# 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) = 12 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? 4. L 2) Solve the inequalit. Write the solution set in interval notation and graph it. 3) > 4(3-12) 3) (-4, ) ) 3 3t ) [2, 7]

2 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 About 20 dollars Graph the equation b using the slope and -intercept. 6) = 4-1 6)

3 Graph the line through the given point with the given slope. 7) (4, 0), m = ) 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 = ) = 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) =

4 State whether the graph is or is not that of a function. ) ) ) Function 11) Not 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 A 13) {(-3, -2), (-2, 9), (2, ), (2, -8)} A) Yes B) No B 12) 13)

5 Solve the sstem b graphing. 14) 2 + = 16 = ) {(3, )} Solve b the substitution method. 1) - = = 12 {(0, -3)} 1) Clear fractions then solve b substitution. 16) = -2 16) 1-1 = - 2 {(-4, -2)} Solve the sstem b the elimination method. 17) 8-6 = = 13 {(-1, 4)} Solve the sstem b elimination. 18) 7 - = 26 17) 18) = 6 {(8, 6)} 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? \$14 seats: 14,000; \$4 seats: 26,000 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? \$9000 at %, \$3000 at 1% 19) 20)

6 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? Raul: 3 mph; Miguel: 1 mph Graph the solution of the sstem. 22) 7-6 < 38 - > ) 22) Simplif the epression. 23) (-32)6 23) (-3) ) Find an epression that represents the area of the figure.(leave π in the answer.) 24) 4t 16πt

7 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) Perform the indicated operation. 26) (2n6 + n - 12) - (-8n + 4n6 + 7) + (n7 + 8) 26) n7-2n6 + 18n - 11 Provide an appropriate response. 27) Find a polnomial that represents the perimeter. 27) Graph the equation b completing the table of values. 28) = ( + 2) )

8 Find the product. 29) (3p - 1)(9p2 + 3p + 1) 29) 27p3-1 Find the product. Use the FOIL method. 30) ( - )(-3-8) 30) ) ( - )( - 9) 31) Perform the division. 32) p 2 + 3p - 26 p ) p p ) ) Factor completel. 34) ) 6(3 + 2)( - ) Factor the binomial completel. If it is prime, sa so. 3) ) (6 + 7)(6-7) Solve the equation. 36) = 0 36) {-, 8} 37) ( - 7)2 + 2 = ( + 1)2 37) {4, 12} 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. 6 cm 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? 4 sec 38) 39)

9 Multipl. Write the answer in lowest terms. r - 1 6r ) 12r2 + 24r 30 - r 40) - 1 4r Multipl or divide as indicated. Write the answer in lowest terms. 41) ) (2 - ) ( - )( + 3) Add or subtract. Write the answer in lowest terms. 42) ) Solve the equation. 43) = ) {-14} 6 m + = 1-1 m - {0, 7} 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? 12 mph 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? 43) 44) 4) 46) 1 9 hr Find all square roots of the number. 47) ) 11 9, Find the square root. 48) ) Not a real number

10 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 18.2 ft? Find the distance between the pair of points. 0), -3 and 2, -18 0) 17 Simplif. 1) ) Rationalize the denominator. Assume that all variables represent positive real numbers. 2) p3r 2m 2) p pmr m Simplif the epression. 3) ( + ) ( + 3) 3) Rationalize the denominator. Write the quotient in lowest terms. 7 4) ) Solve the equation b completing the square. ) = 0 ) {- ± 2 6} Use the quadratic formula to solve the equation. Simplif an radicals. 6) = 0 6) {-3 ± } 7) 42 = )

11 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? 8 in. Give the coordinates of the verte and sketch the graph of the equation. 9) = ) 9) (4, 0) ) The length and width of a rectangle have a sum of 70. What dimensions give the maimum area? Length 3 and width 3 60)

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