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1B CHAPTER 1 TEST Name: Simplify. 2 2 1. 5 + 2(2 + 4) ÷ (1 + 3) − (9 − 3) 2. 5 (7 3) 18 ' 2 (9 2) 2 12 ' (4 2) $ 2 18 2 3. Place grouping symbols in the following expression so that it has the given value. 12 − 6 + 4 ⋅ 2 + 28 ÷ 6 − 4 ; 6 4−5. On a number line, point Y has a coordinate −64 and point X has coordinate of 26. Write the coordinate of each point described. 4. The point one fifth of the way from X to Y. 5. Each point that is twice as far from Y as from X. 6−7. Evaluate each expression for the given values of the variables. 2 2 6. ab − 4b − 2a ; a = −3, b = 4 7. 2 ( x y) ( x y) 2 2 x y xy 2 ; x = 6, y = 4 8. Is the set of nonpositve integers closed with respect to subtraction? If not give an example. 9. Simplify: 24x − 4[3(x − 1) + 5x] − 16 4 2 10. What polynomial must be subtracted from 3x + 2x − 8x − 6 to obtain 4 3 2 −2x − 3x − x + 2x + 9 ? 11. Find the values for a, b and c, so that the given equation is an identity. 2 2 2 (−2x − bx + 3c) − (−4ax + x + 9) = 6x + 4x − 12 12−16. Name the property that justifies each step. c = dx Given 7 12. 1 1 (c) = (dx) d d 13. c 1 = (dx) d d 14. 1 c = d $ d nx d d 15. c = 1$x d 16. c =x d 1B CHAPTER 1 TEST 17. Solve: 18 − (4 − 2x) = −4(x + 1) − 14 18. Solve for x. S = xM Nx M 19. Write an algebraic expression in simplest form for the following. A plane traveled for 5 hours at v km/hr and then increased the speed by 50 km/hr and traveled for 2 more hours. How far did the plane travel? 20. Choose a variable, tell what it represents, and write an equation to represent the facts. DO NOT SOLVE. (You do not have to simplify your equation.) Michael has $2.75 in nickels, dimes, and quarters in his pocket. He has seven fewer quarters than nickels and three times as many dimes as quarters. How many of each type of coin does he have? 21−23. Solve. Choose one variable, tell what the variable represents and any other unknowns, write an equation, solve, and write a sentence to answer the question. 21. A chemist wishes to mix 24 L of pure acid with a certain amount of water to produce a 40% solution. Determine how much water must be used. 22. Bob invested $10,000 in bank certificates and bonds. The certificates pay 9% interest and the bonds pay 6.5% interest. His interest income is $843.75 each year. How much money was invested in the bank certificates? 23. The sum of the digits of a three-digit number is 19. If the hundreds’ digit is two more than the tens’ digit, and the ones’ digit is one-third the hundreds’ digit, find the number. Extra Credit. Use the four step method and solve algebraically. The average of Sue’s, Bill’s, and Tom’s ages is years. In twenty years, Sue will be the same age as Tom is now. Four years ago, Bill was five-elevenths as old as Tom was at that time. How old is each now? 8 Name: