Free Printable AP Calc Review Unit 1-3

1.

A function is continuous if the limit to left exist and is equal to the function value.

a)

True

b)

False

2.

What is the limit? $\lim_{x\rightarrow3}\ \frac{5x+2}{2x-3}$

a)

$\frac{5}{2}$

b)

$\infty$

c)

$-\infty$

d)

$\frac{17}{3}$

e)

$-\frac{2}{3}$

3.

What is the limit ? $\lim_{x\rightarrow6}\ \frac{x^2-36}{6}$

a)

$\infty$

b)

12

c)

DNE

d)

6

4.

Find the limit as x approaches -3

a)

0

b)

DNE

c)

-6

d)

1

e)

$\infty$

5.

Find $\lim_{x\rightarrow2^+}\ f\left(x\right)$

(a)

6.

Find $\lim_{x\rightarrow1^-}\ f\left(x\right)$

(a)

7.

What is the limit? $\lim_{x\rightarrow3}\ \frac{\sqrt{x+1}-2}{x-3}$

(a)

8.

What is the domain of $y=-\frac{3}{x+3}-2$ ?

a)

$x\ \ne-3$

b)

$x\ne-2$

c)

$y\ne-2$

d)

$y\ \ne-3$

9.

What are the Vertical Asymptotes? $\frac{-3\left(x-2\right)\left(x+7\right)}{x^2+5x}$

a)

x = -2, 7

b)

x = 0, 5

c)

x = 2, -7

d)

x = 0, -5

10.

What is the hole? $y=\frac{x^2-25}{x^2-x-20}$

(a)

11.

What asymptote(s) are determined by looking at the denominator?

a)

Vertical

b)

Slant

c)

Horizontal

d)

None

12.

What is the horizontal asymptote(s)? $f\left(x\right)\frac{x-2}{2x+1}$

(a)

13.

When finding the horizontal asymptotes of a function, you should be thinking of...............

a)

“Set Bottom = to Zero”

b)

”f(0)”

c)

“Top = 0”

d)

“ Look at the degree of the top and bottom”

14.

What is the definition of an ASYMPTOTE?

a)

A curved line.

b)

A line that only lives on the first quadrant.

c)

A lone that only touches the origin.

d)

A line that a curve approaches, as it heads toward infinity.

15.

Whic is the equation of vertical asymptote in written form:

a)

x =

b)

y =

c)

None of the above

16.

The holes of a rational function occur when:

a)

My pencil pokes a hole in my math work because I’m done.

b)

The value of f(0).

c)

A factor in the denominator cancels with a factor in the numerator.

d)

There is something left in the denominator.

17.

What is the value of f(a) of the $f\left(x\right)\ =\ 2\ +\ x\ -x^{2\ }given\ \lfloor0,\ 3\rfloor?$

(a)

18.

What is the difference between IVT and MVT?

a)

MVT guarantees a point where the function has a certain value between two given values. ... IVT guarantees a point where the derivative has a certain value.

b)

IVT guarantees a point where the function has a certain value between two given values. ... MVT guarantees a point where the derivative has a certain value.

19.

The derivative of a function is its

a)

Instantaneous ROC

b)

Slant

c)

Slope

d)

function with a chord

20.

$\lim_{h\rightarrow0}\left(\frac{5\left(x+h\right)^2-5x^2}{h}\right)$

(a)

21.

Derivative means the same thing as

a)

Exponent

b)

Slope of secant line

c)

Slope of a normal line

d)

Slope of a tangent line

22.

Check all the boxes that are a correct notation for a derivative.

a)

$y^’$

b)

$\frac{\text{d}x}{\text{d}y}$

c)

$\frac{\text{d}y}{\text{d}x}$

d)

$f’\left(x\right)$

23.

The (a) is a line that touches the function at a given point and has a slope that is equal to the instantaneous rate of change at a given point.

24.

Find the slope of $y\ =\ 3x^2-5$ using the point x = 2.

a)

10

b)

12

c)

11

d)

13

25.

Use the definition of the derivative to find the derivative of with f(x) respect to x. f(x)=3x+1. Be able to show your work.

(a)

26.

$f\left(x\right)=\frac{3}{5x}$ Use the definition of the derivative to find the derivative of with f(x) respect to x. . Be able to show your work.

a)

$\frac{3}{5x^2}$

b)

$\frac{5}{3}x$

c)

$-\frac{3}{5x^2}$

d)

$\frac{3}{5}x$

AP Calc Review Unit 1-3

Total questions: 26

Worksheet time: 36mins

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