. Simplif: 77 ( 9) + 46 7 + ( 68) Practice Questions for MA 09 Final Exam 47 77. What is the first step in evaluating this expression: 86+ 6 ( ) 4? 86+ 6 ( ) 4 ( ) 6. Which one of the following illustrates the Distributive Propert? = abc a+ a = 0 abc ( ) ( ) a 0 0 a a + = + = ( ) 4 4. Simplif: 7 9 9 a b+ c = ab+ ac 8. Select the sentence that is entirel correct. When I evaluate (7) When I evaluate (7) or negative. When I evaluate (7), the answer is positive if ( (7) ) is positive., the answer is negative regardless of whether ( (7) ), the answer is positive if ( (7) ) ( (7) ) is positive., the answer is positive regardless of whether ( (7) ) When I evaluate (7) negative. is positive is negative and negative if is positive or 6. Simplif: ( x + ) x 9 6x 9x + 9 6x
MA 09 Final Exam Practice - Page 7. Check x = 7 to determine if it is a solution to the following equations: (more than one might be es ) x + 0 = x + 4 ( ) ( x )( x ) 6 + = 0 x + = + x = x 8. Graph the following inequalit on the number line 4 x < 7. 9. Determine the correct interval notation for the following inequalit: (, ) [, ) (, ) [, ] 0. Solve the following equation for x: x x = 4 6. Solve for x: 9x 6 = 8x 4 x The solution is in interval x 0. The solution is in the interval x. The solution is in interval x. The solution is in the interval. Solve the inequalit for : 9 8 7 7. Simplif: ( a ) 4 4a 7 4a (e) 6a 0 x. 6a 7 64a
MA 09 Final Exam Practice - Page 4. Simplif: 6 8 mn ( mn ) 6 mn (e) 8 mn mn mn. Express using a positive exponent: t t t (e) t 6. Simplif: 7 ( ) ( ) ( ) 0 t 7 ( ) ( ) 7 t (e) 7 7. Solve x = 0 for the indicated variable: Solve for. x = x = + x = + 0 (e) 7 = x = 8. A customer left a total of $0.00 for a meal that cost $8.4. Determine the tip rate. 0.8% % (e).% 8.% % 9. Nordstrom has advertised a % off sale. If a London Fog coat originall sold for $6.00, find the decrease in price. $6.40 $64.00 (e) $.00 $9.00 $9.0
MA 09 Final Exam Practice - Page 4 0. Given f( x) = x 7x+, find f ( 4) 4 47 (e) 4 9. Add: ( x 4 + 0x 8) + ( 8x 4 4x + x 8) 8 x 4 x 4x 6 6 9 + x x 4 x 4x x 6 4 + (e) x + 6x 6x 8 4 x + 8x 6. 8 Multipl: (9 x )( x ) 7x 6x 40 7x (e) 6x x. Multipl: ( x )( 4x + x ) 7x + x 0 4 x + x x (e) 4 x + x x x+ 4 x + x + x + x 4 x + x + x x+ 4. Multipl: ( x ) x 0x x (e) x 0x+ x +. Write the correct term for the following: The propert of addition/multiplication states that two numbers can be added/ multiplied in either order to get the same result. Two terms with exactl the same variables and exponents are called terms. We can use the propert to remove the parentheses when an expression is multiplied b a quantit. The distance around a geometric figure is called its. (e) The amount of surface that is enclosed b a geometric figure is called its. (f) If both sides of an inequalit are multiplied or divided b a negative number, the resulting inequalit will have the direction from the original one.
MA 09 Final Exam Practice - Page 6. Fill in the blank with the correct term. In an equation, the input variable is called the variable and the output variable is called the variable. The of a line is the point (0, b) where the line intersects the -axis. The of a line is the point (a, 0) where the line intersects the x-axis. A line with slope rises from left to right. (e) The graph of x = is a line. (f) The graph of = 6 is a line. (g) The equation = mx + b is called the form for the equation of a line. 7. Demonstrate an understanding of expression notation b completing the statements below. ( a b) 0 + = = applies the definition of exponents. f () represents the of a function when x =. To add or subtract like terms means to combine their and keep the same variables with the same exponents. (e) ( x x 4) + =. (f) True or False. When asked to perform the indicated operation for ( x 4), the answer would be 9x 6. (g) 0 a =. (h) 0 a =.
MA 09 Final Exam Practice - Page 6 8. Complete the following statements. A is a statement that two ratios are equal. Given the proportion a = c, ad = bc is called the. b d 9. Graphicall, when a sstem of two linear equations has a solution, it is the of the two lines. Graphicall, when a sstem of two linear equations does not have a solution, the lines are. Graphicall, when a sstem of two linear equations has infinitel man solutions, the equations of the sstem are graphed as the. 0. Graph: x+ = 6. Graph: =
MA 09 Final Exam Practice - Page 7. Find the slope of the line that connects these two points: (4, ) and (, ). m = m = m = m = (e) m =. Find the rate of change of the tuition and fees per ear at public two-ear colleges (based on information in the Statistical Abstract of the United States, 99). Public Two-ear College Tuition and fees 400 Dollars 00 000 800 990 99 99 99 994 99 996 997 Year 00 00 00 00 (e) 600 4. Find the equation of the line that passes through the points: (, ) and (, 4).. Solve this sstem of equations graphicall. x = x+ = 4 6. Solve this sstem of equations algebraicall. 8 = 4 4x x+ = 4
MA 09 Final Exam Practice - Page 8 7. Solve this sstem of equations using the TABLE feature of our calculator. x = x + 6 = 0 8. A driver pumped 0 gallons of gasoline into her tank at a cost of $47.8. Write a ratio of dollars to gallons and give the unit cost of gasoline. 9. Find the perimeter of a rectangle that has length 9 feet and width feet. 4 9 4 0 4 44 6 08 4 40. A tree casts a shadow of 6 feet at the same time as a -foot man casts a shadow of 4 feet. Find the height of the tree. 4. Ever ton of reccled paper saves approximatel 7 trees. (It also saves dumping cost, landfill space, and about 7000 gallons of water, and 400 kilowatt-hours of electricit that would be used in making new paper products. Furthermore, to collect and reccle paper provides five times as man jobs as to harvest virgin timber.) If our college reccles 0 tons of paper in a ear, how man trees has it saved? Let x represent the number of trees saved. Which of the following equations could be used to solve for x? Which is the correct equation? x = 7 x = 7 0 0 0 = 0 = 7 x 7 x
MA 09 Final Exam Practice - Page 9 4. If R represents a positive real number, which of these is equivalent to R R+ R R? 4R 4 4R ( R ) 4 R (e) ( R) 4. Given a = and d =, find the first five terms of the arithmetic sequence and graph them on the coordinate plane. n 4 a n 44. True or False. This represents the graph of an arithmetic sequence. x 4. Fill in the following table and then graph the arithmetic sequence using the equation, a = n+ 7 n 4 x a n n
MA 09 Final Exam Practice - Page 0 46. Find the x-intercept and the -intercept for this equation: 7x =. 47. The perimeter of a rectangle is 4 feet. If the length is more than times the width, find the area of the rectangle. 48. Pick the table that best illustrates this inequalit: x 6 8 Entr in = menu Let = x 6 and = 8 x.76 7. 8.77 7.6 8.78 7.7 8.79 7.88 8.76 8 8 x.6 08 8.46 0. 8.6 8.66 4. 8.76 8 8 x.6 8.66 4. 8.76 8 8.86 70. 8.96 8 8 x.7 8.7 4. 8.74. 8.7 6.7 8.76 8 8 49. The world s largest sign for Coca-Cola is located in Arica, Chile. The rectangular sign has a length of 400 feet and has an area of,400 square feet. Find the width of the sign. 0. The length of a rectangular garden is 6 meters. If meters of fencing are required to enclose the garden, find its width.. Piranha fish require. cubic feet of water per fish to maintain a health environment. Find the maximum number of piranhas that ou could put in a tank measuring 8 feet b feet b 6 feet.
MA 09 Final Exam Practice - Page. A financial planner has a client with $,000 to invest. If he invests $0,000 in a certificate of deposit paing % annual simple interest, at what rate does the remainder of the mone need to be invested so that the two investments together ield at least $600 in a earl interest?. The number of music cassettes (in millions) shipped to retailers in the United States from 99 through 000 can be modeled b the equation = 7.x+ 64.4, where x represents the number of ears after 99. Find the x-intercept of this equation (round to the nearest tenth). What does this x-intercept mean? Find the -intercept of this equation. What does this -intercept mean? 4. In 99, the sales of batter operated ride-on tos in the United States were $9 million. In 000, the sales of these ride-on tos had risen to $60 million. Write two ordered pairs of the form (ears after 99, sales of batter-operated ride-on tos) for this situation. Let t = 0 represent the ear 99. The relationship between ears after 99 and sales of batter-operated ride-on tos is linear over this period. Use the ordered pairs from part to write an equation of the line relating ear ( t) to sales of batter-operated ride-on tos. Use the linear equation from part to estimate the sales of ride-on tos in 999.. Solve this sstem of equations using our graphing calculator and the intersect feature. 6 6 = x+ 4 66 6 66 6x 6 = + 4 8
MA 09 Final Exam Practice - Page 6. Select the table that would illustrate a dependent sstem of equations. x x 4. 0.47. 4.... 0.08.. 0. 0.. 0.8 0.7 0. 0.97.7 x 4....... 0. 0.. 0.7 0.7 0..7.7 7. Solve the following equation graphicall: x x x + = + 8 9 7 a) ( 9.8,4.96). 4.... 0... 0.7 0...7 x b) ( 9.8, 4.96) 0 0 c) ( 9.8,4.96 ) d) ( 9.8, 4.96)
MA 09 Final Exam Practice - Page 8. Determine the best SEQUENCE of events b selecting from the list below and putting them in their respective spot. A. The problem is an addition problem. B. The problem is a subtraction problem. C. The signs are the same. D. The signs are different. E. Add their absolute values together. F. Subtract the number with the smaller absolute value from the number with the larger absolute value. G. Use the common sign for the answer. H. Use the sign of the number with the largest absolute value for the answer. I. Change the sign of the second number and the subtraction operation becomes addition. Match the letter sequence from the answer choices column with the problem in the first column. Some ma be used more than once and some ma not be used at all. Examples: 8 + 9 = 7 6 = 7 because _ACEG because BICEG ANSWER CHOICES a. 6 4 = because ACEG b. 8 + ( 9) = because ADFH c. 8 ( 7) = because BDFH d. 8+ ( 6) = because BCEG e. = because BICEG f. 4+ = because BIDFH g. 6 = because ADEH ADEG
MA 09 Final Exam Practice - Page 4 ) b ) d ) d 4) a ) d 6) c 7) a - es b no c no d es 8) [ ) or 9) c 0) 6 ) b ) d ) e 4) b ) d 6) a 7) a 8) b 9) c 0) c ) c ) a ) c 4) d -4 7 ANSWER KEY ) a- commutative b- like c- distributive d- perimeter e- area f reversed or opposite 6) a- independent dependent b- -intercept c- x-intercept d- positive e- vertical f- horizontal g- slope-intercept 7) a- b- negative c- output or value d- coefficients e- x + x 4 f- False g- 0 h- undefined 8) a- proportion b- cross product 9) a- intersection b- parallel c- same line 0) ) ) b ) b x 7 4) = or =.7x.7 4 4 ) 6) no solution (parallel lines) 7) Infinite solutions (same line) 8) $47.8 0 Ratio gal (4,) $.79 Unit Rate gal
MA 09 Final Exam Practice - Page 9) c 40). feet 4) b 4) c 4), 9, 7,, (see Fig. ) Fig. 44) False (the points do not lie on a line) 4),,, 7 (see Fig. ) 46) x-intercept (, 0) -intercept (0, 7 ) 0 0 Fig. 47) square feet 4) (0, 9) and (, 60) 48) c =.8t+ 9 or 49) feet $46. million 0) 4. feet ) x = 0.7 ) 96 piranhas = 4.68 ) Rate 0% 6) b ) (7., 0) 7) d 7. ears after 99, the number of cassettes shipped is zero. (0, 64.4) In 99, there were 64.4 million cassettes shipped. 69t = + 9 8) a.) 04, BICEG b.) 9, ADFH c.) 9, BIDFH d.) 64, ACEG e.) 4, BICEG f.) 7, ADFH g.) 4, BIDFH
MA 09 Final Exam Practice - Page 6. Lines intersect at (4, ) 6. Lines are parallel. 7. Table 7. Graph (same line). Graph. Lines intersect at (0.6, 4.68) 7. Lines intersect at ( 9.84, 4.96)