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1A CHAPTER 1 TEST Name: 1−2. Simplify. 2 2 1. 8 − 2(2 + 1) ÷ (2 + 3) − (7 − 3)3 2. 4 (8 3) 24 ' 2 (7 1) 2 8 ' (7 3) $ 2 24 2 3. On a number line, point X has a coordinate −63 and point Y has coordinate of 18. Write the coordinate of each point that is half as far from Y as from X. 4−5. Evaluate each expression for the given values of the variables. 3 2 4. −ab + 2(b + 4a) ; a = 3, b = −2 5. 2 ( x y) ( x y) 2 2 x 2y xy 2 ; x = 2, y = −4 6. Is the set of irrational numbers closed with respect to subtraction? If not give an example. 7. Simplify: 30x − 3[2(x − 1) + 4x] − 11x 4 2 8. What polynomial must be subtracted from 6x + 7x − 2x − 5 to obtain 4 3 2 2x − 8x − x + x + 4 ? 9. 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) = 18x + 5x − 9 10−19. Name the property or definition that justifies each step. 10. (5x − 4) − x = [5x + (−4)] + (−x) 11. = −x + [5x + (−4)] 12. = [−x + 5x] + (−4) 13. = [−1 ⋅ x + 5x] + (−1)4 14. = [(−1 + 5)x] + (−1)4 15. = 4x + (−1)4 16. = 4x + 4(−1) 17. = 4[x + (−1)] 18. = 4(x − 1) 19. ∴ (5x − 4) − x = 4(x − 1) 4 1A CHAPTER 1 TEST 20. Solve: 22 − (4 − 4x) = −2(x + 9) − 24 21. Solve for x. a = bx ax b 22. Write an algebraic expression in simplest form for the following. Four years ago, Ben was three times as old as his brother Dave. If Dave is D years old now, how old is Ben now? 23. 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.) Mr. Leiby has 20 mL of a 20% methanol solution. How much of a 30% methanol solution should be added to it to make a 28% methanol solution? 24−26. 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. 24. Adult tickets for the art museum cost $1.50 more than children’s tickets. One day 200 adults’ tickets and 160 children’s tickets were sold at the museum. The income from the adults’ tickets was $30 less than twice the income from the children’s tickets. How much does each type of ticket cost? 25. A deck 3 feet wide surrounds a rectangular pool. The pool is 12 feet longer than it is wide. The area of the deck alone is 348 ft2. Find the dimensions of the pool. 26. Two planes leave Midville at the same time to fly to Centerville. One plane is traveling at 744 km/hr and the other at 760 km/hr. If the faster plane arrives 5 minutes before the other, how far is Midville from Centerville? Extra Credit. Use the four step method and solve algebraically. The average of Alex’s, Bonnie’s, and Carl’s ages is 9 years. Four years ago, Carl was the same age as Alex is now. In three years, Bonnie’s age will be twothirds Alex’s age at that time. How old is each now? 5 Name: