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Tips And Tricks For The Ap Calculus Exam

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Tips and Tricks for studying for the AP Calculus exam by an AP reader

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Tips And Tricks For The Ap Calculus Exam

  1. 1. Tips and Tricks for the AP Calculus Exam Karen Miksch TWHS
  2. 2. Ap Calculus Study Guide <ul><li>Know formulas!—Study from Barron’s, Formula Sheet, and/or flashcards </li></ul><ul><li>Calculator: know 4 functions required for the AP exam: roots, points of intersection, nderiv, fnint—be familiar with and use these features to save time on the calculator section, also when no other way to find without a calculator! </li></ul>
  3. 3. <ul><li>Study practice tests—redo problems missed! </li></ul><ul><li>Justify answers IN WORDS…be careful not to use pronouns---be specific in talking about the derivative, the second derivative, etc.(example: the grader should not have to ask slope “of what?”) Write your answers in complete sentences when justifying max/min, increasing or decreasing, concavity, points of inflection even if using number lines to help you determine your answers. </li></ul>
  4. 4. <ul><li>On multiple choice questions—omit problems for which you cannot narrow down the answer choices to three! Do not guess if you have no clue!! Skip around and do the easiest problems first to get your confidence going! Magic number—33 right for a 5, 25 right for a 4, (assuming about equal credit on the free response). </li></ul>
  5. 5. <ul><li>If you finish early, do not just sit there and do not go to sleep!! Check over your answers, go back over omitted questions. Check to be sure you looked carefully at the graph problems labeled f(x) or f’(x)! </li></ul><ul><li>Go back over old free response questions, especially the ones that were hardest for you! Look carefully at the grading rubrics to see how the work should be shown! Be neat, organized, and label each part…also label number lines with appropriate notation (y’ or y”). Don’t forget to write your dx’s and your + C’s!! Make sure decimals are rounded to the nearest thousandths place!! Show upper and lower bounds of integration! </li></ul>
  6. 6. <ul><li>Always show the integral and derivative set-ups on free-response questions—remember, you are trying to get credit for Calculus so…show the CALCULUS!! Do not leave “bald” answers---they earn 0 points!! </li></ul><ul><li>If you can’t do all the free response questions, remember to try to find a reasonable answer and use it for the rest of the parts of the question! Also—it’s better to leave one whole free response question blank than to rush through and get just a few points for each one! </li></ul>
  7. 7. <ul><li>Look out for double and triple answer questions---be sure to answer everything that is asked for, including detailed justifications. </li></ul>
  8. 8. <ul><li>For graph problems, try setting up a number line to represent first and second derivative graph information….remember that first derivative info gives inc/dec., max/min; second derivative info gives concavity and possible points of inflection (must have a change in concavity) and to find y-values of max, min, or pts. of inflection, plug critical number into the original function! </li></ul><ul><li>For tangent line problems (also called local linearization or linear approximation), be sure to check that the point is on the curve! If not, call it (x,y) and use the y-substitution of the original equation! </li></ul>
  9. 9. <ul><li>Don’t forget about vertical tangents and sharp turns in the graph as positions where the derivative is undefined! In order to qualify as a critical number, the original function must be defined there! </li></ul><ul><li>Absolute maximums and minimums can occur at critical numbers, but also at endpoints---be sure to check! </li></ul>
  10. 10. <ul><li>Related Rates—take the derivative on both sides with respect to time t. Make any variable substitutions before differentiating, substitute given numerical values for rates, etc. later. Max/Min problems—goal is to find one equation in one variable(you may need to use a substitution from a secondary equation), then set derivative = 0 and solve, be sure to verify if max or min! </li></ul>
  11. 11. <ul><li>BC—to get BC credit—know formulas for Euler’s method, improper integrals, special forms for L’Hopital’s Rule, logistic growth, partial fractions, integration by parts, convergence tests for sequences and series (study chart!!), parametric, polars, and vectors, plus how to graph slope fields and particular solutions for differential equations. Don’t skip a lot of these problems if you want BC credit—but again, if you have no clue—do skip! Study worked free response questions that you have done through the year. </li></ul>
  12. 12. <ul><li>Get a good night’s sleep before the test, and eat a good breakfast! Don’t panic during the test, just take deep breaths and start writing stuff you know about a problem to refresh your memory. </li></ul><ul><li>Order the free response questions easy, medium, hard and do them in that order to jump-start your confidence. </li></ul>
  13. 13. <ul><li>You’ve worked really hard all year long, and now it’s SHOW-OFF TIME!! </li></ul><ul><li>GOOD LUCK!! </li></ul>

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