Algebra 2 B Semester Exam Review

Transcription

1 Algebra B Semester Exam Review Answers

2 Unit, Topic 3. a. y x y x. a. b. 3. a. LCM = x3x 4. Solution is x b. LCM = xx 9 A student who solves by cross multiplication will get x 0, x, with 0 being extraneous. Solution is x. A student who multiplies by the LCM will not get the extraneous solution. Function f x Function gx x x Even, odd, or neither Odd Even Domain All real numbers but 0 All real numbers but 0 Range All real numbers but 0 All positive real numbers End behavior as x f x 0 gx 0 End behavior as x f x 0 gx 0

3 5. a. 5 hours b. inversely c. H 5 n d hours 6. H 00 s 7. a. Method or Method x 3 x 3 x3 x3 x 6 x 3 x 7 x 3 x 3x7 x 6 x 3 b. Vertical asymptote is x 3. Horizontal asymptote is y. 8. a. Method or Method 5 x 4 5x 4 x4 x4 5x 0 x 4 5x x 4 5 x 45x 5x 0 5 x 4 b. Vertical asymptote is x 4. Horizontal asymptote is y 5.

4 9. a. b $3 50 6x x 50 6x x 5x 50 x 50cakes 0. a. b $ x 8.75 x 500 8x8.75 x 500 8x8.75x x x 50 fruitcakes

5 Unit 3. Values of x and y Quadrant of the Angle Sign of sin Sign of cos x is positive, y is positive Positive Positive x is positive, y is negative 4 Negative Positive x is negative, y is positive Positive Negative x is negative, y is negative 3 Negative Negative. a. b. sin 5 3 sin 7 cos 3 cos 4 7 tan 5 tan o 66.0 o All statements should be selected. 5. a. b. RF c. OF 60 0 or or or.047units d. RF OF e. 0 o or 40 o (or any integer multiples of 360 o added to or subtracted from these) f. 300 o or 40 o (or any integer multiples of 360 o added to or subtracted from these) 6. a. Amplitude: 0, Period: 8, Equation of midline: y 30 b. Amplitude: 8, Period:, Equation of midline: y 0

6 7. a. 9.6 feet b feet c. 8.5 feet o d. 8. a..6 feet 0 5sin b. 7.0 feet c. 8.5 feet d. Since one complete circle takes 36 seconds, the pony rotates 0 degrees per second. Since we want to know where the pony is was 3 seconds, there is a 30 o 0 5sin degree rotation, so 9. d t 0. Amplitude: 5, Period: 36, Equation of midline: y 0 or d 0 5sin t 8. d 0 5sin 0 o t

7 . a. This is not a good idea. There is no explanation as to what was done, and there are only 5 values in the table ; 4 0 b. d d c. All positive real numbers d. If the table were used, I d have to continue the table until I got to.6 lux, or keep measuring using my device until I got.6 lux, then measure the distance. 30 If the formula were used, I would solve the equation.6. It looks like a d simple equation to solve. I would probably do this. If the graph were used, I would go up the y-axis to.6, then go across until I found the corresponding x-value on the graph. It would be hard to do on this graph due to its scale. 3. a. sine (or cosine) and exponential b. sine (or cosine) and quadratic 4. a. Some kind of trig function (sine or cosine). The data appear to be periodic. b. This is not a good model. When I tried to evaluate it at x 0, I got 40, not 0. If I replace sin with cos it will work. (There are other possibilities.) 5. a. The domain is 0 x 0. Since x is a length it must be positive. Its value must be less than 0. Otherwise, the volume will be negative (The 0 x term in the formula will be negative. b. It looks like the side of the square should be a little less than 6 inches, with a corresponding volume of approximately 96 or 97 cubic inches. c. A table would probably not be a good model, since it appears that the maximum volume does not occur at a whole number value.

8 Unit a. R B b. R B c. R B d. R B

9 8. a. b. c. d. e. f. g. h % % % % % % % % 80 0 i. Yes they are independent. The probability that a person likes hockey is the same P H M 0.7 P H F 9. a. 50% b. 60% c. 8% d. 8% whether the person is male or female. e. 8% % 50% 50 f. 8% % 40% 40 g. 8%

10 % % 3. a. 68% b..5% c % d. 6% 4 4 e. If I compute a z-score for 4 days, I get z 5, meaning that this insects life span is 5 standard deviations above the mean. This would be quite unusual. 33. a. greater b. greater 34. All should be selected. 35. z-scores should be computed for each store and compared. Goldie s Store: z.5 Ahmed s Store: Ahmed s sales were two standard deviations above the mean sales for New York, while Goldie s sales were.5 standard deviations above the mean sales for Milwaukee. Ahmed s store should get the reward. 36. z-scores should be computed for each store and compared. Jose s Store: z Jamal s Store: Jose s sales were about standard deviations below the mean for New York stores, while Jamal s sales were 3.95 standard deviations below the mean for Seattle stores. The manager of Jamal s store should be fired.