Free Printable AB Calculus Exam Review #2

1.

The graph of $f\ ',$ the derivative of the function f, is shown. For what values of x is the graph of f concave up?

a)

$b<x<d$

b)

$a<x<0$ and $x>d$

c)

$b<x<c$ and $x>e$

d)

$a<x<b$ and $c<x<e$

2.

The graph of the function f is shown. Which of the following statements about f is not true?

a)

$\lim_{x\rightarrow a}f\left(x\right)=3$

b)

$f\left(a\right)=4$

c)

$\lim_{x\rightarrow b}f\left(x\right)=1$

d)

$f\left(b\right)=2$

3.

The graph of $f\ '$ is shown. Which of the following statements is not true about f ?

a)

f is decreasing for $-3\le x\le1.$

b)

f is increasing for $-4\le x\le-1$ and $2\le x\le4.$

c)

f has a local minimum at x = 2.

d)

f has a local maximum at x = -1.

4.

The shaded regions A, B, and C in the figure are bounded by the graph $y=f\left(x\right)$ and the x-axis. If the area of region A is 4, region B is 3, and region C is 2, what is the value of $\int_{-3}^4\left[f\left(x\right)+2\right]dx?$

a)

8

b)

9

c)

11

d)

13

5.

If $F'\left(x\right)=f\left(x\right)$ for all real numbers x, and if k is a constant, then $\int_1^2f\left(kx\right)dx=$

a)

$\frac{F\left(2\right)-F\left(1\right)}{k}$

b)

$\frac{F\left(2k\right)-F\left(1k\right)}{k}$

c)

$F\left(2k\right)-F\left(1k\right)$

d)

$k\left[F\left(2\right)-F\left(1\right)\right]$

6.

The graph of $f\ '$ is shown. If f is a twice differentiable function which of the following statements must be true?

I. $f\left(a\right)>f\left(b\right)$

II. The graph of f has a point of inflection at $x=b.$

III. The graph of f is concave down on the interval $a<x<b.$

a)

I only

b)

II only

c)

III only

d)

II and III only

7.

The expression $\frac{1}{10}\left[\ln\left(1.1\right)+\ln\left(1.2\right)+\ln\left(1.3\right)+...+\ln\left(2\right)\right]$ is a Riemann sum approximation for

a)

$\frac{1}{10}\int_0^1\ln xdx$

b)

$\int_0^1\ln xdx$

c)

$\frac{1}{10}\int_1^2\ln xdx$

d)

$\int_1^2\ln xdx$

8.

The graph of f is shown for $0\le x\le4.$ Let L, R, and T be the left Riemann sum, right Riemann sum, and the trapezoidal sum approximation respectively, of f(x) on [0, 4] with 4 subintervals of equal length. Which of the following statements is true?

a)

$L<\int_0^4f\left(x\right)dx<T<R$

b)

$L<\int_0^4f\left(x\right)dx<R<T$

c)

$R<\int_0^4f\left(x\right)dx<L<T$

d)

$T<L<\int_0^4f\left(x\right)dx<R$

9.

The graph of $y=f\left(x\right)$ is shown. The shaded region A has area a and the shaded region B has area b. If $g\left(x\right)=f\left(x\right)+3$ what is the average value of g on the interval [-2, 4]?

a)

$\frac{a+b+3}{6}$

b)

$\frac{-a+b+3}{6}$

c)

$\frac{-a+b}{6}+3$

d)

$\frac{a+b}{6}+3$

10.

The graph of the function f is shown in the figure. If $h\left(x\right)=\int_a^xf\left(t\right)dt,$ which of the following is true?

a)

h(x) has a minimum at x = b and a maximum at x = d.

b)

h(x) has a minimum at x = a and a maximum at x = e.

c)

h(x) has a minimum at x = e and a maximum at x = c.

d)

h(x) has a minimum at x = c and a maximum at x = e.

11.

The slope field for a certain differential equation is shown. Which of the following could be a specific solution to the given differential equation?

a)

$y=2e^{-x}$

b)

$y=x+e^x$

c)

$y=x+e^{-x}$

d)

$y=x-e^x$

AB Calculus Exam Review #2

Total questions: 11

Worksheet time: 22mins

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