1. AP CALCULUS AB PRACTICE EXAM

2. 1)Multiply by clever form of 1 3 and 1/3

3. 2) Factor First then use direct substitution

4. 3)Sub in 2 set equal to each other: (2) 2 – 3(2) + 9 = 2k + 1 7 = 2k + 1 6 = 2k 3 = k

5. 4) Chain Rule: Peel the onion

6. 5) F’ sign chart look for where it changes from – to +

7. 6)Chain rule Then sub in 1

8. 7)Multiply and divide by 2 & 1/2 – u-substitution

9. 8) LRAM = 2 (4 + k + 8) = 2 (12 + k) RRAM = 2(12 + 8 + k) = 2(20 + k) (24 + 2k + 40 + 2k)/2 = 52 64 + 4k = 104

10. Work backwards 9)

11. 10) Horizontal asymptote y = 3 a = 3 since debrees are the same Vertical asymptote x = 2 How will x 2 + b give you an answer of 2

12. 11)Quotient Rule Sub in x = 1 right away- don’t simplify first

13. 12) Work backwards antiderive

14. 13) Foil First- then anitderive

15. 14) on 2012 exam Just use the formal definition of derivative

16. 15) Think about what graph the slope field would make

17. 16) f’(x) is defined for all real numbers so f(x) must be continuous, thus eliminating d Also f’(x) is always going to positive so f must be always increasing- only choice E

18. 17)Set equations equal to each other x – 2x 2 = -5x 2x 2 – 6x = 0 2x(x – 3) x = 0, x = 3 Top curve- bottom curve

19. 18) f’(1) = 2(1) + 1 = 3 y – 4 = 3(x – 1) Y = 3x +1 Y= 3(1.2) + 1 Y = 3.6 + 1 = 4.6

20. 19) f’(x) = 3x 2 -12 F’’(x) = 6x -12 6x – 12 = 0 X = 2 Set up chart

21. 20)g’(x) = 2x – 3

22. 21) x – 2 = 20 x = 22

23. 22) set up chart

24. SECTION 1 PART B

25. 76)A particle moves along the x-axis so that any time t > 0 its velocity is given by v(t) = t 2 ln(t + 2). What is the acceleration of the particle at time t = 6? Could do by hand or use calculator: A(t) = v’(t) Calculator: Enter v(t) on calculator Use dy/dx key and evaluate at x = 6 By Hand: A(t) = 2t ln (t + 2) + t 2 ( 1 ) t + 2 Evaluate a(6)

26. 77) If and then

27. 78) Derivative is the RATE of change in the temperature

28. 79) The rate of change in the water is given by the equation Y = 9sin(√(x + 1) Enter into calculator and evaluate the integral from 0 min to 6 min. Get 45.031019 Subtract from 81.637

29. 80)Since graph is increasing from left to right, Left Sum is an underestimates. Trapezoidal underestimates when graph is concave down. (overestimate when graph is concave up) Show graph

30. 81) The first derivative of the function f is given by How many points of inflection does the graph of f have on the interval 0 < x < 2pi ? Graph on calculator setting window from 0 to 2pi and find how many times it crosses the x-axis (Where it is equal to 0) Note: Could also look at the graph of the first derivative and see how many mins and maxs there are

31. 82) Think of a horizontal line or a cubic curve Only c is true has greater than or equal to D) is what Theorem? E) is what theorem

32. 83) x2.52.83.03.1 f(x)31.2539.204548.05 Find the rate of change between 2.8 and 3 (45 – 39.2)/(3 – 2.8) = 29 Find the rate of change between 3 and 3.1 (48.05-45)/(3.1-3.0) = 30.5 The only value it could be is 30 between those two.

33. 84) Where the first derivative is negative (below the x-axis) is where the graph can be decreasing Answer E Where is the graph increasing?

34. 85) Skip Didn’t do cross perpendicular sections 86 & 87 Use table

35. 88)The rate at which water is sprayed on a field of vegetables is given by where t is in minutes and R(t) is in gallons per minute. During the time interval 0 < t < 4, what is the average rate of water flow, in gallons per minute? Average Value: Set up and solve using your calculator

36. 89) h(x) = (2f(x) + 3)(1 + g(x)) Hint: FOIL, Derive, and then substitute h(x) =2f(x) + 2f(x)g(x) + 3 + 3g(x) H’(x) = 2f’(x) + 2f’(x)g(x) +2f(x)g’(x) + 0 + 3g’(x) H’(1) = 2(-2) + 2(-2)(-3) + 2(3)(4) + 3(4)

37. 90) f & g are ____Inverse_______ functions Set up a table- slopes are reciprocals (not opposite reciprocals)

38. 91) A particle moves along the x-axis so that its velocity at any time t > 0 is given by. At t = 0, the particle is at position x = 1. What is the total distance traveled by the particle from t = 0 to t = 4? Take the absolute value and integrate from 0 to 4

39. 92) Calculator method Enter y = sin(x 3 ) in y = screen and use zero key Make sure do left and right bound between 0 and 2 OR Use solver key