Free Printable Diagnostic Quiz for Calculus 1

1.

Determine if the following is a function.

$y=x^2+1$

a)

Function

b)

Not a function

2.

Determine if the following is a function.

$y^2=x^{ }+1$

a)

Function

b)

Not a function

3.

Given $f\left(x\right)=-x^2-13x-10$ , what is $f\left(-5\right)$ ?

a)

80

b)

- 100

c)

30

d)

-50

4.

Given $f\left(x\right)=2^{x-2}+x$ , what is $f\left(6\right)$ ?

a)

16

b)

18

c)

20

d)

22

5.

Given $f\left(x\right)=x^2-3x+6$ , what is $f\left(t+1\right)$ ?

a)

$f\left(t+1\right)=t^2+t-4$

b)

$f\left(t+1\right)=t^2-2t-3$

c)

$f\left(t+1\right)=t^2+2t-3$

d)

$f\left(t+1\right)=t^2-t+4$

6.

Find the domain of $f\left(x\right)=10x+5$ .

a)

$\left[0,\infty\right)$

b)

$\left(-\infty,\infty\right)$

c)

$\left(-\infty,0\right]$

d)

$\left(0,\infty\right)$

7.

Find the range of $h\left(x\right)=\sqrt[]{10-5x}$ .

a)

$\left(-\infty,\infty\right)$

b)

$\left(-\infty,0\right]$

c)

$\left[0,\infty\right)$

d)

$\left(-\infty,0\right)$

8.

Find the domain of $f\left(x\right)=\sqrt[]{5-8x}$ .

a)

$\left(-\infty,\frac{5}{8}\right]$

b)

$\left[0,\infty\right)$

c)

$\left[\frac{5}{8},\infty\right)$

d)

$\left(-\infty,0\right]$

9.

Find the range of $f\left(x\right)=-x^2-5x+8$ .

a)

$\left(-\infty,\infty\right)$

b)

$\left[28,\infty\right)$

c)

$\left(-\infty,33\right]$

d)

$\left(-\infty,28\right]\&\left[33,\infty\right)$

10.

Determine all the roots of $g\left(t\right)=t^2-4t+4$

a)

1 & 4

b)

2

c)

-2 & 2

d)

1 & 2

11.

Given $f\left(x\right)=2x^2-x+3$ and $g\left(x\right)=x+1$ , find $\left(f\circ g\right)\left(x\right)$ .

a)

$x^2-4x-9$

b)

$2x^2+3x+4$

c)

$2x^2-x+4$

d)

$x^2-5x+6$

12.

Given $f\left(x\right)=2x^2-x+3$ and $g\left(x\right)=x+1$ , find $\left(g\circ f\right)\left(x\right)$ .

a)

$x^2-4x-9$

b)

$2x^2+3x+4$

c)

$2x^2-x+4$

d)

$x^2-5x+6$

13.

Given $f\left(x\right)=2x^2-x+3$ and $g\left(x\right)=x+1$ , find $\left(f\circ g\right)\left(0\right)$ .

a)

2

b)

4

c)

6

d)

8

14.

Given $f\left(x\right)=3x-4$ , $g\left(x\right)=2x^2-4x$ , and $h\left(x\right)=x-10$ , find $\left(f+g+h\right)\left(x\right)$ .

a)

$x^2+6$

b)

$x^2-5x$

c)

$2x^2-14$

d)

$2x^2-x-6$

15.

Given $f\left(x\right)=3x-4$ , and $h\left(x\right)=x-10$ , find $\left(f\cdot h\right)\left(x\right)$ .

a)

$3x-34$

b)

$3x^2-34x+40$

c)

$3x-14$

d)

$3x^2-26x-40$

16.

Simplify $2^2\cdot2^4$ .

a)

32

b)

$2^8$

c)

128

d)

$2^6$

17.

Simplify $\left(3^3\right)^2$

a)

$3^9$

b)

$3^6$

c)

$3^5$

d)

54

18.

Simplify $\ln\left(x+1\right)+\ln\left(x^2\right)$ .

a)

$x^2\ln\left(x+1\right)$

b)

$\ln\left(\frac{x+1}{x^2}\right)$

c)

$\ln\left(x^2+x+1\right)$

d)

$\ln\left(x^3+x^2\right)$

19.

Simplify $\log_23+\log_2x$ .

a)

$\log_2\left(3x\right)$

b)

$\log_2\left(3+x\right)$

c)

Cannot be simplified further

d)

$\log_23^x$

20.

Given $f\left(x\right)=\frac{e^{2x}}{e^{-5x}}$ , find $f\left(0\right)$ .

a)

0

b)

e

c)

1

d)

$+\infty$

Diagnostic Quiz for Calculus 1

Total questions: 20

Worksheet time: 8mins

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