Free Printable 2nd Summative Exam Basic Calculus

1.

What is the derivative of xⁿ?

a)

(n-1)xⁿ

b)

nxⁿ⁺¹

c)

(n+1)x^n-1

d)

nx^n-1

2.

What is the derivative of f(x)= cx?

a)

c

b)

x

c)

1

d)

0

3.

Differentiate y= x³ + 2x

a)

3x³+2x

b)

3x²+2

c)

3x+2

d)

3x

4.

find

a)

y = 2 x^-1

b)

y=2 x^-2

c)

y= −2x^-2

d)

y= −2 x^-1

5.

Find the second derivative of the given equation

f(x) = x⁴ + 4x³- 2x²

a)

12x² + 24x²+ 4

b)

12x² + 24x- 4

c)

4x + 12x - 4x

d)

4x³ + 12x²- 4x

6.

Find the derivative of the given equation
f(x) = 1 - x²

a)

1 - 2x

b)

-2x

c)

-2

d)

-1

7.

How many derivatives can you take of a function?

a)

only 3

b)

only 2

c)

only 1

d)

until you can no longer derive it

8.

Find the third derivative of the given equation

f(x) = x³ + x² + 3

a)

0

b)

6x + 1

c)

3x² + 2x

d)

6

9.

Find the second derivative of the function:
f (x) = 2x - 5x⁶

a)

f ''(x)= 2 - 30x

b)

f ''(x) = 2-30x⁵

c)

f ''(x) = -30x⁵

d)

f ''(x) = -150x⁴

10.

Set up the derivative of y=(3x⁴- 7)*(5x²+ 1)

a)

(12x³)*(10x)

b)

(3x⁴ - 7)*(10x) + (12x³)*(5x² + 1)

c)

(3x⁴ - 7)*(10x) - (12x³)*(5x² + 1)

d)

(3x⁴ - 7)/(10x) + (12x³)/(5x² + 1)

11.

If the position function for a particle is s(t) = -t² - t, what is the instantaneous velocity function for the particle?

a)

v(t) = -2

b)

v(t) = -2t - 1

c)

v(t) = t³

d)

v(t) = -t

12.

Find the derivative
f(t) = (t² + 2t)⁵

a)

f'(t) = 5(2t+2)⁴

b)

f'(t) = 5(t² + 2t)⁴

c)

f'(t) = 5(t² + 2t)⁴(2t)

d)

f'(t) = 5(t² + 2t)⁴(2t + 2)

13.

Find the derivative of f(x) = 6x³⁰-2x¹⁵ + 4x³ - 2x + 1

a)

f'(x) = 18x²⁹+ 30x¹⁵ + 12x³

b)

f'(x) = 180x²⁹ - 30x¹⁴+ 12x²

c)

f'(x) = 180x²⁹ - 30x¹⁴+ 12x² - 2

d)

f'(x) = 180x²⁹ - 30x¹⁴+ 12x² +1

14.

Which of the following is the quotient rule for derivatives?

a)

h^'(x)=((g(x)f^'(x) + f(x)g^'(x)) / (g(x))²

b)

h^'(x)=((g^'(x)f^'(x) - f(x)g(x)) / (g(x))

c)

h^'(x)=((g(x)f^'(x) - f(x)g^'(x)) / (g(x))²

d)

h^'(x)=((g^'(x)f^'(x) + f(x)g(x)) / (g(x))

15.

What rule should be used in deriving h(x) = 2(x - 4)³

a)

Power rule

b)

Product rule

c)

Quotient rule

d)

Chain rule

16.

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

a)

$\frac{3}{2x}$

b)

$\frac{3\left(x^2+2\right)}{\left(x^2+2\right)^2}$

c)

$\frac{-3x^2+4x+6}{\left(x^2+2\right)^2}$

d)

$\frac{9x^2-4x+6}{\left(x^2+2\right)^2}$

17.

Which of the following is the product rule for derivatives utilizing the original function h(x) = f(x)g(x) ?

a)

h^'(x)= f^'(x)g^'(x)

b)

h^'(x)=f^'(x)g^'(x) + f(x)g(x)

c)

h^'(x)=f^'(x)g(x) - f(x)g^'(x)

d)

h^'(x)=f^'(x)g(x) + f(x)g^'(x)

18.

Which of the following is the derivative of the function h(x)= (8x⁶ + 2x + 5)^{4 ?}

a)

h^'(x)= 4(8x⁶ + 2x + 5)³(48x⁵ + 2)

b)

h^'(x)= 4(48x⁵ + 2)³

c)

h^'(x)= 4(48x⁵ + 2 + 5)³

d)

h^'(x)= 3(8x⁶ + 2x + 5)⁴(48x⁵ + 2)²

19.

Find the derivative of the given equation
f(x) = $\frac{1}{x^2}$ Hint: rewrite with a negative exponent

a)

f'(x) = 1/2x

b)

f'(x) = -2x^-3

c)

f'(x) = 2x

d)

f'(x) = -2x

20.

Find dy/dx for y = 4x³+ 3x + 1

a)

dy/dx = 4x² + 3

b)

dy/dx = 4x² + 3x

c)

dy/dx = 12x² + 3x

d)

dy/dx = 12x² + 3

21.

f'(x)=

a)

$\lim_{h\rightarrow0}\left(\frac{f\left(x+h\right)-f\left(x\right)}{h}\right)$

b)

the derivative of a function

c)

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

22.

a)

b)

c)

d)

23.

This is NOT a correct notation for a derivative

a)

y ' (say it as "y prime")

b)

f '(x) (say it as "f prime of x")

c)

dy/dx

d)

dx/dy

24.

Which option is using correctly the quotient rule?

a)

b)

c)

d)

25.

What is differentiation?

a)

The process of finding the derivative of a function.

b)

The process of finding the integral of a function.

c)

The process of finding the difference of a function.

d)

The process of finding the sum of a function.

26.

What is the derivative of $y=\left(3x^{ }-7\right)\left(5x^2+1\right)?$

a)

$y'=30x$

b)

$y'=45x^2-70x+3$

c)

$y'=-15x^2+70x+3$

d)

$y'=45x^2-67x-4$

27.

Which of the following is the correct definition of the Power Rule of derivatives?

a)

Given $f\left(x\right)=x^n$ , $f'\left(x\right)=x^{n-1}$

b)

Given $f\left(x\right)=x^n$ , $f'\left(x\right)=nx^{n-1}$

c)

Given $f\left(x\right)=x^n$ , $f'\left(x\right)=\frac{x^{n-1}}{n}$

d)

Given $f\left(x\right)=x^n$ , $f'\left(x\right)=\frac{n}{x^{n-1}}$

28.

Given $f\left(x\right)=3x$ , which of the following is the derivative of the function?

a)

$h'\left(x\right)=3$

b)

$q'\left(x\right)=3$

c)

$b'\left(x\right)=3$

d)

$f'\left(x\right)=3$

29.

a)

8x⁴ -60x²

b)

16x⁴

c)

(8x⁴ -60x²)/(2x²-5)²

d)

3x

30.

$\frac{\text{d}}{\text{d}x}\left[f\left(x\right)g\left(x\right)\right]$

a)

$f'\left(x\right)g'\left(x\right)$

b)

$f'\left(x\right)g\left(x\right)+g'\left(x\right)f\left(x\right)$

c)

$f'\left(x\right)g\left(x\right)g'\left(x\right)$

d)

$f'\left(x\right)g\left(x\right)-g'\left(x\right)f\left(x\right)$

2nd Summative Exam Basic Calculus

Total questions: 30

Worksheet time: 53mins

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