Calculus practice exam with answers

A full practice exam covering differentiation rules, tangents, extrema, limits, antiderivatives and integration techniques. Answer online and get it checked at once, or print it with or without worked answers. New exams with different numbers come with a free account.

10 questions · 56 points · about 80 minutes

1. Question 1

   4 points

   Task

   Find an antiderivative: $f(x)=3e^x-\frac{2}{x}+3\cos (x)$

   $F(x)=$ (with or without $+C$)

   Write like on a calculator: 3x^2 - 2/x, e^(2x), sqrt(x), ln(x), sin(x). Use brackets: e^(2x), not e^2x. Numbers also as 3/4 or e^2 - 1.

   Check Hint

2. Question 2

   8 points

   Task

   Find an antiderivative: $f(x)=e^{3x+4}$

   $F(x)=$ (with or without $+C$)

   Write like on a calculator: 3x^2 - 2/x, e^(2x), sqrt(x), ln(x), sin(x). Use brackets: e^(2x), not e^2x. Numbers also as 3/4 or e^2 - 1.

   Check Hint

3. Question 3

   6 points

   Task

   Find the extrema of $f(x)=-x^3+9x^2-24x+2$.

   $x$ of the maximum

   $x$ of the minimum

   Write like on a calculator: 3x^2 - 2/x, e^(2x), sqrt(x), ln(x), sin(x). Use brackets: e^(2x), not e^2x. Numbers also as 3/4 or e^2 - 1.

   Check Hint

4. Question 4

   4 points

   Task

   Evaluate ${\int }_{-1}^1\left(9x^2-4x-3\right)dx$

   Value of the integral

   Write like on a calculator: 3x^2 - 2/x, e^(2x), sqrt(x), ln(x), sin(x). Use brackets: e^(2x), not e^2x. Numbers also as 3/4 or e^2 - 1.

   Check Hint

5. Question 5

   8 points

   Task

   Find an antiderivative: $f(x)=x{e}^x$

   $F(x)=$ (with or without $+C$)

   Write like on a calculator: 3x^2 - 2/x, e^(2x), sqrt(x), ln(x), sin(x). Use brackets: e^(2x), not e^2x. Numbers also as 3/4 or e^2 - 1.

   Check Hint

6. Question 6

   6 points

   Task

   Find the tangent to $f(x)=x^3+3x^2+3x-1$ at $x_0=-1$ in the form $t(x)=mx+b$.

   Slope $m$

   Intercept $b$

   Write like on a calculator: 3x^2 - 2/x, e^(2x), sqrt(x), ln(x), sin(x). Use brackets: e^(2x), not e^2x. Numbers also as 3/4 or e^2 - 1.

   Check Hint

7. Question 7

   6 points

   Task

   Differentiate: $f(x)=\ln (3x^2+5)$

   $f^{\prime }(x)=$

   Write like on a calculator: 3x^2 - 2/x, e^(2x), sqrt(x), ln(x), sin(x). Use brackets: e^(2x), not e^2x. Numbers also as 3/4 or e^2 - 1.

   Check Hint

8. Question 8

   4 points

   Task

   Differentiate: $f(x)=-3x^5-3x^2+x-2$

   $f^{\prime }(x)=$

   Write like on a calculator: 3x^2 - 2/x, e^(2x), sqrt(x), ln(x), sin(x). Use brackets: e^(2x), not e^2x. Numbers also as 3/4 or e^2 - 1.

   Check Hint

9. Question 9

   4 points

   Task

   Differentiate: $f(x)=5e^x-\ln (x)+5\sin (x)$

   $f^{\prime }(x)=$

   Write like on a calculator: 3x^2 - 2/x, e^(2x), sqrt(x), ln(x), sin(x). Use brackets: e^(2x), not e^2x. Numbers also as 3/4 or e^2 - 1.

   Check Hint

10. Question 10

    6 points

    Task

    Differentiate: $f(x)=3x\sin (x)$

    $f^{\prime }(x)=$

    Write like on a calculator: 3x^2 - 2/x, e^(2x), sqrt(x), ln(x), sin(x). Use brackets: e^(2x), not e^2x. Numbers also as 3/4 or e^2 - 1.

    Check Hint

Practice exam from cleversphere.ch, free online with answers and new questions