AIM3 Math Review Final

36. tan 390 a. rad3/3 b. -rad3 c. rad3 d. rad3/2

A.

40. (y+2)²/64-(x-5)²/36=1 a. b. c. d.

A.

43. a. b. c. d.

A.

45. a. b. c. d.

A.

Convert the equation to the standard form for a hyperbola by completing the square on x and y. 37. 9y² - 25x² - 18y - 100x - 316 = 0 a. (y-1)²/25 - (x+2)²/9=1 b. (x-2)²/9 - (y+1)²/25=1 c. (y-1)²/9 - (x+2)²/25=1 d. (y+1)²/25 - (x-2)²/9=1

A.

Graph the ellipse 38. (x-2)²/16 + (y+2)/4=1 a. b. c. d.

A.

Convert the angle in radians to degrees 33. -47pi/18 a. -rad2 b. rad2/2 c. -2 d. -2rad3/3

A. Multiply by 180/pi Solve

Use the fact that the trigonometric functions are periodic to find the exact value of the expression 34. sec 21pi/4 a. -2 b. rad2/2 c. -2 d. -2rad3/3

A. sec = 1/rad-2/2 Solve

Solve the logarithmic equation. Be sure to reject any value of x that produces the logarithm of a negative number or the logarithm of 0. 29. log 2 (x+3) =1 a. -1 b. 4 c. 5 d. -2

A. x+3=2¹ -3 -3 Solve

Find the vertical asymptotes, if any, of the graph of the rational function 24. h(x) = x-3/x(x+1) a. x=0,x=1 b. x=3,x=-1 c. x=-1 d. no vertical asymptotes

A. Plug zero for x on the bottom always with vertical asymptotes Solve

41. a. b. c. d.

B.

42. a. b. c. d.

B.

Use the reference angles to find the exact value of the expression. Do not use a calculator. 35. csc 4pi/3 a.-rad3 b. -2rad3/3 c. -rad2 d. -1/2

B.

Graph the rational function 26. Refer to packet

B. Can not cross 2 and 3

Solve the equation by isolating the natural logarithm and exponentiating both sides. Express the answer in terms of e. 30. 9 ln 6x = 27 a. e¹/2 b. e³/6 c. e³ d. 3/ ln 6

B. Divide by 9 Add e Solve

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. 28. log2 x²/y⁸ a. 2 log 2 x + 8 log 2 y b. 2 log 2 x - 8 log 2 y c. 8 log 2 y - 2 log 2 x d. 1/4 log 2 x/y

B. Dividing = subtracting Solve

Find the horizontal asymptote, if any, of the graph of the rational function 25. h(x) = -5x+2/5x+2 a. y=-5 b. y=-1 c. y=1 d. no horizontal asymptote

B. Plug zero in for all xs 0 + 2 = 2 -5 x 2 5 x 2 Take your two answers Divide Solve

Divide 23. 6x³-25x²+15x+25/2x-5 a. x²+5x+5 b. 3x²-5x-5 c. x²-5x-5 d. 3x²-5

B. Set up as normal division Solve

Find the product 14. (x+4) (x² - 4x +16) a. x³ +8x² + 8x +64 b. x³ + 64 c. x³ - 8x² - 8x + 64 d. x³ - 64

B. Use the box method Solve

Solve the equation 32. 5⁽¹²⁻3x) =125 a. 4 b. -3 c. 3 d. 25

C. Plug all in Test Solve

Factor by grouping 15. x³ - 4x² - 2x + 8 a. (x² - 4)(x - 2) b. (x² +2)(x + 4) c. (x² - 2)(x - 4) d. (x - 2)(x-4)

C. Use the box method Solve

Perform the indicated operations. Write the resulting polynomial in standard form. 13. (2x⁹ + 10x⁶ - 13x³ + 6) - (10x⁹ - 5x⁴ + 10x³ - 6) a. -8x⁹ + 10x⁶ - 5x⁴ - 23x³ + 12 b. 8x⁹ + 10x⁶ +5x⁴ - 23x³ + 12 c. -8x⁹ + 10x⁶ + 5x⁴ - 23x³ +12 d. 8x⁹ + 10x⁶ - 5x⁴ - 23x³ + 12

C. Distribute the negative Line up the two equations Solve

39. Determine the end behavior of the graph of the function f(x) = -3x⁴-2x+1 a. falls to the left; rises to the right b. rises to the left; rises to the right c. falls to the left; falls to the right d. rises to the left; falls to the right

D.

44. a. b. c. d.

D.

Factor using the formula for the sum and difference of two cubes 16. 125x³ - 8 a. (5x-4) (25x² - 5x +1) b. (5x - 2) (25x² + 6x +4) c. (5x - 2)(25x² + 4) d. Prime - can not be factored

D. All of the equations do not work

Multiply or divide as indicated 18. x²+5x+6/x²+9x+18 x x²+2x/x²+12x+36 a. x+6/x²+6x b. x/x²+9x+18 c. x+6 d. x+6/x

D. Break up like done in number 5 Cancel Solve

27. A scientist found that the number of bacteria in a culture doubled every hour. If there were 3500 bacteria at 7:00 am, how many bacteria were there at 3:00 pm? a. 63,000 b. 448,000 c. 1,792,000 d. 896,000

D. P(t)=P(b)^t P = 3500 B = 2 T = 8 Solve

Solve the problem 31. Find out how long it takes a $3000 investment to double if it is invested at 9% compounded monthly. Round to the nearest tenth of a year. a. 7.5 years b. 8.1 years c. 7.9 years d. 7.7 years

D. Write out equation Fill out variables Solve

Obtain the standard deviation, for the given data. Assume that the data represent sample population data. 1. The test scores of 9 students are listed below. 92, 52, 43, 45, 67, 70, 72, 51, 83 a. 17.2 b. 16.2 c. 263.2 d. 296.1

Step 1: Add up all of the numbers Step 2: Divide all of your answers by 9 and you will get x bar Step 3: Subtract the number of students by 1 Step 4: Make a table that is 3 by 10 Step 5: Take your first number and subtract it by the answer that you got for step 2 (63.9) Step 6: Take that answer that you got from step 5 and square it Step 7: Repeat steps 5 through 6 until you have went all the way through all of the numbers Step 8: Once you have your answers, add them all up Step 9: Take the number that you got from step 2 (8) and divide it by the number that you got in step 8 Step 10: Take the number that you got from step 9 and find the square root of it Your final answer should be: a. 17.2

2. Which of the following is NOT true of the normal distribution? a. the curve is asymmetrical b. the curve is bell-shaped c. the measures of central tendency (mean, median, and mode) are equal in value d. the curve approached the x-axis gradually on either side of the mean

Your answer should be a. the curve is asymmetrical. If you are wondering how I got this, think of it this way: normal distribution is always equal. This eliminate b. c. and d. therefore leaving you with a.

3. A competency test has scores with a mean of 80 and a standard deviation of 10. A histogram of the data shows that the distribution is normal. Use the Empirical Rule to find the percentage of scores between 70 and 90. a. 50% b. 99.7% c. 68% d. 95%

Your answer should be c. 68%. If you are wondering how I got this, think of it this way: once you graph the histogram, then you should be able to figure out that the answer should be 68% because the order of percentages are 68%, 95% and 99.7%.

Find the zeros of the function. 4. f(x) = 9x² + 3x - 2 a. 2 and -1 b. -2/3 and 1/3 c. -2 and 1 d. 2/3 and -1/3

Your answer should have been b. -2/3 and 1/3. If you are wondering how I got this, think of it this way: when you plug in zero, you get 1/3. A positive, not a negative. So you know that it must be b.

Add or subtract terms whenever possible 7. 4rad6 + 2rad24 a. 8rad6 b.-8rad6 c. 6rad6 d. -2rad6

a. 8rad 6 2rad24 6 x 4 = 24 2x3 = 6 2 x 2 =4 4 x 2rad3 x 2 8rad6

Multiply or divide as indicated 5. x²+14x+48/x²+15x+56 * x² +7x/x²+15x+54 a. x/x+9 b. x/x²+15x+56 c. 1/ x+9 d. x²+7x/2+9

a. x/x+9 (x+8)(x+6)/(x+8)(x+7) * x(x+7)/(x+6)(x+9) Cancel them all out to get x/x+9 left.

Evaluate the trigonometric function of the given quadrantal angle 9. cos 13pi/2 a. -1 b. 1 c. 0 d. undefined

c. 0 Draw the unit circle. Identify where 13pi/2 lands. Cos equals x. (0,1)

Give the exact value. 10. sec 30 deg a. 2 b. rad2 c. 2rad3/3 d. rad3/2

c. 2rad3/3 1/rad3/2 1 x 2/rad3 2rad3 x rad3/rad3

Find the measures of two angle, one positive and one negative, that are coterminal with the given angle 8. 86 degrees a. 446 deg;-94 deg b. 176 deg;-4 deg c. 446 deg;-274 deg d. 266 deg; -94 deg

c. 466 deg:-274 deg 86 + 360 = 466 86 - 360 = -274

Solve for x 11. Refer to triangle shown in your packet a. 10.07 b. 12.43 c. 20.59 d. 25.42

d. 25.42 sin (39) = 16 /x 16/0.629 = 25.42