Free Printable Honors Calc Midterm Review

1.

What rule should be used in deriving f(x) = x⁵

a)

Constant rule

b)

Sum rule

c)

Power rule

d)

Difference rule

2.

What is the derivative of f(x) = 2x³- 4x + 5?

a)

f'(x) = 6x² - 4x

b)

f'(x) = 2/3x² - 4x

c)

f'(x) = 3x² - 4

d)

f'(x) = 6x² - 4

3.

Which function has the derivative of g'(x) = 4x³ + 2x - 1

a)

g(x) = 2x⁴ + 2x² - 1

b)

g(x) = x⁴ + x² - x

c)

g(x) = 2x³ + x³ - 2x

d)

g(x) = x⁵ + x² - x

4.

Find the derivative f(x) = xe^x

a)

f'(x) = e^x

b)

f'(x) = xe^x + xe^x

c)

f'(x) = e^x - xe^x

d)

f'(x) = e^x + xe^x

5.

Find the derivative f(x) = x²/e^x

a)

f'(x) = (x²e^x - 2xe^x) / (e^x)²

b)

f'(x) = (2xe^x + x²e^x) / (e^x)²

c)

f'(x) = (2xe^x - x²e^x) / (e^x)²

d)

f'(x) = x²e^x + 2xe^x

6.

Find the derivative.

a)

x⁴cosx - 4x³sinx

b)

x⁴cosx + 4x³sinx

c)

4x³cosx

d)

-4x³cosx

7.

When do we use the product rule to find the derivative?

a)

When we multiply two or more functions

b)

When we divide two or more functions

c)

When we add two or more functions

d)

When we subtract two or more functions

8.

When do we use the quotient rule to find the derivative?

a)

When we multiply two functions

b)

When we divide two functions

c)

When we add two functions

d)

When we subtract two functions

9.

Evaluate $\frac{\text{d}}{\text{d}x}\left[2^x\right]$

a)

$2^x$

b)

$\left(\ln2\right)2^x$

c)

$\left(\ln2\right)e^x$

d)

$2\times2^x$

10.

Evaluate $\frac{\text{d}}{\text{d}x}\left[\log_2x\right]$

a)

$\frac{2}{x}$

b)

$\frac{1}{2x}$

c)

$\frac{1}{\left(\ln2\right)x}$

d)

$\frac{1}{\log_2x}$

11.

Which if the following is not a correct notation for 'derivative?'

a)

f'(x)

b)

y'

c)

dy

d)

dy/dx

12.

What is the derivative of cos(x)?

a)

sin(x)

b)

cos(x)

c)

-sin(x)

d)

-cos(x)

13.

Differentiate f(x) =(2/ x⁵) - 5.

a)

x⁵-3

b)

-10x⁶

c)

x⁵-5

d)

-10/x⁶

14.

What is the derivative of sec(x)?

a)

sec(x)tan(x)

b)

csc(x)cot(x)

c)

-sec(x)tan(x)

d)

-csc(x)cot(x)

15.

What is the derivative of cot(x)?

a)

sec²(x)

b)

-sec²(x)

c)

csc²(x)

d)

-csc²(x)

16.

What is the derivative of csc(x)?

a)

csc(x)cot(x)

b)

-csc(x)cot(x)

c)

-csc²(x)

d)

-cot²(x)

17.

Find the derivative of
$f\left(x\right)=-\frac{2}{3}x^3-\frac{1}{2}x^2+9x$

a)

$-2x^2-x+9$

b)

$-2x^3-x^2+9x$

c)

$-\frac{2}{12}x^4-\frac{1}{6}x^3+\frac{9}{\ 2}x^2$

d)

$-2x^4-x^3+9x^2$

18.

Which of the following is the derivative of $y=\left(3x^4-7\right)\left(5x^2+1\right)$

a)

$\left(12x^3\right)\left(10x\right)$

b)

$\left(3x^4-7\right)\left(10x\right)+\left(12x^3\right)\left(5x^2+1\right)$

c)

$\left(3x^4-7\right)\left(10x\right)-\left(12x^3\right)\left(5x^2+1\right)$

d)

$\frac{3x^4-7}{10x}+\frac{12x^3}{5x^2+1}$

19.

y=x
y'=

a)

x

b)

1

c)

-1

d)

0

20.

When we "take the derivative" of a function what are we finding?

a)

What's a derivative?

b)

The rate at which our struggles in Calculus are increasing.

c)

The slope of the secant line

d)

The slope of the tangent line

21.

What is the derivative of ax?

a)

a

b)

x

c)

1

d)

0

22.

What is the derivative of a constant, C?

a)

C

b)

1

c)

0

23.

a)

b)

c)

d)

24.

a)

b)

c)

d)

25.

Use the table data and the rules of differentiation to solve each problem.
If $h\left(x\right)=f\left(x\right)+g\left(x\right)$ Find $h'\left(2\right)$

a)

$\frac{3}{2}$

b)

$\frac{-3}{2}$

c)

$\frac{-1}{2}$

d)

1

26.

The derivative of ln(x) is:

a)

x

b)

1/x

c)

1/(x ln(x))

d)

e^x

27.

Find f ' ( $\frac{\pi}{2}$ ), given f(x) = cos(x)

a)

1

b)

90

c)

0

d)

-1

28.

Find y ' given

y=3^x\sin\left(x\right)

a)

$3^x\cos\left(x\right)$

b)

$3^x\ln\left(3\right)\cos\left(x\right)$

c)

$3^x\ln\left(3\right)\sin\left(x\right)+3^x\cos\left(x\right)$

d)

$3^x\sin\left(x\right)+3^x\cos\left(x\right)$

29.

Find y' given $y=11e^x$

a)

$11\ln\left(x\right)$

b)

$11e^x$

c)

$11e^x\ln\left(11\right)$

d)

$\frac{1}{x\ln\left(11\right)}$

30.

Find the derivative of the given equation
f(x) = 7

a)

7

b)

0

c)

7x

d)

14

31.

What is the derivative of xⁿ?

a)

(n-1)xⁿ

b)

nxⁿ⁺¹

c)

(n+1)x^n-1

d)

nx^n-1

32.

Find f '(2) if
f(x) = x² + 2x

a)

2x + 2

b)

6

c)

12

d)

2x

33.

Name the discontinuity at x=2.

a)

Infinite Discontinuity

b)

Removable Discontinuity

c)

Jump Discontinuity

d)

Continuous at x=2

34.

Name the discontinuity at x=2.

a)

Infinite Discontinuity

b)

Removable Discontinuity

c)

Jump Discontinuity

d)

Continuous at x=2

35.

What are the three types of nonremovable discontinuities?

a)

Infinite

b)

Hole

c)

Oscillating

d)

Jump

36.

A polynomial function is continuous to all real numbers.

a)

TRUE

b)

FALSE

37.

Which of the following graphs presents jump discontinuity at x = 1?

a)

b)

c)

d)

38.

Which of the following graphs presents a removable/hole discontinuity at x = -2?

a)

b)

c)

d)

39.

This function has discontinuities at the value(s) x=

a)

2

b)

-4

c)

4

d)

-1

40.

A vertical asymptote of a function is also known as a(n) _________ discontinuity.

a)

Jump

b)

Infinite

c)

removable

d)

oscillating

41.

What is the limit?

a)

DNE

b)

Infinity

c)

6

d)

12

42.

What is the limit?

a)

Infinity

b)

20

c)

DNE

d)

12

43.

a)

0

b)

-1

c)

infinity

d)

-infinity

44.

$\lim_{x\rightarrow\infty}\ \frac{2x-3}{4x\ +1}$

a)

0

b)

DNE

c)

1/2

d)

2

45.

$\lim_{x\rightarrow\infty}\left(2x^3+3x-1\right)=$
Hint: Think of the end behavior

a)

$\infty$

b)

$-\infty$

c)

2

d)

2/3

46.

Find the limit

a)

⁶/₅

b)

0

c)

$\infty$

d)

$-\infty$

47.

$\lim_{x\rightarrow\infty}\ \frac{x^3-x^2+1}{5-3x-x^4}=...$

a)

0

b)

-1

c)

-5

d)

$\infty$

e)

$-\infty$

48.

$\lim_{x\rightarrow\infty}\ \frac{1-2x+2x^3}{x^3+x+1}=\ ...$

a)

- 4

b)

- 2

c)

1

d)

2

e)

$\infty$

49.

$\lim_{x\rightarrow\infty}\ \frac{x+7}{\sqrt{4x^2+3x}}=...$

a)

$-\infty$

b)

$\infty$

c)

$\frac{1}{2}$

d)

0

e)

$-\frac{1}{2}$

50.

Evaluate the limit.

a)

$\infty$

b)

$-\infty$

c)

11

d)

DNE

51.

What is the limit as -2 from the left?

a)

$\infty$

b)

$-\infty$

c)

0

d)

$-\frac{1}{4}$

52.

lim_x→2f(x)=

a)

3

b)

2

c)

0

d)

1.7

53.

lim_x→0f(x)=

a)

1.5

b)

-3

c)

0

d)

dne

54.

lim_x→1f(x)=

a)

1

b)

2

c)

0

d)

-1

55.

lim_{x→ 3}f(x)=

a)

1

b)

0

c)

not possible (hole)

d)

dne

56.

lim_x→6⁺f(x)=

a)

0

b)

-4

c)

Not enough information given

d)

dne

57.

lim_x→6-f(x)=

a)

0

b)

-4

c)

Not enough information given

d)

dne

58.

lim_x→0-f(x)=

a)

No answer (there is a hole)

b)

-3

c)

1.5

d)

dne

59.

lim_x→0⁺f(x)=

a)

1.5

b)

-3

c)

No answer (there is a hole)

d)

dne

60.

lim_{x→ 4}-f(x)=

a)

3

b)

−4

c)

∞

d)

dne

61.

lim_{x→ −2}f(x)=

a)

-.5

b)

∞

c)

−∞

d)

dne

62.

Find the derivative of f(x) = (x⁶ + 4)⁵

a)

f '(x) = 5x⁵(x⁴ + 4)⁴

b)

f '(x) = 6x⁵(x⁶ + 4)⁴

c)

f '(x) = 30x⁵(x⁶ + 4)⁴

d)

f '(x) = 30x⁶(x⁶ + 4)⁴

63.

find y' for y= sin(2x²)

a)

4sin(2x²)

b)

4xcos(2x²)

c)

2xcos(2x²)

d)

xcos(4x²)

64.

Find the derivative of $y=\left(2x-1\right)^3$

a)

$6\left(2x-1\right)^2$

b)

$3\left(2x-1\right)^2$

c)

$-3\left(2x-1\right)^2$

d)

$-4\left(2x-1\right)^2$

65.

Differentiate

y=3^{\left(x^2-1\right)}

a)

$x^2\left(\ln3\right)\left(3^{x^2-1}\right)$

b)

$\left(\ln3\right)\left(3^{x^2-1}\right)$

c)

$\left(2x\right)\left(3^{x^2-1}\right)$

d)

$2x\left(\ln3\right)\left(3^{x^2-1}\right)$

66.

Find the derivative:
y=11^x²

a)

y′=11^x²(2x)(ln11)

b)

y′=2x(ln11)

c)

y′=11^x²(2x)(lnx)

d)

y′=11^x²(x)(ln11)

67.

Find the derivative:
y=e^5x

a)

y'=e^5x

b)

y'=5e^5x

c)

y'=5e^x

d)

y'=(1/5)e^5x

68.

Find the derivative of

f\left(x\right)=\log_5\left(4x\ -\ 3\right)

a)

$f'\left(x\right)=\frac{4}{\left(4x-3\right)\ln5}$

b)

$f'\left(x\right)=\frac{4}{4x-3}$

c)

$f'\left(x\right)=\frac{\left(4x-3\right)}{\ln5}$

d)

$f'\left(x\right)=\frac{4}{\ln5}$

69.

Find the derivative of

f\left(x\right)=5^{\cot x}

a)

$f'\left(x\right)=5^{\cot x}\ln5$

b)

$f'\left(x\right)=\cot x\cdot5^{\cot x}\cdot\ln5$

c)

$f'\left(x\right)=\cot x\cdot5^{\cot x}$

d)

$f'\left(x\right)=-\csc^2x\cdot5^{\cot x}\cdot\ln5$

70.

If $f\left(x\right)=3x^{2\ }+2x\ ,\ then\ \ \lim_{x\rightarrow0}\ \frac{f\left(x+h\right)-f\left(x\right)}{h\ }\ is....$

a)

6x

b)

0

c)

DNE

d)

2

e)

6x+2

Honors Calc Midterm Review

Total questions: 70

Worksheet time: 24mins

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