1 st Semester Final Review Date No
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1 CHAPTER 1 REVIEW 1. Simplify the epression and eliminate any negative eponents. Assume that all letters denote positive numbers. r s 6r s. Perform the division and simplify Simplify the epression. 1 y y. Two cyclists, 90 mi apart, start riding toward each other at the same time. One cycles twice as fast as the other. If they meet h later, at what average speed is each cyclist traveling? 5. Factor the epression completely Perform the subtraction and simplify Rationalize the denominator Solve 1 a. 9 b Solve. Leave answers in interval notation. a. 10 b The approimate distance d (in feet) that drivers travel after noticing that they must come to a sudden stop is given by the formula d, where is the 0 speed of the car in mi/h. If a car travels 175 ft before stopping, what was its speed before the brakes were applied? ANSWERS Chapter 1 1. r s y a. -9 8b. -1/. 18 mph & 6 mph 9a. 7, 1 9b., 6,
2 CHAPTER REVIEW 1. Find the domain of each function. a. f 9 b. f. Graph each function. State the domain and range for each. a. f 1 b. g 1 c. h d. f if 1 if. Find the equation for the for the transformed graph: f ; shift units to the right, stretch vertically by a factor of, and reflect in the -ais.. For the given graph of a function, determine the average rate of change between the indicated values For the function f t t determine the average rate of change between the values t 0 and t h Describe how the graph of y f obtained from the graph of f can be 7. Determine whether the function in the figure is even, odd, or neither. 8. If f 1 and g a. f g, find b. fg c. f g.
3 9. Find the inverse of the function. f 5 ANSWERS Chapter 1a. or 1b. all real #s,. f. -1 a. b h 1 c. d. 6. shrink towards y-ais; Reflect over -ais; Shift up 7. even 8a. 1 8b. 8 8c f 1 5
4 CHAPTER REVIEW 1. Epress the quadratic function in standard form. f 1 1. The profit P (in dollars) generated by selling units of a certain commodity is given by the function P What is the maimum profit and how many units must be sold to generate it? a. Graph y. Find the quotient and remainder of 10 using long division. b. Graph y Is a factor of the polynomial? P Find a polynomial of degree with constant coefficient 6 and zeros and, with a double zero. 7. Find a polynomial with integer coefficients that has zeros of i, and Factor the polynomial completely. p 9. Find all rational, irrational, and comple zeros. P Find all zeros. P 6 8
5 11. Find all rational, irrational, and comple zeros. 1. Find all vertical asymptotes of the function r 1a. Graph y 1b. Graph y ANSWERS Chapter 1. f 11. $7500 for 1500 units a. b no (remainder ) , i 10., 1 i ,1, a. 1b.
6 CHAPTER REVIEW 1. Sketch each graph. State the domain and range. Label any asymptotes. a. f 1. Sketch each graph. State the domain and range. Label any asymptotes. a. g log 1 b. f 1 b. g log. Evaluate the logarithm. log 75. Epand the logarithmic epression. ln y 1 5. Solve the equation. Find the eact solution Solve the equation. Find the eact solution. log log log 7. Jennifer wants to invest $,000 at an interest rate of.5% per year, compounded quarterly. How long will it take her investment to double? 8. How long will it take an investment of $,00 at an interest rate of 5% per year compounded continuously to reach $10,000? 9. The half-life of radium-6 is 1600 years. How much of a -mg sample remains after 000 years? 10. Solve 7 7 1
7 11. Combine into a single logarithm. 1. Solve the equation. Find the eact solution. ln y ln y log 1 log1 ANSWERS Chapter 1a. 1b. a. b ln ln 1 ln ln y 6. or years years mg y ln y
8 CHAPTER 5 REVIEW 1a. Find the reference number determined by t. Find the eact value of sec 1b. Find the reference angle for 0. Find tant given that 5 cost and sin t 0 a. Graph y cos 8 b. Graph y tan 1 5a. Find the eact value of the epression. Draw triangles 1 tan cos Find the eact value of sect cot t if tan t and the terminal point for t lies in quadrant III. 5b. Find the eact value of the epression. Draw triangles. 1 sin cos 10 ANSWERS Chapter 5 1b.. - 1a a. 5a. 5b. 60 b
9 CHAPTER 6 REVIEW 1. Find the radian measure that corresponds to 5. Find an angle between 0 and that is coterminal 15 with. Find the length of an arc of a circle of radius 8 ft if the arc subtends a central angle of 00. Find the measure of the central angle in a circle of radius 5 ft if the angle is subtended by an arc of length ft. 5. Find the area of a sector with central angle 10 in a circle with radius 6 m. 6. A 76-ft tree casts a shadow that is 100 ft long. What is the angle of elevation of the sun? 7. A 00 ft guy wire is attached to the top of a tower. If the wire makes a 55 angle with the ground, how tall is the tower? 8. Find sin and cot given that sec and tan Solve the triangle. A 5, B 70, b A plane leaves the airport at :00 pm and heads in the direction N10 E at a constant speed of 50 mi/h. Fortyfive minutes later, a jet leaves the same airport and flies N60 W at a constant speed of 50 mi/h. Find the distance between the plane and the jet at 5:0 pm. 11. Find the area of a triangle with sides of length 8 and 10 and included angle 5 1. Solve the triangle. a 15, b 0, c 18 ANSWERS Chapter ft mi sin ;cot 15 C 75 ; a 9., c m ft B 7 ; C 60 ; A 6
10 CHAPTER 7 REVIEW 1. Find all solutions of sin 0. Solve the equation in the interval 0,60 sin sin 0. Solve the equation in the interval 0, 1cos sin. Find the eact value. 5 cos 1 5. Find the eact value. tan80 tan 0 1 tan 80 tan 0 6. Find sin, given that quadrant IV. tan and is in 7 7. Find the eact value. 1 tan sin 8 8. Verify the identity: sin sin cot 1cos 1cos ANSWERS Chapter 7 1. k; k , 18., 180, ,, 7. 55
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