Preparing for Math 7 Accelerated William Allen Middle School Middle Moorestown, New Jersey Student Name:
Preparing for Math 7 Accelerated The purpose of the packet is to help you review and reinforce concepts/topics that are necessary for seventh grade math. Instructions: Complete all sections of this packet (18 pages). You MUST show all work (use additional paper if necessary). You will return this completed packet to your math teacher during the first week of school. This packet will be collected the Friday after Labor Day and graded for accuracy. All work must be shown and final solutions should be circled. You will be tested on the concepts covered in this packet during the 2 nd week of school It may be necessary to seek assistance on some questions/concepts that is fine! Websites that may be of assistance: www.mathforum.org/dr.math Use this web site if you have a math questions that you need answered. www.allmath.com This website will provide you with links to games, reference, general math help and resources. www.mathforum.com This online community includes teachers, students, researchers, parents and educators who have an interest in math and math education. The site includes Ask Dr. Math, Problems of the Week, discussion groups and much more. www.aaamath.com. Customized by grade level and topic, AAA Math features explanations of various mathematical topics, practice problems and fun, challenging games. www.coolmath.com This fully interactive site and allows the user to sharpen basic math skills, play games and explore new math concepts. www.figurethis.org This site helps families enjoy mathematics outside school through a series of fun and engaging challenges. The more math you explore the more prepared you will be in September! 2
Adding Integers Adding Integers with the Same Signs: Add the number together and keep the sign. -7 + -6 = -13 Adding Integers with Different Signs: Subtract the numbers and use the sign of the number with the greater absolute value. Find each sum. No Calculator. -7 + 6 = -1 7 + (-6) = 1 1. 5 + (-8) 2. -6 + 6 3. -4 + (-9) 4. -7 + 13 5. -9 + (-9) 6. 14 + (-27) 7. 15 + (-10) 8. 19 + (-10) 9. -12 + (-18) 10. -14 + (-12) 11. -12 + (-8) 12. -28 + 16 13. -8 + (-10) + 15 14. 15 + (-8) + 7 15. -10 + (-10) + 5 3
Subtracting Integers Change each subtraction problem into an addition problem, by adding the opposite number, and then use the rules for adding integers. -10 15-10 (-15) -10 + (-15) = -25-10 + (+15) = 5 Rewrite each subtraction problem as an addition problem and then find each sum. No Calculator. 1. 6 (-8) 2. -2-3 3. -8 (-10) 4. 9 14 5. 36 (-12) 6. 5 12 7. 15 (-8) 8. -16 6 9. -4 9 10. -17 13 11. 12 (-9) 12. 14 (-22) 13. 5 (-25) 14. -19 (-50) 15. 12 (-52) 4
Multiplying Integers Multiply the numbers together and use the following rules negative negative = positive negative positive = negative Remember multiplication is commutative, so order doesn t matter. -7(-6) = 42 7(-6) = -42 Find each product. No Calculator. 1. 2(-8) 2. -3(-4) 3. 8(-4) 4. (-5)(-5) 5. -12(5) 6. -12(13) 7. 14(-3) 8. -14(-5) 9. -7(-8) 10. (-4) 2 11. (-11) 2 12. (-5) 3 13. (-2)(-3)(5) 14. 3(-4)(-2)(-1) 15. (-2) 4 5
Dividing Integers Divide the numbers together and use the following rules negative negative = positive negative positive = negative Once again in deciding whether the answer is negative or positive, order doesn t matter. 42 (-6) = -7-42 (-6) = 7 Find each quotient. No Calculator. 1. -16 (-4) 2. -100 10 3. -28 7 4. 52 (-4) 5. -125 (-25) 6. -32 (-16) 7. -120 (-12) 8. 45 (-9) 9. 33 (-3) 10. -36 12 11. -200 (-25) 12. -88 11 13. 14. 15. 6
Operations with Rational Numbers Use your integer rules together with the rules for operations with rational numbers to simplify each expression. Simplify each numerical expression, show all your steps. No Calculator. 1. 1 1 3 5 2. 2 3 5 2 1 6 5 3. 6 1 2 7 3 4. 5.87 12.22 5. 1 5 3 1 3 6 6. -3.88 + 9.8 7. -3.1(2.1) 8. 392 49 7
Order of Operations Grouping Symbols: Parenthesis, brackets, fraction bars Exponents Multiply and/or Divide from left to right Add and/or Subtract from left to right Simplify each numerical expression, show all your steps. No Calculator. 9. 3 + 5(4) 10 10. 2(5) + 3(4) 11. 18 20(2) + 5 2 12. -5[3 + 10(2)] 13. (15 + 13) (6-10) 14. 16 [(4 2) 2 + 1] 15. 18 (-2 1) 3 16. 4 + (-5) 10(2) 8
Evaluating Algebraic Expressions Substitute each variable with its assigned value. Simplify the expression using the order of operations. Be careful! When replacing a variable with a negative value, put parentheses around the value in the expression. Evaluate 4xy when x = -2 and y = -5 4(-2)(-5) = 40 Evaluate each expression, if a = -2, b = 4 and c = 10. Show all your steps. No Calculator. 1. 2a + b 2. ab 3. ab + c 4. 3a b 5. ac b 6. 4a b 7. 6a + 5b 8. 9
Simplify Expressions Simplify each expression by following the order of operations and combining like terms together. No Calculator. 4x + 3(x 2) 4x + 3x 6 7x 6 1. 2a 5a + 2a - 8 2. 3(x + 2) 3. 10x (-2x) 4. -3(x + 12) 5. 2x 5x + 7x 6. -2(3x + 3 3) 7. 4 + 2(x + 1) 8. 4 2(x 5) 10
Solve Equations Work backwards through the order of operations and show each inverse operation as you isolate the variable. Use a separate piece of paper if needed. No Calculator. 4x + 3 = 11-3 -3 4x = 8 4 4 x =2 1. 2a 5 = 11 2. -11b = 121 3. -2a + 17 = 24 4. 6 3b = -9 5. -5a 6 = 24 6. 3a + 12 = -12 7. 9 = 16b + 51 8. 1.2x + 3.7 = 34.6 11
9. -12 = 7x 5 10. x 8 = 12 16 11. r 5 = 65 75 12. c 5 = 650 6.5 13. 2(x 3) = -20 14. 4(2x + 5) 8 = 36 15. 15 4x + 5 = 32 16. -9(6 + x 2) = -10 12
Fraction/Decimal/Percent Complete the table below. Remember percent means out of 100. You may use a calculator. Do NOT round any answers, use fractions or repeating decimals. All fractions must be in simplest form. Fraction Decimal Percent 1 2 20% 0.48 11 12 2 3 1.12 0.256 1.5% 13
Percent Problems Use a proportion or an equation to answer each question. Round to the nearest tenth when needed. You may use a calculator. part whole = percent 100 1. 40% of what number is 82? 2. 6.25% of what number is 190? 3. What percent of 76 is 14? 4. What is 84% of 180 5. 85% of 190 is what number? 6. 25 is what percent of 365? 7. 8.25% of 180 is what number? 8. What percent of 185 is 35? 14
Application Show all your steps in each problem below. No Calculator. 1. The wait time for a ride at the county fair is 9 minutes when 45 people are in line. At this rate, what is the wait time when 270 people are in line? 2. Maggie places 20 marbles on one side of a balance to equal the weight of four cans of cat food on the other side of the balance. How many marbles would equal the weight of two cans of cat foot? 3. The temperature at 5:00 PM was 12 F. Over the next seven hours, the temperature dropped a total of 15 degrees. Write an expression for the temperature at midnight and then find the temperature. 4. Marci owes her brother $11 and her Mom $7. Write an expression for the amount of money Marci will have left if she has $25. Then find the amount she has left. 5. Tina paid $56 for 8 yards of material. Find the unit price. 6. Last summer, Chris made $1275 cutting lawns in the neighborhood. Find a unit rate to represent Chris average monthly earnings over the 3-monthly period. 15
Geometry and Application To find the area of a 2 dimensional figure, you must know the formulas. A few things to remember: 1. The base and height are perpendicular (they form a right angle) 2. In a trapezoid, the two bases are parallel (they do not intersect) 3. Base is any flat side. Use the one that has the height drawn to it. Write the area formula for each shape. 1. Rectangle 2. Parallelogram 3. Triangle 4. Trapezoid Find the area of each figure. Do NOT use a calculator. 6. 7. Find the area in mm 2 16
8. 9. Find the height if the AREA = 35 cm 2 10. 11. 17
12. 13. Graph the following ordered pairs on the coordinate plane, connect the vertices to form a polygon and find the area of the polygon: A(-3, 1); B(0, 7) and C(3, 1) 18
PREPARING FOR MATH 7 ACCELERATED Answer Key (Evens Only) Simplify: Adding Integers (p. 3) 2. 0 4. 6 6. -13 8. 9 10. -26 12. -12 14. 14 Simplify: Subtracting Integers (p. 4) 2. -5 4. -5 6. -7 8. -22 10. -30 12. 36 14. 31 Simplify: Multiplying Integers (p. 5) 2. 12 4. 25 6. -156 8. 70 10. 16 12. -125 14. -24 Simplify: Dividing Integers (p. 6) 2. -10 4. -13 6. 2 8. -5 10. -3 12. -8 14. -2 Solve Equations (p. 11-12) Operations with Rational Numbers (p. 7) 7 2. 2 30 4. -6.35 6. 5.92 8. -8 Order of Operations (p. 8) 2. 22 4. -115 6. 11 8. -21 Evaluating Algebraic Expressions (p. 9) 2. -8 4. -10 6. -12 8. -1 Simplify Expressions (p. 10) 2. 3x + 6 4. -3x 36 6. -6x 8. -2x + 14 2. b = -11 4. b = 5 6. a = -8 8. x = 25.75 10. x = 6 12. c = 600 14. x = 3 16. x = 2 8 9
Fraction / Decimal / Percent (p. 13) Fraction Decimal Percent 0.5 50% 1 2 48 12 100 = 0.48 48% 25 11 12 0.916 91 2 3 % = 91.6% 64 = 250 125 32 0.256 25.6% Percent Problems (p. 14) 2. 3,064.5 4. 151.2 6. 6.8% 8. 18.9% Geometry and Application (p. 16-18) 6. 40 cm 2 8. 75 cm 2 10. 48 in 2 12. 75 square units Application (p. 15) 2. 10 marbles:2 cans of cat food 4. expression: 25 11 7 $7 left over 6. $425 per month