5 Steps to a 5 AP Calculus AB 2019 - William Ma

MA 3972-MA-Book April 11, 2018 12:11

20 STEP 2. Determine Your Test Readiness

3.1 Getting Started!

Taking the Diagnostic Test helps you assess your strengths and weaknesses as you begin

preparing for the AP Calculus AB exam. The questions in the Diagnostic Test contain both

multiple-choice and open-ended questions. They are arranged by topic and designed to

review concepts tested on the AP Calculus AB exam. All questions in the Diagnostic Test

should be done without the use of a graphing calculator, except in a few cases where you

need to find the numerical value of a logarithmic or exponential function.

3.2 Diagnostic Test

Chapter 5

1. Write an equation of a line passing through
   the origin and perpendicular to the line
   5 x− 2 y=10.


2. Solve the inequality 3| 2 x− 4 |>6 graphically.
   Write the solution in interval notation.


3. Givenf(x)=x^2 +1, evaluate
   f(3+h)−f(3)
   h

.

4. Solve forx:4lnx− 2 =6.


5. Given f(x)=x^3 −8 andg(x)= 2 x−2, find
   f(g(2)).

Chapter 6

6. A functionf is continuous on [−2, 0], and
   some of the values off are shown below.

x − 2 − 10

f 4 b 4

If f(x)=2 has no solution on [−2, 0], then

bcould be

(A) 3

(B) 2

(C) 0

(D)− 2

7. Evaluate limx→−∞

√

x^2 − 4

2 x

.

8. If

h(x)=

{√

x ifx> 4

x^2 − 12 ifx≤ 4

find limx→ 4 h(x).

9. If f(x)=| 2 xex|, what is the value of
   xlim→ 0 + f′(x)?

Chapter 7

10. Evaluate limx→π
    ex−eπ
    xe−πe

.

11. Given the equationy=(x+1)(x−3)^2 , what is
    the instantaneous rate of change ofyatx=−1?


12. What is lim
    Δx→ 0

tan

(

π

4

+Δx

)

−tan

(

π

4

)

Δx

?

Chapter 8

13. The graph of fis shown in the figure below.
    Draw a possible graph of f′on (a,b).

ac 0 de fbx

f

y