Precalculus 2nd Semester Review 2014

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1 Precalculus 2nd Semester Review 2014 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the coordinates of the center of the ellipse represented by. 2. Find the coordinates of the vertices and co-vertices of the ellipse in the previous problem. 3. Use the discriminant to identify the conic section. a. parabola c. ellipse b. hyperbola d. circle 4. Find the coordinates of the foci of the hyperbola represented by. 5. Write the standard form of the equation of the parabola with directrix at and focus at. 6. Write the standard form of the equation of the circle with center at and radius of 3.

2 7. Which graph represents a curve given by and over the interval? 8. Find the vertical component of v with a magnitude of 6.1 inches and a direction angle of 55. a in. c in. b in. d in. 9. Find a unit vector u with the same direction as. 10. Find the measure of the angle between vectors. a c b d Find the component form and magnitude of with initial point A(-4.3, -0.9) and terminal point B(-2.8, 0.2).

3 12. A force of 6 newtons pulls due north. A force of 8 newtons pulls due east. Find the magnitude and direction of the resultant force. a. 10 N; 53.1 c. 10 N; 36.9 b. 14 N; 53.1 d. 14 N; Find the cross product of and. 14. A cruise ship s path is represented by the vector. It then follows a new path represented by the vector. What is the resultant path? 15. Find the polar coordinates that do not describe the point in the given graph. a. (-3, 45 ) c. (3, 225 ) b. (-3, -135 ) d. (-3, -315 ) 16. AIRPLANES Two airplanes at the same altitude have polar coordinates and, where r is in miles. Find the distance between them. a miles c miles b miles d miles 17. Find the equation which is graphed below.

4 18. Identify the graph for the polar equation. 19. Find rectangular coordinates for the point with polar coordinates if and. 20. Express in polar form. 21. Express in rectangular form.

5 22. Find the next two terms of the sequence. a. -53, -74 c. -42, -53 b. -43, -54 d. -22, Find the 27th term in the arithmetic sequence. a. 174 c. 235 b. 226 d In an arithmetic sequence, what is d if is 14 and? a. 1.6 c. 2.6 b. 2.1 d Write in expanded form and then find the sum. 26. Which are the two geometric means between 175 and 1.4? a. 0.2, 0.04 c. 35, 7 b. 1.4, d , What is the fifth term in the expansion? 28. The expression is the expansion of which binomial? 29. What is the mean of the probability distribution? a c. 3.5 b d What is the standard deviation of the distribution in the previous problem? a c b d. 7.65

6 31. RAFFLE You buy a raffle ticket for $2. If your ticket is selected from the 500 sold, you will win $750. What is the expected value of your net gain? a. -$0.75 c. -$0.25 b. -$0.50 d. $ What is X if,, and? a. -42 c. 44 b. 28 d STRESS Recruits for a security position must take a stress test. The scores are normally distributed with a mean of 400 and a standard deviation of 100. What percent of the recruits scored higher than a recruit who scored 644? a. 0.73% c. 49.3% b. 7.3% d. 99.3% 34. Out of 500 randomly selected recruits described in Question 8, about how many scored higher than a recruit who scored 644? a. 4 c. 247 b. 37 d In a normal distribution with and, a random sample of 40 values is selected. Find the probability that the sample mean is between 87 and a. 1.8% c. 10.1% b. 3.9% d. 28.9% 36. In a binomial distribution,. Find. a. 14.5% c. 26.3% b. 20.0% d. 32.8% TIRES A random sample of 30 similar tires found an average life span of 36,200 miles. Assume that the standard deviation is 3800 miles. 37. Find the maximum error of estimate for a 99% confidence level. a c b d Find a 99% confidence interval for the mean population lifespan. a. 34,413-37,987 c. 35,506-36,894 b. 34,840-37,560 d. 35,952-36, For a maximum error of 1500 miles and a 90% confidence level, what is the minimum number of samples that should be chosen? a. 10 c. 18 b. 15 d. 26

7 40. Use the graph of above to find. a. -1 c. 1 b. 0 d Use the graph from the previous problem to find. a. -3 c. -1 b. -2 d Evaluate. 0 b. 1 d. 43. Evaluate. 44. Evaluate a. - c. 2 b. -7 d. 7 0 b. -5 d.

8 45. Find the derivative of. 46. Find the derivative of 47. Find the slope of the line tangent to the graph of at the point. a. 2 c. -1 b. 1 d Find an equation for the instantaneous velocity v(t) if the height of an object is defined as any point in time t. for 49. HEIGHT The height of a ball in feet after t seconds is given by for. Find. a. -32 ft/s c. 24 ft/s b. -16 ft/s d. 120 ft/s 50. FALLING OBJECTS Tito drops a pebble from a 900-foot tower. The position of the pebble after t seconds is given by. How fast is the pebble falling after 2 seconds? a ft/s c. -32 ft/s b. -64 ft/s d. 836 ft/s

9 Precalculus 2nd Semester Review 2014 Answer Section MULTIPLE CHOICE 1. B 2. A 3. B 4. D 5. D 6. A 7. A 8. A 9. D 10. D 11. C 12. C 13. C 14. C 15. B 16. B 17. C 18. B 19. C 20. C 21. D 22. A 23. B 24. A 25. D 26. C 27. D 28. D 29. B 30. A 31. B 32. D 33. A 34. A 35. B 36. A 37. D 38. A 39. C 40. C 41. C

10 42. C 43. C 44. A 45. D 46. B 47. D 48. D 49. C 50. B

3. A( 2,0) and B(6, -2), find M 4. A( 3, 7) and M(4,-3), find B. 5. M(4, -9) and B( -10, 11) find A 6. B(4, 8) and M(-2, 5), find A

3. A( 2,0) and B(6, -2), find M 4. A( 3, 7) and M(4,-3), find B. 5. M(4, -9) and B( -10, 11) find A 6. B(4, 8) and M(-2, 5), find A Midpoint and Distance Formula Class Work M is the midpoint of A and B. Use the given information to find the missing point. 1. A(4, 2) and B(3, -8), find M 2. A(5, 7) and B( -2, -9), find M 3. A( 2,0)

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3. A( 2,0) and B(6, -2), find M 4. A( 3, 7) and M(4,-3), find B. 5. M(4, -9) and B( -10, 11) find A 6. B(4, 8) and M(-2, 5), find A

3. A( 2,0) and B(6, -2), find M 4. A( 3, 7) and M(4,-3), find B. 5. M(4, -9) and B( -10, 11) find A 6. B(4, 8) and M(-2, 5), find A Midpoint and Distance Formula Class Work M is the midpoint of A and B. Use the given information to find the missing point. 1. A(, 2) and B(3, -8), find M 2. A(5, 7) and B( -2, -), find M (3. 5, 3) (1.

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