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1 MATD 090 INTERMEDIATE ALGEBRA Review for Test Test covers all cumulative material, including new sections.-.8,.-.,.6-.7, and Bring a non-graphing calculator and something to write with and erase with. Be prepared to show your work on all test problems in order to receive full or partial credit.. For the line given by the equation y 6 Find the - and y-intercepts. Find the slope of the line.. Find a linear function with slope, passing through the point,.. y varies directly as the square of. When is, then y is 8. Find y when = 6.. y varies inversely with. When is, then y is. Find the variation constant, k.. y varies directly with. When = 6, then y = 0. Find y when = Hooke s law states that the distance D a spring stretches varies directly with the weight W attached to the spring. When a weight of 0 pounds is attached, the spring stretches inches. Epress the distance that a spring stretches as a function of the weight attache Find the distance that the spring stretches from a 6 pound weight attache 7. Ohm s law states that the amount of current that flows through a wire varies inversely as the resistance. If a current of 9 amps flows through a wire with a resistance of ohms, then what current flows through a wire with a resistance of ohms? 8. Factor completely. If the polynomial cannot be factored, state that it is prime. 6abab g. 8y 8 9 h. 6 9 y i. 6 y 0y j. 8 0 e. 9 6 k. 8 f. 7s 6t l

2 9. Solve e f. 0. For the function P 0 7, solve P.. A rectangular garden has an area of 6 square feet. Its length is feet less than twice its width. What are the dimensions of the garden?. The base of a triangular sail is seven meters less than the height. If the area is 0 square meters, what are the base and height?. The outside border of a picture frame has a length of inches and a height of 8 inches. Inside the frame, an area of 6 square inches of picture is visible. The frame is the same width all the way around the picture. Find the width of the frame.. The height ht, in feet, of a penny t seconds after it is dropped from the top of a building is ht given by 00 6t. How much time will pass before it hits the ground? (Hint: The height at the ground is zero.). Simplify. 9 y 6 y y 0 y a a a a Multiply or divide, as indicated, and simplify your answer ac a a a 7c 9p 6q 6p8q 9p 6q 6pq page of 6

3 7. Simplify. 8. Simplify. 70 y y 9. Add or subtract, as indicated, and simplify your answer. 0. For the function f What is the domain? Find all values a such that f a. Solve.. Solve for the indicated variable. z : z y y : z y R : R r r s : s s v t page of 6

4 . Simplify. Use absolute value notation where appropriate. 8 8y. Evaluate Simplify, and epress your answer using positive rational eponents, if appropriate. 8 8 h h 8c 6 a For problems 6, you must define variables, and set up and solve equations. Show your work. 6. Robert can paint a room in hours. Julio can paint the same room in 8 hours. How long will it take them to paint the room together? 7. An airplane travels at a rate of 00 miles per hour in still air. One day it travels 00 miles against the wind in the same amount of time it takes to travel 800 miles with the win What is the wind speed? 8. The current of a river flows at a rate of 8 miles per hour. A rowboat travels 6 miles downstream in the same amount of time it takes to travel 6 miles upstream. What is the still water speed of the rowboat? 9. John rides his bicycle at a speed miles per hour slower than his friend Alice. If Alice rides 0 miles in the same time that John rides miles, how fast does each of them ride? 0. A man who is 0 feet tall casts a shadow that is feet long. At the same time and place, a sign casts a shadow that is feet long. How tall is the sign?. A pool can be emptied in 6 hours with both a strong pump and a weak pump working together. The weak pump alone requires hours more than the strong pump alone to empty the pool. How long does it take each pump alone to empty the pool?. The triangles below are similar. Find the length of the sides marked and y y page of 6

5 ANSWERS:. -int = 6, 0 y-int = 0, slope = f.. y 768. k 0. y 6. D W or D 0. W 8 8 or 8. inches amps 8. ab a b y y e. prime (sum of squares) f. s t9s st 6t g. y0yy h. i. 6 y 8y j. k. 6 l ,7 0, 0.,, e., f.,,. width = 6. feet length = 0 feet. base = meters height = meters. inches.. seconds (At the ground, height is zero. Equation: t ) 8 y. a a 6. a 9c p q p q pq page of 6

6 y y 6 y z y z rr R r r s s vt y 8 0 h 7c a hours miles per hour miles per hour 9. John rides 6 miles per hour, and Alice rides 0 miles per hour. 0. feet tall. The strong pump alone can empty the pool in 0 hours, and the weak pump alone can empty the pool in hours.. 8. and y. page 6 of 6