# Math 100 Final Exam Review

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1 Math 0 Final Eam Review Name The problems included in this review involve the important concepts covered this semester. Work in groups of 4. If our group gets stuck on a problem, let our instructor know. Be prepared to write soltuions on the board if called upon. 1) Find the missing length in the similar triangles. 1) Objective: (2.6) Solve Apps: Similar Triangles 2) In a chemistr class, 9 liters of a 4% silver iodide solution must be mied with a % solution to get a 6% solution. How man liters of the % solution are needed? Objective: (2.7) Solve Apps: Mitures 2) Solve the inequalit. Write the solution set in interval notation and graph it. 3) > 4(3-12) 3) Objective: (2.8) Solve and Graph Inequalit (Multi-Step) 4) 3 3t ) Objective: (2.8) Solve Three-Part Inequalit Solve b graphing. Label the aes and show where the solution is located on the graph. ) The cost, c, in dollars of car rental is + 0.2m, where m is the number of miles driven. Graph the equation and use the graph to estimate the cost of car rental if the number of miles driven is 40. ) m Objective: (3.2) Solve Apps: Graphing Linear Equations

2 Graph the equation b using the slope and -intercept. 6) = 4-1 6) Objective: (3.4) Graph Equation Using Slope and -Intercept Graph the line through the given point with the given slope. 7) (4, 0), m = ) Objective: (3.4) Graph Line Given Slope and Point Write an equation of the line through the given point with the given slope. Write the equation in slope -intercept form. 8) (2, 4); m = ) Objective: (3.4) Write Equation Given Slope and Point Write the slope-intercept form of the equation for the line passing through the given pair of points. 9) (-9, 0) and (-6, 2) 9) Objective: (3.) Write Equation Given Two Points (Slope-Intercept Form)

3 State whether the graph is or is not that of a function. ) ) Objective: (3.7) Decide if Graph Represents a Function 11) 11) Objective: (3.7) Decide if Graph Represents a Function MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Tell whether or not the relation is a function. 12) {(-3, -2), (2, -3), (, -), (7, -3), (, 9)} A) Yes B) No Objective: (3.7) Decide if Ordered-Pair Relation is a Function 12) 13) {(-3, -2), (-2, 9), (2, ), (2, -8)} A) Yes B) No Objective: (3.7) Decide if Ordered-Pair Relation is a Function 13)

4 Solve the sstem b graphing. 14) 2 + = 16 = ) Objective: (4.1) Solve Linear Sstem b Graphing Solve b the substitution method. 1) - = = 12 Objective: (4.2) Solve Sstem b Substitution 1) Clear fractions then solve b substitution. 16) = -2 16) 1-1 = - 2 Objective: (4.2) Clear Fractions and Solve b Substitution Solve the sstem b the elimination method. 17) 8-6 = = 13 Objective: (4.3) Solve Sstem b Elimination I 17) Solve the sstem b elimination. 18) 7 - = 26 18) = 6 Objective: (4.3) Solve Sstem b Elimination II Write a sstem of equations for the problem, and then solve the sstem. 19) There were 40,000 people at a ballgame in Los Angeles. The daʹs receipts from \$14 reserved seats and \$4 general-admission seats were \$300,000. How man of each tpe of seat were sold? Objective: (4.4) Solve Apps: Linear Sstems II 20) Paul invested three times as much mone in an account paing % interest than he did in an account paing 1% interest. If the total interest paid was \$480, how much did he invest in each? Objective: (4.4) Solve Apps: Linear Sstems II 19) 20)

5 21) At the beginning of a biccle ride, Raul and Miguel are 0 miles apart. If the leave at the same time and ride in the same direction, Raul overtakes Miguel in hours. If the ride toward each other, the pass each other in 2 hours. What are their speeds? Objective: (4.4) Solve Apps: Linear Sstems III 21) Graph the solution of the sstem. 22) 7-6 < 38 - > ) Objective: (4.) Graph Sstem of Linear Inequalities Simplif the epression. 23) (-32)6 23) Objective: (.1) Use Combination of Rules to Simplif 24) Find an epression that represents the area of the figure.(leave π in the answer.) 24) 4t Objective: (.1) Solve Apps: Area and Volume Simplif b writing the epression with positive eponents. Assume that all variables represent nonzero real numbers. 2) (3 26) -3 (9-1) 2 (6) - 2) Objective: (.2) Use Combination of Rules to Simplif Perform the indicated operation. 26) (2n6 + n - 12) - (-8n + 4n6 + 7) + (n7 + 8) 26) Objective: (.4) Add/Subtract Polnomials (One Variable)

6 Provide an appropriate response. 27) Find a polnomial that represents the perimeter. 27) Objective: (.4) Solve Apps: Geometr Graph the equation b completing the table of values. 28) = ( + 2) ) - - Objective: (.4) Graph b Completing Table Find the product. 29) (3p - 1)(9p2 + 3p + 1) 29) Objective: (.) Multipl Polnomials Find the product. Use the FOIL method. 30) ( - )(-3-8) 30) Objective: (.) Multipl Binomials 31) ( - )( - 9) 31) Objective: (.) Multipl Binomials Perform the division. 32) p 2 + 3p - 26 p ) Objective: (.7) Divide Polnomial b Binomial/Trinomial 33) ) Objective: (.7) Divide Polnomial b Binomial/Trinomial

7 Factor completel. 34) ) Objective: (6.3) Factor Trinomial Completel Factor the binomial completel. If it is prime, sa so. 3) ) Objective: (6.4) Factor Binomial Solve the equation. 36) = 0 36) Objective: (6.) Solve Quadratic Equation b Factoring I 37) ( - 7)2 + 2 = ( + 1)2 37) Objective: (6.) Solve Quadratic Equation b Factoring III 38) The length of a rectangular frame is cm more than the width. The area inside the frame is 66 square cm. Find the width of the frame. Objective: (6.6) Solve Apps: Geometr II 38) Round to the nearest tenth, if necessar. 39) If an object is propelled upward from a height of 64 feet at an initial velocit of 48 feet per second, then its height h after t seconds is given b the equation h = -16t2 + 48t After how man seconds does the object hit the ground? Objective: (6.6) Solve Apps: Motion 39) Multipl. Write the answer in lowest terms. r - 1 6r ) 12r2 + 24r 30 - r 40) Objective: (7.2) Multipl Rational Epressions Multipl or divide as indicated. Write the answer in lowest terms. 41) ) Objective: (7.2) Multipl/Divide Rational Epressions I Add or subtract. Write the answer in lowest terms. 42) ) Objective: (7.4) ^Add/Subtract Rational Epressions Solve the equation. 43) = ) Objective: (7.6) Solve Rational Equation II

8 44) 6 m + = 1-1 m - 44) Objective: (7.6) Solve Rational Equation II 4) The speed of a stream is 4 mph. If a boat travels 66 mi downstream in the same time that it takes to travel 33 mi upstream, what is the speed of the boat in still water? 4) Objective: (7.7) Solve Apps: Distance, Rate, Time II 46) Frank can tpe a report in 7 hr. James can tpe it in 2 hr. How long will it take the two of them working together? 46) Objective: (7.7) Solve Apps: Work Find all square roots of the number. 47) ) Objective: (8.1) Find All Square Roots of a Number Find the square root. 48) ) Objective: (8.1) Find Square Root Give the answer to the nearest thousandth if necessar. 49) Below is a diagram of a water slide. The slide is 28 ft long. The ladder leading to the slide is 21 ft long. How far is it from the end of the slide to the foot of the ladder? 49) 21 ft 28 ft? Objective: (8.1) Solve Apps: Pthagorean Theorem Find the distance between the pair of points. 0), -3 and 2, -18 0) Objective: (8.1) Find Distance Between Two Points Simplif. 1) Objective: (8.4) Rationalize Radical Product 1) Rationalize the denominator. Assume that all variables represent positive real numbers. 2) p3r 2m Objective: (8.4) Rationalize Denominator (Variables) 2)

9 Simplif the epression. 3) ( + ) ( + 3) 3) Objective: (8.) Simplif Products of Radical Epressions (Numbers) Rationalize the denominator. Write the quotient in lowest terms. 7 4) ) Objective: (8.) Rationalize Binomial Denominator Solve the equation b completing the square. ) = 0 ) Objective: (9.2) Solve Equation b Completing the Square I Use the quadratic formula to solve the equation. Simplif an radicals. 6) = 0 6) Objective: (9.3) Solve Equation Using Quadratic Formula I 7) 42 = ) Objective: (9.3) Solve Equation Using Quadratic Formula II 8) The length of a table is 11 inches more than its width. If the area of the table is 2726 square inches, what is its length? Objective: (9.3) Solve Apps: The Quadratic Formula 8) Give the coordinates of the verte and sketch the graph of the equation. 9) = ) Objective: (9.4) Find Verte and Graph Quadratic Equation 60) The length and width of a rectangle have a sum of 70. What dimensions give the maimum area? Objective: (9.4) Solve Apps: Quadratic Equations 60)

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