Algebra Prep Summer Math Packet

Transcription

1 Google Classroom Code: 3c7sdre Algebra Prep Summer Math Packet Name Loiederman Middle School

2 Table of Contents Section Description IM Unit Page Order of Operations Evaluate expressions using the order of operations Perfect Squares and Square Roots Evaluate expressions using laws of exponents Evaluate perfect squares and perfect cubes 6 7 Evaluate square roots Linear Equations Identify proportional relationships in and out of context 1 10 Completing an Input Output Table 1 11 Plot points on the coordinate plane Identify the slope of a line Solving 2-Step Equations Glossary NA 17 Information - Each section of this packet has been created specifically for what you need to know as you head into Algebra I. The Mild sections are a refresher/introduction to the content. The Medium questions are what you should be able to do starting out in Algebra I. The Spicy sections are to challenge what you already know. - If you are confused on the directions in a section, please read the bulleted items. - If you are confused on the material covered in a section, go to the google classroom page and use the links provided for the major topics. The google classroom code is 3c7sdre. - If you do not have computer access but would like to see any videos posted online or other tools, the school Media Center is open during the summer on weekdays. Call the main office to double check that the Media Center is available on a given day. - The last page of the packet is a glossary with key words that are used in the packet or in the beginning of Algebra I. - The Summer Packet is due two weeks into the new school year, September 14, Turn in your packet to your Algebra I teacher for a prize. 1

3 Order of Operations The Order of Operations tells us in what order to do different parts of a problem. You can remember it by using the mnemonic PEMDAS Example: 5 (3 + 2) 4 2 5(5) 4 2 5(5) Evaluate the following expressions using Order of Operations. Complete at least 10. Mild 2 + 4(8 3 ) ( 3 2) (6 2 ) 2 24( 3 5 ) ( 2 + 4) 2 2

4 Medium ( ) (5 1) 5 ( 3 + 1) ( 15 10) 2 ( ) Spicy 3

5 Exponent Laws 1) The product of two expressions with the same base equals the base raised to the power of the sum of the exponents. Why does this property work? Let s look at an example: Therefore So Try These: 2) The quotient of two expressions with the same base equals the base raised to the power of the difference of the exponents. Why does this property work? Let s look at an example: Therefore So Try These: 4

6 3) An exponential expression raised to a power is equal to the base raised to the power of the product of the exponents. Why does this property work? Let s look at an example: ( 3 8 ) 4 = ( 3 8 )(3 8 )(3 8 )(3 8 ) = = 3 32 Try These: 4) The expressions and are equal. Why does this property work? Let s look at an example: By the quotient property: By the definition of exponents: Try These: Therefore from the previous two lines, MIXED REVIEW Write each of the following as a power of two. Your answer should be in the form of 2 raised to a power. 5

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8 Evaluate Perfect Squares and Perfect Cubes To find the area of a rectangle, we multiply the length times width. When the rectangle is a square, the length and width are the same. The area of a square is the side length squared. To find the volume of a rectangular prism, we multiply the length times width times height. When the rectangular prism is a cube, the length, width, and height are the same. The volume of a cube is the side length cubed. Complete the table for the perfect squares and cubes of the numbers 1-12 s s 2 s

9 Evaluating Square Roots If a perfect square represents the area of a square with a given side, the square root represents the side length of a square with a given area. We represent a square root using a radical. Identify the square root for each of the following Because a negative times a negative is positive and a positive times a positive is also positive, a positive number can have two square roots, the positive side and the negative side. Example: 25 = 5 or 5 Go back and complete the square roots for the above problems. Because a negative times a negative is positive and a positive times a positive is also positive, negative numbers do not have a real square root. In these cases we write no real solution. Mild Identify the square root of each of the following. 4 = 9 = 36 = 0 = 121 = 1 = 9 = 100 = 8

10 Spicy If a square root cannot be simplified, we leave the radical alone. If one of the factors of a square root is a perfect square, we can pull out root of the perfect square and leave the other factors inside. Example: Simplify the following square roots 48 = 54 = 75 = 200 = 32 = 98 = 9

11 Identifying Proportional Relationships Linear equations have a common rate of change. We call it the slope or the unit rate. No matter which two rows you choose, the rate of change is the same. Find the rate of change of the following tables x y x y x y Find the rate of change for the following word problems. Be sure to include units. A climber is on a hike. After 2 hours he is at an altitude of 400 feet. After 6 hours, he is at an altitude of 700 feet. What is the average rate of change? A teacher weighed 145 lbs in 1986 and weighs 190 lbs in What was the rate of change in weight? 10

12 Completing an Input-Output Table Input-Output Tables are helpful for finding points on a line. The input is the x and the output is the y. Plug the input value into the rule and the answer will be the output. Complete the following input-output tables Plotting Points on a Coordinate Plane Coordinates are given in the form ( x,y ). The x value tells you where to go on the x axis and the y value tells you where to go on the y axis. Mild Write the coordinates for each of the plotted shapes below 11

13 Medium Spicy Thomas knows how to plot point J as (-3,4) on a coordinate grid. Thomas needs to plot point K at (-3.5,4). Lisa needs to plot point L at (-3.5, -4). Explain where point K is on the coordinate grid in relation to point J. Identify any similarities between the ordered pair for point K and the ordered pair for point L. Explain which quadrant point L, J, and K. 12

14 Slope on a Coordinate Plane Slope is the rate of change of a linear function. It is similar to finding the unit rate. On a graph we find the slope by creating a fraction of the change in y or rise and the change in x or the run. Mild Find the slope of the following graphs 13

15 Spicy: How many miles per gallon does the car get? How many miles can the car travel using 9 gallons of gas? The two graphs below show the total time spent on the phone by the people of Ohio over a span of 9 weeks. Study the graphs and answer the following questions. Which graph s total time spent is proportional to the number of weeks? Which graph s total time spent is not proportional to the number of weeks? 14

16 Solving Multi-Step Equations In order to solve equations, we use the Order of Operations to get the variable alone on one side. Solve for x in the following problems Mild x + 3 = 15 2 x = 10 2 x + 5 = 17 x 9 = 91 3x 7 = 20 2 (x + 1 ) = 6 Medium ( x + 3 ) = 14 x+1 3 = 5 x + 3 = 2x 7 2 x + 1 = 4x 9 6x 19 = 5x 2 3 (x + 4 ) = 2 (2x + 3.5) 15

17 Spicy The city wants to collect $79424 in bridge tolls. If the tolls is $7 for each car, how many cars will have to cross for the bridge for the city to meets its goal? Calculate value of x. 4x+9x 8 8x = 7 16

18 Glossary: Word Spanish Translation Definition area el área the total amount inside a 2 dimensional shape domain dominio the set of x values exponent la exponente the small number that represents the number of times a number is multiplied by itself integer número entero positive or negative whole numbers irrational number el número irracional a number that cannot be represented as a ratio length distancia o longitud the measure of how long something is linear lineal a function that creates a line mean median media mediana The average of the data set. Add the numbers together then divide by how many numbers there are The middle of the data. Order the numbers from least to greatest and find the center mode modo The number that appears most often radical raíz cuadrada (square root) range rango the set of y values The "house" that represents a square root rate of change tasa de cambio the change in y divided by the change in x ratio proporcion A comparison of two things rational number el número racional a number that can be represented as a ratio rectangle el rectángulo a shape with two sets of parallel sides four 90 degree angles slope pendiente Rise over Run, the rate of change square unit rate el cuadro o el cuadrado ( x 2 ) tasa unidad a rectangle with 4 equal sides or multiplying a number by itself "how many" per one (miles per hour, drops per second, beats per minute) 17