Intermediate Algebra Review for Exam 1 - Spring 2005

Size: px

Start display at page:

Download "Intermediate Algebra Review for Exam 1 - Spring 2005"

Monica Cox
5 years ago
Views:

1 Intermediate Algebra Review for Eam - Spring 00 Use mathematical smbols to translate the phrase. ) a) 9 more than half of some number b) 0 less than a number c) 37 percent of some number Evaluate the epression. ) -, for = 8 and = 9 3) m + n(9 + n), for m = and n = 3 Classif the statement as true or false. Consult the following list as needed. N = the set of natural numbers W = the set of whole numbers Z = the set of integers Q = the set of rational numbers H = the set of irrational numbers R = the set of real numbers (Remember: E means "is an element of" and W means "is a subset of") ) a) 73.7 E N d) -9 E Z b) 7 E Q e) Q P R c) 9 H H f) W W N Perform the indicated operation. Make sure to simplif our answer. ) a) b) c) d) ) 3(c - ) = c - 3 ) - ( - ) = 3) 7 + (3 - ) = - - ) 3 - = ) -7.q = -. -.q Classif the given equation as a conditional equation, an identit, or a contradiction. ) a) (3f + ) = f + 0 b) 8m + 9 = 3(m - ) c) 8k + = (k + ) 7) A rectangle's length is twice its width and its perimeter is 8 m. Find the dimensions. 8) One angle of a triangle is times as great as a second angle. The third angle measures e less than twice the second angle. Find the measures of the angles. 9) An emploee earned $8,9 this ear. This was a raise of 9% over last ear. What was his salar last ear? ) a) 3 d 0 b) d Solve the formula for the specified variable. 0) A = bh, for b Simplif using the rules for order of operations. 7) a) 8 œ œ b) d œ 3 Find -. 8) a) = - b) = 9.09 ) C = m + e for ) John wants to invest mone to earn $9 in 9 months. He found an investment at 8%. How much must he invest? Solve the equation. 9) 30 = ) m + 0 = - 3m

2 Review for Eam - Page 3) A garden is being constructed in the shape of a trapezoid. Given that the height of the trapezoid is 8 m, the length of one of the bases is m, and the area of the garden is 3 m, what is the length of the unknown base? (Hint: Area of a trapezoid = h (b + b ) ). Evaluate the epression. ) a) - b) - ) a) (-)- b) -- Simplif. Write the answer using positive eponents onl. ) a) (7)(3z0) b) ( -3-8 )( -3 ) 7) a) ) a) 8-8- b) 7w (w - ) 3 (w ) - b) - z - c) 9) a) 9-7 œ 9 - b) ) 3 3 3) 8-3) 3-33) Decide whether the ordered pair is a solution of the given sstem. 3) (3, -) + = 3 + = 7 Solve the sstem b graphing. 3) + = = 8 Identif the sstem as consistent or inconsistent, and dependent or independent. 3) + = 3 - = 37) 3 - = = -0 38) 3 = = 3 Use the substitution method to solve the sstem of linear equations. If a sstem has an infinite number of solutions or no solution, state this. 39) 3 + = = -8 Solve using the elimination method. If a sstem has an infinite number of solutions or no solution, state this. 0) + = = Solve the sstem. If a sstem has an infinite number of solutions or no solution, state this. ) + = = 8 ) + = + = 3) a + b = 3 3a = -b + 9 ) Don runs a charit fruit sale, selling boes of oranges for $ and boes of grapefruit for $0. If he sold a total of 7 boes and his total income was $8, how man boes of oranges did he sell? ) Mardi received an inheritance of $0,000. She invested part at 9% and deposited the remainder in ta-free bonds at %. Her total annual income from the investments was $300. How much did she deposit in each tpe of investment?

3 Review for Eam - Page 3 ) The Nut House sells cashews worth $.80 per pound and peanuts worth $.0 per pound. How man pounds of each should be mied to obtain a 0 pound miture worth $. per pound? Determine whether each correspondence is a function. 3) a) 7) In a chemistr class, a % silver iodide solution must be mied with a 0% silver iodide solution to get 0. liters of a % solution. How man liters of each solution are needed? 8) Two sailboats are 9.8 miles apart and sailing toward each other. the larger boat, the Pthagoras, sails miles per hour faster than the smaller boat, the Apollo. The two boats pass each other after 0.7 hour. Find the speed of each boat. 9) A freight train leaves a station traveling at 0 mph. Eight hours later, a passenger train leaves the same station traveling in the same direction at 0 mph. How long does it take for the passenger train to catch up to the freight train? How far have the travelled when this happens? b) c) Domain: All students attending ACC Correspondence: Each student's teachers Range: A set of teachers d) Domain: A set of shapes Correspondence: The area of each shape Range: A set of numbers For each graph, determine (a) f(3); (b) the domain; (c) an -values for which f() = ; and (d) the range. ) I) 3 Graph. 0) = -3 ) = - 3 II) ) f() =

4 Review for Eam - Page Find the function value. ) a) Find f() when f() = b) Find f(-) when f() = d) Find f(a + 3) when f() = - 3. Find the domain of f(). ) a) f() = b) f() = c) f() = + d) f() = v-7 - v 7) The Fahrenheit temperature corresponding to the Celsius temperature is described b the function F(C) = 9 C + 3. Find the Fahrenheit temperature equivalent to e C. Determine the slope and the -intercept. 8) = -3 + Find the slope of the line containing the two given points. 9) (-, 7) and (-3, -7) Find a linear function whose graph has the given slope and -intercept. 0) a) Slope -, -intercept 8 b) Slope -, -intercept Find the rate of change. Use appropriate units. ) Value of Car in Thousands of Dollars Number of Years of Use ) A deep sea diving bell is being lowered at a constant rate. After 9 minutes, the bell is at a depth of 00 feet. After 30 minutes the bell is at a depth of 00 feet. What is the average rate of lowering per minute? 3) The cost of manufacturing a molded part is related to the quantit produced during a production run. When 00 parts are produced, the cost is $300. When 300 parts are produced, the cost is $00. What is the average cost per part? Match the graph with the most appropriate sentence. ) Amount of butter used (in hundreds of pounds) Das A) The pounds of butter used continued to rise after da at the same rate. B) The pounds of butter used continued to rise after da but at a faster rate. C) The pounds of butter used remained level after da. D) The pounds of butter used continued to rise after da but at a slower rate. This model is of the form f() = m + b. Determine what m and b signif. ) The cost, in dollars, of cellular phone service with Econo-phone is given b C() = , where is the number of minutes used in one month.

5 Answer Ke Testname: TEST REVIEW SP0 ) a) + 9 or + 9 b) - 0 c) 0.37 ) 3) 70 ) a) F d) T b) F e) F c) T f) F ) a) b) - 7 c) - 8 d) - 0 ) a) b) ) a) - 3 b) 9 8) a) b) ) -8 0) - 7 ) ) 3) ) -30 ) ) a) Identit b) Conditional c) Contradiction 7) 8 m b m 8) 0e, e, 3e 9) $7,3 0) b = A h C ) = m + e ) $0.00 3) m ) a) - b) 7) a) -7 b) 7w7 8) a) b) z 83 c) 9) a) 9 b) - 30) 38 3) 8 3) 33) 3 8 3) Yes 3) (-, 3) 3) Consistent and independent 37) Consistent and dependent 38) Inconsistent and independent 39) (, -) 0) (-, 0) ) (-, 8) ) No solution 3) infinite number of solutions ) 0 boes ) $30,000 ) 38 lbs. cashews, lbs. peanuts 7) 7 liters of % solution 3. liters of 0% solution 8) Pthagoras: 9 mph Apollo: mph 9) 8 hours, 90 miles 0) ) a) - 3 b) ) a) 08 b) 0

6 Answer Ke Testname: TEST REVIEW SP0 ) ) a) f() = b) f() = - + ) -$3000 per ear ). ft per minute 3) $.00 per part ) D ) 0.8 signifies the cost per minute, and 7.0 signifies the monthl service charge. ) ) a) No b) Yes c) No d) Yes ) I. a) f(3) = b) Domain: {v - } c) f() = when =, 0 d) Range: { 0 } II. a) f(3) = b) Domain: { - < } c) f() = when = { < } d) Range: {-,, } ) a) b) -7 c) a + a + ) a) {v -} b) 3 c) the set of all real numbers d) the set of all real numbers 7) 77e F 8) Slope = -3, -intercept = (0, ) 9) - 3

INTERMEDIATE ALGEBRA REVIEW FOR TEST 1

INTERMEDIATE ALGEBRA REVIEW FOR TEST 1 Write the set using the roster method. 1) a) { is a counting number less than 7} b) { is a whole number between 4 and 8} Let A = {0, 2, 4, 6, 8, }, B = {0,, 6, 9},