6 th Grade - TNREADY REVIEW Q3 Expressions, Equations, Functions, and Inequalities

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1 6 th Grade - TNREADY REVIEW Q3 Expressions, Equations, Functions, and Inequalities INSTRUCTIONS: Read through the following notes. Fill in shaded areas and highlight important reminders. Then complete the practice questions that follow. Due Date: Friday, March 16 EXPRESSIONS NOTES: Evaluating Expressions - PEMDAS: Remember to rely on Order of Operations when evaluating expressions P E M D A S - Exponents: Represent repeated multiplication. The base represents the factor being multiplied and the exponent is the number of times the factor is being multiplied by itself. - Combine like terms: Add constants with constants, and coefficients of like variables - ONE STEP AT A TIME: Don t do it all in your head! Simplify one step at a time! (Ice Cream Cone Style) - Substitute for a Variable: Be precise! Replace the given value for the specified variable NOTES: Writing Expressions - Define your Variable: Remember variable stand for SPECIFIC values. Make sure you know what each variable stands for in each expression - Operation Vocabulary: Sum (+), Difference (-), Product (x), Quotient (/) - Properties of Operations: Pay attention to your operations and their properties * Addition and Multiplication are COMMUTATIVE: Order doesn t matter * Subtraction and Division: ORDER MATTERS! What are you subtracting? What are you dividing? NOTES: Equivalent Expressions - Remember your properties!!!! Can you use them to make equivalent expressions? Associative: Commutative: Distributive: Identity: Zero: - Can you combine like terms? - Can you factor an expression using GCF? GSWAC G-Given S-Substitute W-Work A-Answer C-Check

2 EQUATIONS NOTES: Solving One-Step Equations - ISOLATE THE VARIABLE: What is your goal????? Look at your variable you need to get it by itself on one side of the equal sign. - Inverse Operation: What is being done to the variable? Use the inverse (opposite) operation to undo the actions * Opposites (+ and -), (x and /) - HELPFUL HINTS: 1) Draw your Nile, 2) Isolate the Variable! 3) No one crosses the river without a BUDDY! NOTES: Writing Equations - Define your Variable: Remember variables stand for SPECIFIC values. Make sure you know what each variable stands for in each equation. - Don t forget your EQUAL SIGN - Properties of Operations: Pay attention to your operation (+, -, x, /) and their properties Addition and Multiplication are COMMUTATIVE: Order doesn t matter Subtraction and Division: ORDER MATTERS! What are you subtracting? What are you dividing? - HELPFUL HINT: Start from the solution! If your first instinct to solve the problem is to divide.your equation probably has the variable multiplied by a number (think inverse operations!!!!) FUNCTIONS NOTES: Functions - Input: independent variable (usually x) - Output: dependent variable (usually y) - Function rule: expression or equation that explains the relationship between the independent and dependent variable. Ex. y = 2x - Graphing: Values for a given function rule can be written in a function table. Those values can be written as ordered pairs and graphed on the coordinate plane. *NOTE: Linear functions will graph as straight lines! NOTES: Same Rules as Equations, EXCEPT - Review your inequalities: INEQUALITIES - When solving.bring DOWN THE SYMBOL: you bring down the < or >, < or > instead of the = sign

3 PRACTICE QUESTIONS 1. Which expressions are equivalent to 4(5 + 3)? A. 4(8) B C D. 4 + (5 + 3) E. (5 + 3) + (5 + 3) + (5 + 3) + (5 + 3) 2. Select the expression that shows using the greatest common factor times the sum of two numbers. A. 2(18+ 27) B. 3( ) C. 6(6 + 9) D. 18(2 + 3) 3. Apples cost $1.59 per pound. Write an equation that could be used to find the total cost, y, of x pounds of apples. 4. Find the value of w that makes this equation true: w = Select all of the expressions that are equivalent to 4 + w + 16w. A w B. 17w C. 4(1 + 4w) + w D w E. 2(2 + 16w 2 ) 6. John is participating in a math competition. He earns 20 points for each correct response, c. He loses 10 points for each wrong response, w. Which expression represents Quinn s total points in the trivia competition? A. 20c + 10w B. 20c C. 10c 20w D. 20c 10w 7. A gallon of milk costs $2.75. Use the equation p = 2.75g to find a total cost with price, p, and gallons, g. Match each number of gallons on the left with its equivalent dollar amount on the top. Mark your answers on your answer document. 10 gallons 4 gallons 8 gallons $27.50 $11.00 $22.00

4 8. Which expression is equivalent to the product of 7 and y? A. 7 + y B. 7 y C. 7 y D. 7y 9. At a bake sale, plates of brownies, b, are sold for $6 each. The amount of money from the sale of brownies is expressed as dollars, d. Which equation represents the earnings of the bake sale? Plates of brownies (b) Earnings (d) A. b = 6d B. d = b + 6 C. d = b 6 D. d = 6b 10. Jordan has $40 in his savings account for his beach trip. He plans to deposit $10 into his savings account each month. Select all expressions that could be used to find the amount of money Jordan will have in his savings account after x months of making deposits. A. 10x 40 B. 10x + 40 C x D x E x 11. What is the value of 1200 ( ) 15? 12. What is the value of 3(x + 14) 15 when x = 6? 13. Select the value of r that makes 4r = 36 true. A. 1 9 B. 9 C. 32 D Select ALL of the expressions that are equivalent to 5 4. A. 5 4 B C D E

5 15. What is the value of the expression (4 2) 2 4? 16. Kayla is wrapping a gift for her best friend s birthday. The gift fits into a cube shaped box with a side length of 5 inches. How many square inches of wrapping paper does she need to cover the box without the paper overlapping? Use the formula A = 6s 2 so that s equals the side length and A equals the surface area. A. 42 square inches B. 60 square inches C. 150 square inches D. 900 square inches 17. Matt earns d dollars for each lawn he mows. He earns $5 more per lawn if he trims the hedges. Which expression would you use to show how much money Matt would earn if he mows at 10 houses and at 3 other houses, he mows and trims the hedges? A. 13d + 15 B. 13d + 65 C. 10d + 15 D. 10d Which expression is equivalent to 4(3y + 6) - 2y? A. y + 24 B. 12y + 24 C. 10y + 24 D. 12y Select 3 expressions that are equivalent to 12x+8. A. 4(3x + 2) B. 6x + 2(3x + 4) C. 12(x + 8) D. 2(3x + 3) + 2(3x + 1) E. 8(4x + 1) 20. Select the inequality that has the set (-12, -9, -3, 12, 21) as possible solutions for x. A. x > -5 B. x > -25 C. x < -5 D. x < Wes is buying bulk candy at the store. Bulk candy cost $0.54 per pound. Wes buys p pounds of candy, and the total cost is $2.70. PART A) An equation that correctly represents the situation is A. 0.54p = 2.70 B p = 2.70 C = p D. 2.70p =.54 PART B) Wes was able to buy A. 0.2 pounds B. 5 pounds C pounds D pounds

6 22. Lucy and Lainey were picking out different types of shells to make a necklace. Lucy picked out at least 6 fewer shells than Lainey. If Lainey picked out 20 shells, which inequality best represents the possible number of shells, s, that Lucy picked out? A. s 26 B. s 26 C. s 14 D. s Part A: Connor is buying board games that cost $10 each. He has a coupon for $5 off his total purchase. Select an equation that can be used to find c, the total amount he will spend on any number of board games, b A. 10b = c B. c = 10b + 5 C. 10b 5 = c D. c = (b+10) - 5 Part B: The amount Connor will spend to buy 4 board games is A. $40 B. $45 C. $35 D. $9 24. Aidan has more than $25 in his bank account. Let d represent the number of dollars in his bank account. Which inequality best represents how many dollars Aidan has in his bank account? A. d < 25 B. d > 25 C. d 25 D. d The algebraic expression 3x 2 +5x+2 represents the area of a rectangle. What is the area of the rectangle when x = 4 feet? A. 46 square feet B. 70 square feet C. 166 square feet D. 40 square feet 26. Select Yes or No to indicate whether the pairs are equivalent expressions. A. 36+9x and 9(4+x) (yes or no) B. 3(3x-y) and 9x-3y (yes or no) C. 10(x+2y) and 10x+2y (yes of no) 27. Select 3 equations where x=5 is a solution. A. 3x + 6 = 21 B x = 14 C. 5x = 1 D. 7x = 35 E. 6x 10 = 20 F. 5 x = 15

7 28. The high school band sold tickets to a car wash on four different days. The table below shows the number of tickets sold and the amounts of money collected from ticket sales. Day Number of Tickets Sold Amount Collected 1 40 $ $ $ $ Select the equation that can be used to find y, the amount of money collected for selling x car wash ticket. A. y=300+x B. y=40x C. y=7.5x D. y=0.13x 29. The graph below shows the number of miles traveled each hour of a road trip Which equation can be used to find the total number of miles, y, for any number of hours, x? A. y=75x B. y=75+x C. x=75y D. x=75+y