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Precalculus Spiral

Prepare for your precalculus final exam with this comprehensive guide covering algebra, graphing, exponential functions, trigonometry, limits, statistics, and probability. Practice with a variety of questions and topics to improve your skills.

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Precalculus Spiral

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  1. Precalculus Spiral Final exam preparation questions Algebra Graphing Exponential Trigonometry Limits Stat/probability

  2. Functions: find f(2) and f(-3) • 1.) • 2.) • 3.)

  3. Composition: find f(g(x)) • 1.) • 2.) • 3.)

  4. Operations: Subtract and multiply • 1.) • 2.) • 3.)

  5. Y = mx + b • 1.) (-3, 2), (-4, 1) • 2.) (5, -2), (2, 4) • 3.) (-3, 4), (2, 4)

  6. Inverse: find f-1 • 1.) • 2.) • 3.)

  7. Synthetic Division: divide • 1.) • 2.) • 3.)

  8. Parent graphs • Draw the parent graphs for: • Find Domain and Range for each graph

  9. Transformations- describe them • 1.) • 2.) • 3.)

  10. Transformations- write equation • 1.) x2, up 2, left 5, reflect over x-axis • 2.) absolute value, wider, right 2 • 3.) square root, thinner, down 3

  11. Transformations: find them from graph, then find the domain

  12. Piecewise- find equation

  13. Piecewise: Graph • 1.) • 2.)

  14. Domain- equation • 1.) • 2.) • 3.)

  15. Asymptotes- equation-VA &HA • 1.) • 2.) • 3.)

  16. Asymptotes- graph-VA &HA

  17. Roots-given roots- find equation, then graph • 1.) roots of 3 and -5, • 2.) roots of 2, -2, 0 • 3.) roots of 2, 2i, -2i

  18. Roots- roots from graph

  19. Roots- Find roots from equation • 1.) • 2.) • 3.)

  20. Factor: trinomials and grouping • 1.) • 2.) • 3.) • 4.)

  21. Quadratic formula: • 1.) • 2.) • 3.)

  22. Graph • 1.) • 2.) • 3.)

  23. Solve- log and ln • 1.) • 2.) • 3.) • 4.) • 5.) • 6.) • 7.) • 8.) • 9.)

  24. Properties: expand • 1.) • 2.) • 3.)

  25. Properties: condense • 1.) • 2.) • 3.)

  26. Word problems- interpret variablesCompoundedContinuousPopulation

  27. Word Problems • 1.) If $3000 is invested at 3.5% interest compounded quarterly, what is the value after 10 years? • 2.) If $9500 is invested at 5% interest compounded daily, what is the value after 7 years? • 3.) Problem # 2 compounded continuously.

  28. Word Problems (2) • 4.) You invest $2500 in an account that earns 7% interest compounded continuously. When will it double? • 5.) You invest $4550 in an account that earns 4.5% interest compounded continuously. When will it be worth $10,000? • 6.) You invest $1000 in an account that is compounded monthly. In 5 years it is worth $1475. Find the rate.

  29. Word Problems (3) • 7.) The initial amount of bees is 50. They grow at a rate of 10% a day compounded continuously. Find the number of bees in 20 days. • 8.) The initial amount of a mass of radium is 4.5 tons. It decays at a rate of -.5% compounded continuously. Find the amount of radium in 100 years.

  30. Convert • To degrees: • 1.) • 2.) • 3.) • To radians: • 1.) 225° • 2.)-300° • 3.) 280°

  31. Evaluate • 1.) • 2.) • 3.) • 4.) • 5.) • 6.)

  32. Given trig- find trig • 1.) If sinΘ = ¾ in quadrant II, find cotΘ • 2.) If cosΘ = -2/7 in quadrant III, find sinΘ • 3.) If cscΘ = 3 in quadrant I, find tanΘ

  33. Graph- describe the graph • 1.) y = 3cosΘ -2 • 2.) y = cos(Θ-2) • 3.) y = 3cos 2Θ -2 • 4.) y = 3cos(2Θ-2) • 1.) • 2.) • 3.)

  34. Simplify • 1.) • 2.) • 3.)

  35. Solve • 1.) • 2.) • 3.) • 4.)

  36. Law of Sines • 1.) • 2.) • 3.)

  37. Law of Cosines • 1.)a = 3, b = 5, c = 7, angle A = ? • 2.) a = 4, b = 8, c = 11, angle B = ? • 3.) a = 2, b=7, c = 8, angle B = ?

  38. Find the limit • 1.) • 2.) • 3.)

  39. Find the limit • 1.) • 2.) • 3.)

  40. Find the limit • 1.) • 2.) • 3.) • 4.) Do # 1-3 as x approaches -∞

  41. Find the Limit at x=3+, 3- , 3

  42. Find the Limit at x=0+, 0- , 0

  43. Find the limit at x = 2 2 1 2

  44. Find the limit at x =3-, 3+ -1, 0-, -2-, 5+Is the graph continuous or discontinuous at those values? f (-2)= f (3)= 4 f (-1) = 2 -2 -1 3 5 -2

  45. Where is the function discontinuous?

  46. Continuity • 1.) Define f(2) in a way that extends to be continuous at x = 2. • 2.) Define g(-4) in a way that extends to be continuous at x = -4. • 3.) Define h(1) in a way that extends to be continuous at x = 1.

  47. Find the domain and range • 1.) • 2.) • 3.) • 4.)

  48. Find the domain and range

  49. Write the equation of the piecewise function

  50. Combinations • 1.) From a group of 10 men and 12 women, how many committees of 5 men and 5 women be formed? • 2.) From a group of 14 men and 8 women, how many committees of 5 men and 6 women be formed? • 3.) From a group of 12 men and 15 women, how many committees of 6 men and 4 women be formed?

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