation- find the solution

  4. solution- the number that makes the equation truewrite and equation and solve it x-7=512-7=5Formula-an equation that relates to one or more quantantsperimeter- the sum of all sides of a shapeAREA- the space inside of a shapesolve this problem- 5*(18-2)+(14+4)/ 6+3 -2 *4+9

  5. Algebra-the area of math where we use lettersVariable-A letter that a takes the place of a numberVariable Expression-an variable expression that contains letters, numbers, and at least one operation

  6. Chapter 2 • Integers-all the whole numbers and there opposites the negatives • Absolute Value- the distances from zero on a number line • Coordinate System-A coordinate system is two intersecting number lines used to graph things. • X-axis- Horizontal number line in a coordinate Y-axis- the vertical number line in a coordinate systemOrigin- The point where the number lines intersect in a coordinate system • Quadrant-A coordinate system that broken into four sectionsOrdered pair- two numbers that give the exact location of a point in a coordinate system

  7. x-coordinate- tells how far across the x axis the point is in a coordinate system • y-coordinate- tells how far up and down the y axis the point is in a coordinate system 8 RULES FOR INTEGER OPERATIONS1. the sum of two positive integers will always be positive to get the answer add2. the sum of two negative integers will always be negative to get the answer add3. the sum of two integers with different signs will have the signs of the larger number to get the answer subtract4. to subtract two integers, chance the subtraction to addition and change the second number to its opposite(add a line, change the sign)5.the product of two integers with the same sign will always be positive to get your answer multiply.6.The product of two integers with two different signs will always be negative to get your answer multiply.7. The quotient of two integers with the same sign will always be positive to get the answer divide.8.the quotient of two integers with different signs will always be negative to get the answer divide.

  8. -6+ -8=14 ; -5+7=-12 ; 3+15=1812-18=-6 ; 4-(-7)=-3 -12* -7=84 ; 11* - 8 =-88 ; -3*2= -6-14/-2=7 ; 12/-3=-4 ; -15/5=-3Commutative property- go back and forth and it will be the same.Associative property- grouping symbols can move and the problem doesn't change. Identity property- what doesn't change anything. • Reciprocal- the inverse of 5/12 is 12/5 because 5/12 *12/5=1 • Distributive property -give out even

  9. Chapter 3 1. To solve an equation you always do what? order of operations backwards.2. when solving two step equations how do you know what operation to undo first? The last step on the order of operations3. Add- plus, more, increased, total, sum 4.Subtracting- minus, difference, decrease, fewer than, less than, subtract5.Multiply-times, product, multiply, of.6. Divide- divide, quotient, per7. Inequality-is a statement form by placing and inequality symbol between two expressions8.Solution of an inequality- is the set of numbers that you can substitute for the variable to make the inequality true9.when do we reverse the inequality symbol-when you get two negatives!

  10. 10. solve the following and show the work!x + 24=31-24 -24x =7-3a=81+3 +3a = 84 2x + 10=46-10 -102/2x =2/36x= 136/-6y>-96/6y=16y*9_9 =14*9 y=126c-12=26+12c=38x-14/35 < 35/35

  11. Chapter 4 • Prime Numbers- A number greater than one, with only two factors namely one and its selfComposite numbers- a number greater than one with more than two factorsFactor tree- What we use to find prime factorization.Prime factorization - 3 to the 4th power, 12,4, 2 to the 2nd powerPrime factorization- writing a composite number as a product of prime numbersFactors- a is a factor of a if a divides evenly into b. Ex.48-12x4,6x816x3,24x2,1x48G.C.F.(greatest common factor)-the largest number that divides evenly into all of the given numbers.ex.12 -2,3,4,6,1240-2,4,8,10 .......G.c.f is 4Relatively prime-two numbers whose G.c.f is 1Multiple- a is a multiple a b if b divides into a evenlyex.4-4,8,12,16,20,24.....

  12. Common Multiple-a multiple that two numbers shareL.C.M.(Least Common multiple)- the smallest of the common multiples.Ex.8-8,16,24,32,(40)10-10,20,30,(40)x^4 * x^7= x11y^8 /y^4= y 4How do you change a number with a negative exponent to a positive exponent? You make it into a fraction.Any thing equal to zero is equal to what? The same number like 65 is equal to 65put 12,300,000,000= 12.34.5* 10 8 = 000,000,000,45

  13. Chapter 6 • Write the order in which you solve multi-step equations (i.e. combining like terms, solving a 2-step equation, distributing, getting variables on one side) First, you subtract the number that is by itself on both sides. Then, you divide what's left other than the variable. You should get a number =x • How can you tell if you have to combine like terms? If they are like terms • How can you tell if you have to distribute? If there's a number outside of parenthathess • How can you tell if you have to move variables to the same side? If the problem isn't equal.

  14. Solve the following equations: • 5(x + 6) = 45 3+6=9x5=45 • 6y + 12 – 3y + 15 = 51 6y-3y+3 3y+3 6=y • 2x + 14 = 4x – 10 14-10=4 2x+4 4x x=2 • 3(x + 4) + 9x = 48 x=3 • 6(x – 7) + 8x = 7(x + 4) x=2

  15. Proportion – solve this proportion • Scale Drawing Scale • 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?

  16. Chapter 7 • Ratio- write this ratio as a fraction in simplest form and two other ways 15 to 40 3/8,3 to 8, 3:8 • Rate- two measurements are related to each other • Unit Rate- quantity corresponds to one unit of the second type of quantity • How do you change a rate to a unit rate? Find exchange rate

  17. Proportion – solve this proportion 18 divided by 3 =6 6x5=30 3/10 • Scale Drawing- a drawing with dimensions at a specific ratio relative to the actual size of the object drawn Scale-used to determine distance, or size • 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? 2 ½ inches apart. • 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?675 miles

  18. Chapter 11 • Relation-a generalization of arithmetic relations, such as "=" and "<", • Input-The number or value that is entered • Output- • The number or value that comes out from a process. • Function- • A function f of a variable x is a rule that assigns to each number x in the function's domain a single number f(x) • Domain- • The set of numbers x for which f(x) is defined • Range-The range of a set of numbers is the largest value in the set minus the smallest value in the set. • Scatter Plot- • A graphical representation of the distribution of two random variables as a set of points whose coordinates represent their observed paired values. • Solution of an equation with two variables-subtract a whole number from each side until you get down to variables then just subtract the numbers in front of the variable then you should have a number = x • Linear equation-linear function • A function of the form f(x) = mx + b where m and b are some fixed numbers. The names "m" and "b" are traditional.

  19. Is the following a function? (2,3), (3,5), (7,2), (9,1) No • Name the domain and the range of the set of points above. 3,5,9,1 • Find three solutions of y = 6x + 5, and tell if this is a linear equation. • 3=23,5=35,4=29,no • Does the number of days we’ve been in school and how many days are left in the school year have a positive relationship, a negative relationship, or no relationship? positive

  20. Chapter 12 • Range • The range of a set of numbers is the largest value in the set minus the smallest value in the set • Median "Middle value" of a list. The smallest number such that at least half the numbers in the list are no greater than it. If the list has an odd number of entries, the median is the middle entry in the list after sorting the list into increasing order. If the list has an even number of entries, the median is equal to the sum of the two middle (after sorting) numbers divided by two. • Stem and leaf plot-in statistics, is a device for presenting quantitative data in a graphical format, similar to a histogram, to assist in visualizing the shape of a distribution. • Lower quartile-a quartile is any of the three values which divide the sorted data set into four equal parts • Lower extreme-The smallest or least number out of a data set, usually farther away from interquartile range than other data in set. • Line graph-Graphical device that displays quantitative information or illustrates relationships between two changing quantities ( variables) • Tree diagram-Graphical device that displays quantitative information or illustrates relationships between two changing quantities ( variable • Complementary- Two angles are said to be complementary if their sum is 90o • Odds- are a way of expressing a probability as the ratio of the number of things that you are not looking for to the number of things that you are looking for • Independent events-Two events A and B are independent if the probability that they happen at the same time is the product of the probabilities that each occurs individually; i.e., if P(A & B) = P(A)P(B). In other words, learning that one event occurs does not give any information about whether the other event occurred too: the conditional probability of A given B is the same as the unconditional probability of A, i.e., P(A/B) = P(A)

  21. Mean • Median Mode • Stem and leaf plot Box-and-Whisker plot • Lower quartile Upper quartile • Lower extreme Upper extreme • Circle graph Line graph • Tree diagram Fundamental Counting Princip • Complementary Unfavorable outcome • Probability Dependent events

  22. Chapter 13

  23. Geometry

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