Review for Intermediate Algebra (MATD 0390) Final Exam Oct 2009


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1 Review for Intermediate Algebra (MATD 090) Final Eam Oct 009 Students are epected to know all relevant formulas, including: All special factoring formulas Equation of a circle All formulas for linear equations Both forms of equations of (slope formula, slopeintercept and parabolas pointslope forms) All formulas needed to solve Quadratic formula applications in this review, such as Distance between two points distance, and direct and inverse Midpoint between two points variation In order to be prepared for the final eam, students should be able to do all of the following problems and related problems as well. Practice Problems Simplif. All eponents should be positive integers a 7 b c a b c. Find the slope, intercept, and intercept. Then graph the line with equation. Find the slope and intercept, and use them to graph the line with equation. Graph and give the slope for each line: a. b Write the slopeintercept equation for the line containing the points, and 8,. 8. Identif the slope and intercept for this line. Then give the equation in slopeintercept form. 9. Write the equation (in slopeintercept form) for the line through the point, perpendicular to. 0. Write the equation (in slopeintercept form) for the line through the point, parallel to the line through the points, and,.. Determine without graphing whether the pair of lines is parallel or perpendicular, or neither: 7 8 and 8
2 . Determine if the following relations represent functions or not. Give the domain and range of each. a. {(, ), (, ), (, )} b. {(, ), (, ), (, 7), (, 0)} c. d. (,) (,) (,8) (7,0) (0,) e. f. Y X (,) (0,) Y X For f and g 7 a. f b. f g( a), find the following. f g d. c. f g(). For the function f, shown below, find the following. e. The domain of f g a. f b. f c. For what value(s) of is f d. Which value is larger: f or f?. Give the slope and intercept, and graph the linear function: f.
3 . Suppose 8. million pounds of coffee are sold when the price is $ per pound and 0. million pounds are sold at $ per pound. a. Find a linear function sold) as a function of the price per pound. D that epresses the consumer demand (amount of coffee b. Use this function to predict the consumer demand if the price is $9 per pound. c. At what price can ou epect to sell no coffee at all? Round our answer to the nearest cent. 7. At a particular college, student loans were distributed in 980 and loans were given during 990. During this tenear period, the number of loans disbursed each ear followed a linear pattern. a. Write a linear equation that epresses the annual number of loans given ( ) as a function of the number of ears ( ) since 980. (That is, 0 corresponds to 980, corresponds to 98, etc.) b. Use the equation from part (a) to find the number of loans given in Maria's wages are $00 plus.% commission on monthl sales. a. Write a function epressing the relationship between Maria's wages, w, and her monthl sales,. b. Find her sales for the month if her wages for the month are $ Solve the following sstems of linear equations in two variables: 7 7 a. b. c The sum of two numbers is 9. One of the numbers is 7 more than the other. What are the numbers?. A canoe and a motor boat travel toward each other from a distance of 70 miles. The motor boat moves miles per hour faster than the canoe. The two boats pass after. hours. How fast does each boat move?. A crosscountr flight traveling with the wind covers 000 miles in hours. The same plane then changes direction and travels to Teas, against the wind, covering 00 miles in hours. What are the wind speed, and the speed of the plane in still air?. A lab contains ounces of iodine solution of strength %. How much pure iodine would ou mi with it to get an iodine solution of strength %?. An investment portfolio of stocks and bonds, with an initial investment of $0,000, gained $0,800 over its life. If the stocks gained % and the bonds gained %, how much was invested in each? Solve the linear inequalities. Graph the solution and give the answer in interval notation Divide the polnomials: and or
4 . Solve the equation for and simplif, if possible: 8. Graph the solution to the inequalit on an coordinate plane.. Graph the solution to each sstem of inequalities on an coordinate plane. a. b. 0 Factor completel, if possible: Solve the equations for and simplif, if possible Find the domain of the following. f a ab cb a c r 0 Perform the indicated operation and simplif (reduce), if possible b. g
5 7. Find the three sides of this right triangle. Hint: Use the Pthagorean theorem: a b c. 8. The length of a rectangle is cm less than twice the width. The area is 7 square cm. Find the length and the width. Solve the equations for and simplif, if possible Carl, an eperienced shipping clerk, can fill a certain order in hours. Tim, a new clerk, needs 8 hours to complete the same job. How long would it take for both working together to fill the order?. Caleb's average driving speed is kilometers per hour slower than Ling's. In the same length of time it takes Caleb to drive km, Ling drives 97 km. What is Caleb's average speed?. Solve for R: ne I R nr Simplif. Assume all variables are greater than or equal to zero. 7. / 8. 8 z 9. Solve for r: rl H r k 9. 9 b c Multipl and simplif. Assume all variables are greater than or equal to zero 7. Evaluate: / 8 7. / 7. / 7. Solve the equation for and simplif, if possible: 7 Perform the indicated operation and epress the answer in standard form, a + bi: i i i i i i 79. i i 80.
6 Solve each equation for and simplif, if possible For each equation, use the discriminant to determine whether the quadratic equation has two unequal rational solutions, two unequal irrational solutions, one repeated real solution, or two comple solutions that are not real. a. 0 b. 7 0 c Find the intercepts, if an, and intercept of the function. f a. b. g h 0 c. 87. Graph the function f. From the graph, give the ais of smmetr and the verte. 88. Graph the function f and determine whether it has a minimum or maimum value. Then find the minimum or maimum value. 89. In business, the total profit P is the difference between the revenue R and the cost C. For units produced, R 000 and C 000 C () are dollar amounts. Find the following: a. the total profit function P (), where R () and b. the value of (number of units) at which the maimum total profit occurs c. the maimum total profit. 90. The stopping distance d of a car after the brakes have been applied varies directl as the square of the speed r. A car traveling 0 mph can stop in 00 ft. a. Epress stopping distance as a function of speed. b. What stopping distance corresponds to a speed of mph? 9. The current I in an electrical conductor varies inversel as the resistance R of the conductor. If the current is 0. amperes when the resistance is 0 ohms, what is the current when the resistance is 90 ohms? 9. Given the points A:, and :, B, find the distance from A to B and find the midpoint of the line segment joining A and B. and radius Find an equation for the circle with center, 9. Find the center and radius of each circle: a. b. 0
7 ANSWERS... c a. Slope: ; intercept:,0 ;  intercept:. Slope:. 7. (,0) 0, (0,) ; intercept: 0,   a. Slope: 0 b. Slope: undefined (b) (a)  8. Slope: 0.8 ; intercept: 0, Parallel... a. Function. Domain: {,, } Range: {,, } b. Not function. Domain:,, Range:0,,,7 c. Not function. 7 or,7 or, D: R: d. Function. 0 or,0 or,8 D: R: 8 e. Function. D: or, R: or, f. Not function. a. b. c. 7 d. or, or, D: R: a a a a 7 e. 0, 7 a. 0 b. c. ., ., d. f
8 . Slope: ; intercept: 0,., / 7., 8., 7 8, , a. D.. b. million pounds c. $9. a. b. loans a. w b. $8,000 a. (, ) b. (, ) c. No solution. The canoe moves 8 mph. The motor boat moves 0 mph.. Still air speed is 0 mph. Wind speed is 0 mph.. ounces. $7,00 in stocks $7,00 in bonds.. 7, ) , a. b
9 Prime (Sum of squares) a cb b. r r r.. 0, 7., a. 0, b. all real numbers.... )(.. 7., 8, 0 8. L = 0 cm, W = 7. cm No Solution ( is not in domain) hours. km/h.. 7. ne R I r Hk L H nri 8. z 9. b c c
10 7. 7. ( is etraneous) i 78. i 79. i 80. i i Ais of smmetr: Verte:, i a. Two imaginar solutions b. Two real (irrational) solutions c. Two real (rational) solutions a. intercepts:,0,,0 intercept: (0, ) b. intercepts:,0,,0 intercept: 0, c. No intercepts; intercept: 0, The function f has a minimum value of . P( ) a. 99 units b. $,00 a. d r 8 b. 7 ft amperes 9. d ; midpoint is , a. Center:, ; Radius: 8 b. Center: 8, ; Radius: 7
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) Simplif: z z z 6 6 z 6 z 6 ) Simplif: 9 9 0 ) Simplif: a a a 0 a a ) Simplif: 0 0 ) Simplif: 9 9 6) Evaluate: / 6 6 6 ) Rationalize: ) Rationalize: 6 6 0 6 9) Which of the following are polnomials? None
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