ࡱ> } }bjbj55 9__*# I I I !"4 #^C$Y$Y$$G=.u== `nEI HB58C=HBHBY$$Z\8M8M8MHBY$I $8MHB8M8Mj!Y$X\ B݄2r0JΑE&ΑdYΑI Y=>8M?#@%===K&===HBHBHBHBΑ========= : Northwest High Schools Algebra 1      Summer Review Packet 2009 DUE THE FIRST DAY OF SCHOOL Student Name ________________________________________ This packet has been designed to help you review various mathematical topics that will be necessary for your success in Algebra 1. Instructions: DO ALL PROBLEMS WITHOUT USING A CALCULATOR. Show all work that leads you to each correct solution. Additional copies of this packet may be obtained from the Northwest High School website:  HYPERLINK "https://northwesths.net" https://northwesths.net ALL work should be completed and ready to turn in on the FIRST DAY of school. This packet will count as part of your first quarter grade. Due Date: August 31, 2009 Deadline: September 8, 2009 If you have any questions regarding the summer math packet, please call Vic Weinstein at (301) 601-4651. ENJOY YOUR SUMMER! WE ARE LOOKING FORWARD TO SEEING YOU IN THE FALL.  Table of Contents Order of Operations page 1 Operations with Signed Numbers page 2 Rounding Numbers page 4 Evaluating Expressions page 5 Combining Like terms page 6 Graphing page 7 Solving Equations page 9 8. Word Problems page 10 Order of Operations To avoid having different results for the same problem, mathematicians have agreed on an order of operations when simplifying expressions that contain multiple operations. 1. Perform any operation(s) inside grouping symbols. (Parentheses, brackets above or below a fraction bar) 2. Simplify any term with exponents. 3. Multiply and divide in order from left to right. 4. Add and subtract in order from left to right. One easy way to remember the order of operations process is to remember the acronym PEMDAS or the old saying, Please Excuse My Dear Aunt Sally. P - Perform operations in grouping symbols E - Simplify exponents M - Perform multiplication and division in order from left to right D A - Perform addition and subtraction in order from left to right S Example 1 Example 2 2 32 + (6 + 3 x 2) -7 + 4 + (23 8 -4) 2 32 + (6 + 6) -7 + 4 + ( 8 8 -4) 2 32 + 12 -7 + 4 + ( 8 - -2) 2 9 + 12 -7 + 4 + 10 -7 + 12 -3 + 10 = 5 = 7 Order of Operations Evaluate each expression. Remember your order of operations process (PEMDAS). 1. 6 + 4 2 " 3 = 2. 15 3 " 5  4 = 3. 20  7 " 4 = 4. 50  (17 + 8) = 5. 12 " 5 + 6 6 = 6. 3(2 + 7)  9 " 7 = 7. 16 2 " 5 " 3 6 = 8. 10 " (3  62) + 8 2 = 9. 32 [16 (8 2)] = 10. 180 [2 + (12 3)] = 11. 5 + [30  (8  1)2] = 12. 5(14  39 3) + 4 " 1/4 = Operations with Signed Numbers Adding and Subtracting Signed Numbers Adding Signed Numbers Like SignsDifferent Signs Add the numbers & carry the sign Subtract the numbers & carry the sign of the larger number ( + ) + ( + ) = + ( +3 ) + ( +4 ) = +7  ( + ) + ( ) = ? ( +3 ) + (2 ) = +1 ( ) + ( ) = ( 2 ) + ( 3 ) = ( 5 ) ( ) + ( + ) = ? ( 5 ) + ( + 3 ) = 2  Subtracting Signed Numbers Dont subtract! Change the problem to addition and change the sign of the second number. Then use the addition rules. ( +9 ) ( +12 ) = ( +9 ) + ( 12) ( +4 ) (3 ) = ( +4 ) + ( +3 )  ( 5 ) ( +3 ) = ( 5 ) + ( 3 ) ( 1 ) ( 5 ) = ( 1 ) + (+5)  Simplify. Do not use a calculator for this section 1. 9 + -4 2. 20 -6 3. -8 + 7 4. -14 6 5. -6 -7 6. -30 + -9 7. 14 20 8. 1 -12 Multiplying and Dividing Signed Numbers If the signs are the same, If the signs are different, the answer is positive the answer is negative Like SignsDifferent Signs (+ ) ( + ) = + ( +3 ) ( +4 ) = +12  ( + ) ( ) = ( +2 ) ( 3 ) = 6 ( ) ( ) = + ( 5 ) ( 3 ) = + 15 ( ) ( + ) = ( 7 ) ( +1 ) = 7  (+ ) / ( + ) = + ( +3 ) / ( +4 ) = +12  ( + ) / ( ) = ( +2 ) / ( 3 ) = 6 (+ ) / ( + ) = + ( +3 ) / ( +4 ) = +12  ( ) / ( + ) = ( 7 ) / ( +1 ) = 7  Simplify. Do not use a calculator for this section. (-5)(-3) = 5. -20 = -1 (-1)(-5) = -6 = 6. (3) (-4) = 2 (2)(4) = 7. 8 = -4 -12 = 8. -16 = -4 8 Rounding Numbers Step 1: Underline the place value in which you want to round. Step 2: Look at the number to the right of that place value you want to round. Step 3: If the number to the right of the place value you want to round is less than 5, keep the number the same and drop all other numbers. If the number to the right of the place value you want to round is 5 or more, round up and drop the rest of the numbers. Example: Round the following numbers to the tenths place.  Tenths 23.1246 23.1  2. 64.2685 64.3   3. 83.9721 84  Round the following numbers to the tenths place. 1. 18.6231 _____________ 6. 0.2658 ______________ 2. 25.0543 _____________ 7. 100.9158 _____________ 3. 3.9215 _____________ 8. 19.9816 ______________ 4. 36.9913 _____________ 9. 17.1083 ______________ 5. 15.9199 _____________ 10. 0. 6701 ______________ Evaluating Expressions Example Evaluate the following expression when x = 5 Rewrite the expression substituting 5 for the x and simplify. 5x = 5(5)= 25 -2x = -2(5) = -10 x + 25 = 5 + 25 = 30 5x - 15 = 5(5) 15 = 25 15 = 10 3x + 4 = 3(5) + 4 = 19 Evaluate each expression given that: x = 5 y = -4 z = 6 1. 3x 5. y + 4 2. 2x2 6. 5z 6 3. 3x2 + y 7. xy + z 4. 2 (x + z) y 8. 2x + 3y z Combining Like Terms What is a term? The parts of an algebraic expression that are separated by an addition or subtraction sign are called terms. The expression 4x + 2y 3 has 3 terms. What are like terms? Terms with the same variable factors are called like terms. 2n and 3n are like terms, but 4x and 3y are not like terms because their variable factors x and y are different. To simplify an expression, you must combine the like terms.  Simplify 1. 5x + 8x 2. 3y 6y 5x + 8x = (5 + 8)x = 13x 3y 6y = (3 6)y = -3y 3. 3x + 4 2x + 3 4. 2b + 5c + 3b 6c 3x 2x + 4 + 3 = (3 2)x + 4 + 3 = x + 7 2b + 3b + 5c 6c = (2+3)b + (5 6)c = 5b c Practice: Simplify each expression 6n + 5n 2. 37z + 4z x 5x 4. 3n + 1 2n + 8 7t + 9 4t + 3 6. 4r + 3r +6y 2y 8g + 9h 4g 5h 8. 2m + 3n 4m + 5n Graphing Points in a plane are named using 2 numbers, called a coordinate pair. The first number is called the x-coordinate. The x-coordinate is positive if the point is to the right of the origin and negative if the point is to the left of the origin. The second number is called the y-coordinate. The y-coordinate is positive if the point is above the origin and negative if the point is below the origin. The x-y plane is divided into 4 quadrants (4 sections) as described below.    All points in Quadrant 1 has a positive x-coordinate and a positive y-coordinate (+ x, + y). All points in Quadrant 2 has a negative x-coordinate and a positive y-coordinate (- x, + y). All points in Quadrant 3 has a negative x-coordinate and a negative y-coordinate (- x, - y). All points in Quadrant 4 has a positive x-coordinate and a negative y-coordinate (+ x, - y). Plot each point on the graph below. Remember, coordinate pairs are labeled (x, y). Label each point on the graph with the letter given. 1. A(3, 4) 2. B(4, 0) 3. C(-4, 2) 4. D(-3, -1) 5. E(0, 7)  Example: F(-6, 2)      Determine the coordinates for each point below: Example. ( 2 , 3 ) 6. (____, ____) 7. (____, ____)    8. (____, ____) 9. (____, ____) 10. (____, ____)  Solving Equations To solve an equation means to find the value of the variable. We solve equations by isolating the variable using opposite operations.  Example: Solve. 3x 2 = 10  + 2 + 2 Isolate 3x by adding 2 to each side. 3x = 12 Simplify 3 3 Isolate x by dividing each side by 3.   x = 4 Simplify Check your answer. 3 (4) 2 = 10 Substitute the value in for the variable. 12 2 = 10 Simplify 10 = 10 Is the equation true? If yes, you solved it correctly! Try These: Solve each equation below. 1. x + 3 = 5 3. c 5 = -8 5. -7k = 14 7.  EMBED Equation.3  = 5 9. 2x 5 = 11 2. w 4 = 10 4. 3p = 9 6. x = -17 8.  EMBED Equation.3  = 7 10. 5 j 3 = 12  EMBED Equation.3  + 10 = 15  EMBED Equation.3  4 = 2 Word Problems Translate each word problem into an algebraic equation, using x for the unknown, and solve. Write a let x = for each unknown; write an equation; solve the equation; substitute the value for x into the let statements(s) to answer the question. For Example: Kara is going to Maui on vacation. She paid $325 for her plane ticket and is spending $125 each night for the hotel. How many nights can she stay in Maui if she has $1200? Step 1: What are you asked to fine? Let variables represent what you are asked to find. How many nights can Kara stay in Maui? Let x = The number of nights Kara can stay in Maui Step 2: Write an equation to represent the relationship in the problem. 325 + 125 x = 1200 Step 3: Solve the equation for the unknown 325 + 125 x = 1200 - 325 -325 125 x = 875 x = 7 Kara can spend 7 nights in Maui Word Problem Practice Set A video store charges a one-time membership fee of $12.00 plus $1.50 per video rental. How many videos can Stewart rent if he spends $21? Bicycle city makes custom bicycles. They charge $160 plus $80 for each day that it takes to build the bicycle. If you have $480 to spend on your new bicycle, how many days can it take Bicycle City to build the bike? Darel went to the mall and spent $41. He bought several t-shirts that each cost $12 and he bought 1 pair of socks for $5. 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