Name: Date: Block: This test covers learning targets related to evaluating expressions, solving equations, and simplifying radicals.

Transcription

1 Algebra Test STUDY GUIDE A., A.4, A.3 Epressions, Equations, Radicals Name: Date: Block: This test covers learning targets related to evaluating epressions, solving equations, and simplifing 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 justif steps using the properties of equalit. o Alwas verif our solution b substituting the solution back into the equation. o Solve word problems using the skills above. o Simplif radicals, including simplifing irrational denominators Make sure ou answer ever question on this stud guide and use the answers on the last page to check our work. Sometimes working backwards from the answer can ou help ou figure out questions with which ou are having trouble Practice showing all work on a piece of scratch paper, since ou must show all work on quizzes and tests to receive full credit. Practice managing our time when working on the stud guide. Answer the questions ou know first, then go back and work on the ones ou need to think about more. You want to use the same strateg on the test! Practice questions: ) Write an algebraic epression for the following statements: a) the sum of two times a number b and four b) Twent less than the quotient of a number and 6 c) Eight more than the product of 3 times a number and another number d) The difference of nine times a number and the same number e) one eighth of a number m plus five f) Four-fifths of a number

2 Algebra Test STUDY GUIDE A., A.4, A.3 Epressions, Equations, Radicals Page g) the product of 5 and cubed h) The sum of twice a number and one-fourth of the number i) fift less than one-half of a number j) The product of a number and the quantit another number divided b two ) Write an equation or inequalit for the following statements, then solve it. a) Four less than five times a number is si. b) Fift three plus four times a number q is as much as twent- one. c) The sum of five and a number is at least four. d) Twice the sum of r and ten is identical to r minus 4. e) Five more than twice a number is three times the difference of that number and two. What is the number? f) Twice the sum of four and a number is si less than that same number. What is the number? g) The quotient of thirt nine and a number is three. What is the number? h) The product of a number and another number is at most ten (don t solve this one). i) The quotient of two different numbers is no more than siteen (don t solve this one). j) Three times a number decreased b four is at least five times a different number (don t solve this one). 3) Use the order of operations to evaluate the epressions: a) b) 6( - 7) - 4( + ) c) (-3) + 6 (3 5) d) e) 8 [3 + (6 3 + )] f) g) h) (4 (-) 3 + (-3) ) 3 7

3 i) 6 ( + ) j) 75 [6(8-6) + 3] Algebra Test STUDY GUIDE A., A.4, A.3 Epressions, Equations, Radicals Page 3 k) [ + ( - 8) ] 4) Substitute the given variable values in the epressions and evaluate: a) ( ) ( + z) for = 3, = -4, z = -5 b) 3 + for = -3, = c) when = -4 d) ⁴ +5( 3) for =-, =5 e) (z ) z for =3, =8, z=9 5) The following problems require two steps. First, translate the English phrase into a math epression using variables. Second, substitute the variables in our epression with the values = - and = -4. a) Five less than three times a number. Translation: Value: b) Si more than the quotient of a number squared and. Translation: Value: 6) A skating rink holds parties and charges a rink rental fee of $00, plus $30 per person. a) Write an epression that the rink can use to determine how much to charge. b) Use the epression ou wrote in part a) to determine how much will be charged if 50 people attend a part. c) How much would it cost if 50 people attend and the customer has a coupon for $00 off the total? 7) The area of a triangle is given b 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 first stage of a rocket burns 8 seconds longer than the second stage. If the total burning time for both stages is 5 seconds, how long does each stage burn?

4 Algebra Test STUDY GUIDE A., A.4, A.3 Epressions, Equations, Radicals Page 4 9) The length of a rectangular map is 5 inches and the perimeter is 50 inches. Find the width. ( perimeter = L + W where L is the length and W is the width) 0) Karin s mom runs a dair farm. Last ear Elsie the cow gave 375 gallons less than twice the amount from Bessie the cow. Together, Elsie and Bessie produced 464 gallons of milk. How man gallons did each cow give? ) Janice is considering purchasing a refrigerator from three different dealers. Dealer A has given a good price. Dealer B's offer was $00 more than Dealer A's price. Dealer C said he'd double Dealer A's price, but then subtract $500. If Dealer B and Dealer C had the same price, what was Dealer A's offer? ) In 00, Stock A and Stock B had the same price. Since then, the price of Stock A has tripled. In the same time span, the price of Stock B has increased b $500. If both stocks are once again at the same price, what was the original price? What is the price of each now? 3) Estimate to the nearest whole number: a) 40 b) 0 Simplif the radicals: 4) 50 5) 48 6) 4 7) 6 8) ) ) 54 4 ) ) z 7 3) 9 4

5 Algebra Test STUDY GUIDE A., A.4, A.3 Epressions, Equations, Radicals Page 5 Rationalize the denominators 4) 5) 6) 7) ) 4 9) Solve the equations, justifing steps for the first 5 problems. Verif our solutions for all problems b substituting the solution back into the equation. a) = 4 b) 4 3 = 4 c) 3 + = 4 d) = 0 e) 5 4(-3) = 7 f) 0 + = 4 7 g) 0z = 5(z 3) h) 8( + 3) - = i) 4 3( + ) = -5 j) = 4 6 k) 0 - (4 + 5) = 8 l) 5 7 = - m) 7 5 n) step : 6( - ) = 39 3 step : - 6 = 39 3 ) What field propert justifies step? ) Finish solving equation. 30) Solve the inequalities and graph the solutions on a number line. a) 4( ) < - +5 b) -4 < - c) + 3 7

6 Algebra Test STUDY GUIDE A., A.4, A.3 Epressions, Equations, Radicals Page 6 ANSWERS ) a) b + 4 b) 0 c) d) 9n n e) m f) g) h) i) 50 j) 4 ) a) 5 4 = 6 ( = ) b) 53+4q (q -8) c) 5+ 4 ( -) d) (r 0) r 4 (r=-4) e) +5=3(-) (=) f) (4 + ) = - 6 (=-4) 39 g) 3 (=3) h) 0 i) 6 j) ) a) b) c) -3 d) 7 3 e) 4 f) 4 g) 7 h) 9 i) 9 j) 60 k) 7 4) a) 3 b) -6 c) 7 5 d) 6 e) 6 5) a) Translation: 3 5 value: - b) Translation: 6 value: - 6) a) = b) $600 c) $400 7) a) A = (b)(b) ()b b b) A = 64 in 8) = 5; first stage ( +8) = 90; second stage () = 6 9) (5)+w = 50; w = 0 0) E=B 375; E+B = 464; B-375+B=464; Bessie = 63 gals; Elsie = 85 gals ) A+00 = A 500; A = $600 ) A=B; 3A = B+500; 3A = A+500; A = B = $750 3) a) 6 b) 4) 5 0 5) 4 3 6) 6 7) 6 6 8) 5 9) ) 3 ) 3 ) 4 z 3 5z 3) 6 4) 0 5 5) 6) 7) 8) 4 9) a) = 36 (addition prop. of equalit) b) = 8 (add. prop of =; mult. prop of equalit) c) = 4 (subtraction prop. of equalit; division prop of equalit) d) = 5 (combine like terms; add. prop. of equalit; div. prop. of equalit) e) = 5 (distributive prop.; combine like terms; subtraction prop. of equalit) f) = 9 g) no solution h) all real numbers i) = j) no solution k) no solution l) = m) = n) ) distributive propert ) = 3 30) a) < b) > 3 c)