Name: Date: Block: This test covers learning targets related to evaluating expressions, solving equations, and simplifying radicals.
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1 Algebra Test STUDY GUIDE A., A., A. Epressions, Equations, Radicals Name: Date: Block: This test covers learning targets related to evaluating epressions, solving equations, and simplifying radicals. Know how to: o Use the order of operations (PEMDAS) to evaluate a numeric epression o Use the order of operations to evaluate an algebraic epression using substitution for the variables. o Translate verbal epressions in English into algebraic epressions, equations, or inequalities. o Solve equations, including those using grouping, fractions, and that have variables on both sides of the equal sign. o Know when there are no solutions to equations, or all real numbers are solutions. o Know how to justify steps using the properties of equality. o Always verify your solution by substituting the solution back into the equation. o Solve word problems using the skills above. o Simplify radicals, including simplifying irrational denominators Make sure you answer every question on this study guide and use the answers on the last page to check your work. Sometimes working backwards from the answer can you help you figure out questions with which you are having trouble Practice showing all work on a piece of scratch paper, since you must show all work on quizzes and tests to receive full credit. Practice managing your time when working on the study guide. Answer the questions you know first, then go back and work on the ones you need to think about more. You want to use the same strategy on the test! Practice questions: ) Write an algebraic epression for the following statements: a) Twenty less than the quotient of a number and 6 b) Eight more than the product of times a number and another number c) The difference of nine times a number and the same number d) one eighth of a number m plus five e) The sum of twice a number and one-fourth of the number f) The product of a number and the quantity another number divided by two
2 Algebra Test STUDY GUIDE A., A., A. Epressions, Equations, Radicals Page ) Write an equation or inequality for the following statements, then solve it. a) Four less than five times a number is si. b) Fifty three plus four times a number q is as much as twenty- one. c) The sum of five and a number is at least four. d) Five more than twice a number is three times the difference of that number and two. What is the number? e) Twice the sum of four and a number is si less than that same number. What is the number? f) The quotient of thirty nine and a number is three. What is the number? g) The product of a number and another number is at most ten (don t solve this one). h) The quotient of two different numbers is no more than siteen (don t solve this one). ) Use the order of operations to evaluate the epressions: a) 6 + b) 6( - 7) - ( + ) c) (-) + 6 ( ) 9 d) e) 8 [ + (6 + )] f) g) h) 7 [6(8-6) + ] ) Substitute the given variable values in the epressions and evaluate: a) ( y) (y + z) for =, y = -, z = - b) + y for = -, y = c) when = - d) ⁴ +(y ) for =-, y= ) The following problems require two steps. First, translate the English phrase into a math epression using variables. Second, substitute the variables in your epression with the values = - and y = -.
3 Algebra Test STUDY GUIDE A., A., A. Epressions, Equations, Radicals Page a) Five less than three times a number. Translation: Value: b) Si more than the quotient of a number y squared and. Translation: Value: 6) A skating rink holds parties and charges a rink rental fee of $00, plus $0 per person. a) Write an epression that the rink can use to determine how much to charge. b) Use the epression you wrote in part a) to determine how much will be charged if 0 people attend a party. c) How much would it cost if 0 people attend and the customer has a coupon for $00 off the total? 7) The area of a triangle is given by A = bh where b = the length of the base and h = the height of the triangle. If the height of a triangle is times its base, what is its area if its base is 8 inches? a) Write an epression that describes the situation in terms of the base, and b) find the value of the area of the triangle. 8) The length of a rectangular map is inches and the perimeter is 0 inches. Find the width. ( perimeter = L + W where L is the length and W is the width) 9) Estimate to the nearest whole number: a) 0 b) 0 Simplify the radicals: 0) 0 ) 8 ) ) 6 ) ) 7 6) 8
4 Algebra Test STUDY GUIDE A., A., A. Epressions, Equations, Radicals Page 7) 8) 0 9) 9 8 Rationalize the denominators 0) ) ) 00 8 ) ) Solve the equations, justifying steps for the first problems. Verify your solutions for all problems by substituting the solution back into the equation. a) = b) c) + = d) 9 = 0 e) (-) = 7 f) 0 + = 7 g) 0z = (z ) h) 8( + ) - = 8 + i) = 6 j) 0 - ( + ) = 8 7 k) l) step : 6( - ) = 9 step : - 6 = 9 ) What field property justifies step? ) Finish solving equation.
5 Algebra Test STUDY GUIDE A., A., A. Epressions, Equations, Radicals Page ANSWERS y ) a) 0 b) y + 8 c) 9n n d) m e) f) 6 8 ) a) = 6 ( = ) b) +q (q -8) c) + ( -) 9 d) +=(-) (=) e) ( + ) = - 6 (=-) f) (=) g) y 0 h) 6 y ) a) b) c) - d) e) f) g) 7 h) 60 7 ) a) b) -6 c) 7 d) 6 y ) a) Translation: value: - b) Translation: 6 value: - 6) a) y = 00+0 b) $600 c) $00 7) a) A = (b)(b) ()b b b) A = 6 in 8) ()+w = 0; w = 0 9) a) 6 b) 0) 0 ) ) 6 ) 6 6 ) ) 6 0) 6) ) 6 0 7) ) ) a) = 6 (addition prop. of equality) b) = 8 (add. prop of =; mult. prop of equality) 8) 9) 6 ) c) = (subtraction prop. of equality; division prop of equality) d) = (combine like terms; add. prop. of equality; div. prop. of equality) e) = (distributive prop.; combine like terms; subtraction prop. of equality) f) = 9 g) no solution h) all real numbers i) no solution j) no solution k) = l) ) distributive property ) =
Name: Date: Block: This test covers learning targets related to evaluating expressions, solving equations, and simplifying radicals.
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