Calculus for dummies: 1,001 calculus practice problems

Patrick Jones

Chapter 1

Algebra Review - all with Video Answers

Educators

Chapter Questions

Problem 1

Simplify the given fractions by adding, subtracting, multiplying, and/or dividing.
$\frac{1}{2}+\frac{3}{4}-\frac{5}{6}$

Ramzi Deek

Ramzi Deek

Numerade Educator

Problem 2

Simplify the given fractions by adding, subtracting, multiplying, and/or dividing.
$\frac{11}{3}+\frac{3}{5}+\frac{17}{20}$

Erika Bustos

Numerade Educator

Problem 3

Simplify the given fractions by adding, subtracting, multiplying, and/or dividing.
$\left(\frac{2}{3}\right)(21)\left(\frac{11}{14}\right)$

Zach Steedman

Numerade Educator

Problem 4

Simplify the given fractions by adding, subtracting, multiplying, and/or dividing.
$\frac{5 / 6}{15 / 22}$

Pammi Eswari

Numerade Educator

Problem 5

Simplify the given fractions by adding, subtracting, multiplying, and/or dividing.
$\frac{5}{y x}+\frac{7}{x^2}+\frac{10 x}{y}$

Alison Rodriguez

Alison Rodriguez

Numerade Educator

Problem 6

Simplify the given fractions by adding, subtracting, multiplying, and/or dividing.
$\frac{x}{x-1}-\frac{x-4}{x+1}$

Erika Bustos

Numerade Educator

Problem 7

Simplify the given fractions by adding, subtracting, multiplying, and/or dividing.
$\left(\frac{x^2-1}{x y^2}\right)\left(\frac{y^3}{x+1}\right)$

Susan Cooper

Numerade Educator

Problem 8

Simplify the given fractions by adding, subtracting, multiplying, and/or dividing.
$\frac{\frac{x^2-5 x+6}{6 x y^3}}{\frac{x^2+3 x-10}{10 x^3 y^2}}$

Cory Kuzinski

Numerade Educator

Problem 9

Simplify the given fractions by adding, subtracting, multiplying, and/or dividing.
$\frac{x^3 y^4 z^5}{y^2 z^{-8}}$

Joshua Eastwood

Joshua Eastwood

Numerade Educator

Problem 10

Simplify the given fractions by adding, subtracting, multiplying, and/or dividing.
$\frac{(x+3)^2 x^4(y+5)^{14}}{x^6(x+3)(y+5)^{17}}$

Priyanka Sadarangani

Priyanka Sadarangani

Numerade Educator

Problem 11

Simplify the given fractions by adding, subtracting, multiplying, and/or dividing.
$\left(\frac{4 x^2 y^{100} z^{-3}}{18 x^{15} y^4 z^8}\right)^0$

AG

Ankit Gupta

Numerade Educator

Problem 12

Simplify the given fractions by adding, subtracting, multiplying, and/or dividing.
$\frac{x^4 y^3 z^2+x^2 y z^4}{x^2 y z}$

Erika Bustos

Numerade Educator

Problem 13

Simplify the given fractions by adding, subtracting, multiplying, and/or dividing.
$\frac{\left(x^2 y^3\right)^4\left(y^4\right)^0 z^{-2}}{\left(x z^2\right)^3 y^{-5}}$

Check back soon!

Problem 14

Simplify the given radicals. Assume all variables are positive.
$\sqrt{50}$

AG

Ankit Gupta

Numerade Educator

Problem 15

Simplify the given radicals. Assume all variables are positive.
$\frac{\sqrt{8} \sqrt{20}}{\sqrt{50} \sqrt{12}}$

Erika Bustos

Numerade Educator

Problem 16

Simplify the given radicals. Assume all variables are positive.
$\sqrt{20 x^4 y^6 z^{11}} \sqrt{5 x y^2 z^7}$

AG

Ankit Gupta

Numerade Educator

Problem 17

Simplify the given radicals. Assume all variables are positive.
$\sqrt[3]{x^4 y^8 z^5} \sqrt[3]{x^7 y^4 z^{10}}$

AG

Ankit Gupta

Numerade Educator

Problem 18

Simplify the given radicals. Assume all variables are positive.
$\frac{\sqrt[3]{8 x^3 y^6} \sqrt[5]{x^{10} y^{14}}}{\sqrt[7]{x^{14} y^{14}}}$

Victor Salazar

Numerade Educator

Problem 19

Convert between exponential and radical notation.
Convert $4^{1 / 3} x^{3 / 8} y^{1 / 4} z^{5 / 12}$ to radical notation. (Note: The final answer can have more than one radical sign.)

Amy Jiang

Numerade Educator

Problem 20

Convert between exponential and radical notation.
Convert $\sqrt[3]{4 x^2 y} \sqrt[5]{z^4}$ to exponential notation.

AG

Ankit Gupta

Numerade Educator

Problem 21

Use the horizontal line test to identify one-toone functions.
21. Use the horizontal line test to determine which of the following functions is a one-to-one function and therefore has an inverse.
(A) $y=x^2+4 x+6$
(B) $y=|2 x|-1$
(C) $y=\frac{1}{x^2}$
(D) $y=3 x+8$
(E) $y=\sqrt{25-x^2}$

Bobby Barnes

University of North Texas

Problem 22

Use the horizontal line test to identify one-toone functions.

Use the horizontal line test to determine which of the following functions is a one-to-one function and therefore has an inverse.
(A) $y=x^2-4$
(B) $y=x^2-4, x \geq 0$
(C) $y=x^2-4,-2 \leq x \leq 8$
(D) $y=x^2-4,-12 \leq x \leq 6$
(E) $y=x^2-4,-5.3 \leq x \leq 0.1$

James Kiss

Numerade Educator

Problem 23

Use the horizontal line test to identify one-toone functions.

Use the horizontal line test to determine which of the following functions is a one-to-one function and therefore has an inverse.
(A) $y=x^4+3 x^2-7$
(B) $y=4|x|+3$
(C) $y=\cos x$
(D) $y=\sin x$
(E) $y=\tan ^{-1} x$

Charles Carter

Numerade Educator

Problem 24

Find the inverse of the one-to-one function algebraically.
$f(x)=4-5 x$

James Kiss

Numerade Educator

Problem 25

Find the inverse of the one-to-one function algebraically.
$f(x)=x^2-4 x, x \geq 2$

Nick Johnson

Numerade Educator

Problem 26

Find the inverse of the one-to-one function algebraically.
$f(x)=\sqrt{8-5 x}$

Vishal Parmar

Numerade Educator

Problem 27

Find the inverse of the one-to-one function algebraically.

$f(x)=3 x^5+7$

James Kiss

Numerade Educator

Problem 28

Find the inverse of the one-to-one function algebraically.

. $f(x)=\frac{2-\sqrt{x}}{2+\sqrt{x}}$

James Kiss

Numerade Educator

Problem 29

Find the inverse of the one-to-one function algebraically.

$f(x)=\frac{2 x-1}{x+4}$

AG

Ankit Gupta

Numerade Educator

Problem 30

Solve the given question related to a function and its inverse.
The set of points $\{(0,1),(3,4),(5,-6)\}$ is on the graph of $f(x)$, which is a one-to-one function. Which points belong to the graph of $f^{-1}(x)$ ?

Erika Bustos

Numerade Educator

Problem 31

Solve the given question related to a function and its inverse.
$f(x)$ is a one-to-one function with domain $[-2,4)$ and range $(-1,2)$. What are the domain and range of $f^{-1}(x)$ ?

Jennifer White

Numerade Educator

Problem 32

Solve the given question related to a function and its inverse.
Suppose that $f(x)$ is a one-to-one function. What is an expression for the inverse of $g(x)=f(x+c)$ ?

Victoria Dollar

Victoria Dollar

Numerade Educator

Problem 33

Solve the given linear equation.
$3 x+7=13$

Ali Soave

Numerade Educator

Problem 34

Solve the given linear equation.
. $2(x+1)=3(x+2)$

James Kiss

Numerade Educator

Problem 35

Solve the given linear equation.
$-4(x+1)-2 x=7 x+3(x-8)$

Elizabeth Xu

Numerade Educator

Problem 36

Solve the given linear equation.
$\frac{5}{3} x+5=\frac{1}{3} x+10$

AG

Ankit Gupta

Numerade Educator

Problem 37

Solve the given linear equation.
$\sqrt{2}(x+3)=\sqrt{5}(x+\sqrt{20})$

Sherrie Fenner

Numerade Educator

Problem 38

Solve the quadratic equation.
Solve $x^2-4 x-21=0$.

Jake Zanazzi

Numerade Educator

Problem 39

Solve the quadratic equation.
Solve $x^2+8 x-17=0$ by completing the square.

Jennifer Stoner

Jennifer Stoner

Numerade Educator

Problem 40

Solve the quadratic equation.

Solve $2 x^2+3 x-4=0$ by completing the square.

Nathaniel Plew

Numerade Educator

Problem 41

Solve the quadratic equation.

Solve $6 x^2+5 x-4=0$.

Check back soon!

Problem 42

Solve the quadratic equation.

Solve $3 x^2+4 x-2=0$.

AG

Ankit Gupta

Numerade Educator

Problem 43

Solve the quadratic equation.

Solve $x^{10}+7 x^5+10=0$.

Jake Zanazzi

Numerade Educator

Problem 44

Solve the polynomial equation by factoring.
$3 x^4+2 x^3-5 x^2=0$

Sherrie Fenner

Numerade Educator

Problem 45

Solve the polynomial equation by factoring.
. $x^8+12 x^4+35=0$

K H

Numerade Educator

Problem 46

Solve the polynomial equation by factoring.
$x^4+3 x^2-4=0$

Erika Bustos

Numerade Educator

Problem 47

Solve the polynomial equation by factoring.
$x^4-81=0$

Erika Bustos

Numerade Educator

Problem 48

Solve the given absolute value equation.
. $|5 x-7|=2$

Kamalesh Bagrecha

Kamalesh Bagrecha

Numerade Educator

Problem 49

Solve the given absolute value equation.
$|4 x-5|+18=13$

Kamalesh Bagrecha

Kamalesh Bagrecha

Numerade Educator

Problem 50

Solve the given absolute value equation.
$\left|x^2-6 x\right|=27$

Shamshad Waris

Numerade Educator

Problem 51

Solve the given absolute value equation.
$|15 x-5|=|35-5 x|$

Kamalesh Bagrecha

Kamalesh Bagrecha

Numerade Educator

Problem 52

Solve the given rational equation.
$\frac{x+1}{x-4}=0$

Priyanka Sadarangani

Priyanka Sadarangani

Numerade Educator

Problem 53

Solve the given rational equation.
$\frac{1}{x+2}+\frac{1}{x}=1$

Priyanka Sadarangani

Priyanka Sadarangani

Numerade Educator

Problem 54

olve the given rational equation.
$\frac{x+5}{x+2}=\frac{x-4}{x-10}$

AG

Ankit Gupta

Numerade Educator

Problem 55

Solve the given rational equation.
$\frac{1}{x-2}-\frac{2}{x-3}=\frac{-1}{x^2-5 x+6}$

Priyanka Sadarangani

Priyanka Sadarangani

Numerade Educator

Problem 56

Solve the given polynomial or rational inequality.
$x^2-4 x-32<0$

Ashley Volpe

Numerade Educator

Problem 57

Solve the given polynomial or rational inequality.
$2 x^4+2 x^3 \geq 12 x^2$

Lauren Shelton

Numerade Educator

Problem 58

Solve the given polynomial or rational inequality.
$\frac{(x+1)(x-2)}{(x+3)}<0$

Lauren Shelton

Numerade Educator

Problem 59

Solve the given polynomial or rational inequality.
$\frac{1}{x-1}+\frac{1}{x+1}>\frac{3}{4}$

James Kiss

Numerade Educator

Problem 60

Solve the absolute value inequality.
. $|2 x-1|<4$

Lucas Finney

Numerade Educator

Problem 61

Solve the absolute value inequality.
$|5 x-7|>2$

Kamalesh Bagrecha

Kamalesh Bagrecha

Numerade Educator

Problem 62

Solve the absolute value inequality.
$|-3 x+1| \leq 5$

Suman Saurav Thakur

Suman Saurav Thakur

Numerade Educator

Problem 63

Solve the given question related to graphing common functions.
What is the slope of the line that goes through the points $(1,2)$ and $(5,9)$ ?

Rishi Kavikondala

Rishi Kavikondala

Numerade Educator

Problem 64

Solve the given question related to graphing common functions.
What is the equation of the line that has a slope of 4 and goes through the point $(0,5)$ ?

Heather Zimmers

Heather Zimmers

Numerade Educator

Problem 65

Solve the given question related to graphing common functions.
What is the equation of the line that goes through the points $(-2,3)$ and $(4,8)$ ?

Natalie Anderson

Natalie Anderson

Numerade Educator

Problem 66

Solve the given question related to graphing common functions.
Find the equation of the line that goes through the point $(1,5)$ and is parallel to the line $y=\frac{3}{4} x+8$.

Heather Zimmers

Heather Zimmers

Numerade Educator

Problem 67

Solve the given question related to graphing common functions.
Find the equation of the line that goes through the point $(3,-4)$ and is perpendicular to the line that goes through the points $(3,-4)$ and $(-6,2)$.

Babita Kumari

Numerade Educator

Problem 68

Solve the given question related to graphing common functions.
What is the equation of the graph of $y=\sqrt{x}$ after you stretch it vertically by a factor of 2 , shift the graph 3 units to the right, and then shift it 4 units upward?

AG

Ankit Gupta

Numerade Educator

Problem 69

Solve the given question related to graphing common functions.
Find the vertex form of the parabola that passes through the point $(0,2)$ and has a vertex at (-2,-4).

Kirsten Bauck

Numerade Educator

Problem 70

Solve the given question related to graphing common functions.
Find the vertex form of the parabola that passes through the point $(1,2)$ and has a vertex at $(-1,6)$.

Joseph Lentino

Numerade Educator

Problem 71

Solve the given question related to graphing common functions.
A parabola has the vertex form $y=3(x+1)^2$ +4 . What is the vertex form of this parabola if it's shifted 6 units to the right and 2 units down?

Edward Downes

Numerade Educator

Problem 72

Solve the given question related to graphing common functions.
What is the equation of the graph of $y=e^x$ after you compress the graph horizontally by a factor of 2 , reflect it across the $y$-axis, and shift it down 5 units?

Harshita Goel

Numerade Educator

Problem 73

Solve the given question related to graphing common functions.
What is the equation of the graph of $y=|x|$ after you stretch the graph horizontally by a factor of 5 , reflect it across the $x$-axis, and shift it up 3 units?

Cory Kuzinski

Numerade Educator

Problem 74

Solve the given question related to graphing common functions.
Find the equation of the third-degree polynomial that goes through the points $(-4,0)$, $(-2,0),(0,3)$, and $(1,0)$.

Raj Bala

Numerade Educator

Problem 75

Solve the given question related to graphing common functions.
Find the equation of the fourth-degree polynomial that goes through the point $(1,4)$ and has the roots $-1,2$, and 3 , where 3 is a repeated root.

Varsha Aggarwal

Varsha Aggarwal

Numerade Educator

Problem 76

Solve the given question related to graphing common functions.
A parabola crosses the $x$-axis at the points $(-4,0)$ and $(6,0)$. If the point $(0,8)$ is on the parabola, what is the equation of the parabola?

Charles Carter

Numerade Educator

Problem 77

Solve the given question related to graphing common functions.
A parabola crosses the $x$-axis at the points $(-8,0)$ and $(-2,0)$, and the point $(-4,-12)$ is on the parabola. What is the equation of the parabola?

Lucas Finney

Numerade Educator

Problem 78

Find the domain and range of the function with the given graph.
Graph can't copy

Karly Williams

Numerade Educator

Problem 79

Find the domain and range of the function with the given graph.
Graph can't copy

Karly Williams

Numerade Educator

Problem 80

Find the domain and range of the function with the given graph.
Graph can't copy

Karly Williams

Numerade Educator

Problem 81

Find the end behavior of the given polynomial. That is, find $\lim _{x \rightarrow-\infty} f(x)$ and $\lim _{x \rightarrow \infty} f(x)$.
$f(x)=3 x^6-40 x^5+33$

Donald Albin

Numerade Educator

Problem 82

Find the end behavior of the given polynomial. That is, find $\lim _{x \rightarrow-\infty} f(x)$ and $\lim _{x \rightarrow \infty} f(x)$.
$f(x)=-7 x^9+33 x^8-51 x^7+19 x^4-1$

Donald Albin

Numerade Educator

Problem 83

Add the given polynomials.
$(5 x+6)+(-2 x+6)$

KT

Kristen Tumminia

Numerade Educator

Problem 84

Add the given polynomials.
$\left(2 x^2-x+7\right)+\left(-2 x^2+4 x-9\right)$

KT

Kristen Tumminia

Numerade Educator

Problem 85

Add the given polynomials.
$\left(x^3-5 x^2+6\right)+\left(4 x^2+2 x+8\right)$

Julie Silva

Numerade Educator

Problem 86

Add the given polynomials.
$\left(3 x+x^4+2\right)+\left(-3 x^4+6\right)$

KT

Kristen Tumminia

Numerade Educator

Problem 87

Add the given polynomials.
$\left(x^4-6 x^2+3\right)+\left(5 x^3+3 x^2-3\right)$

KT

Kristen Tumminia

Numerade Educator

Problem 88

Subtract the given polynomials.
$(5 x-3)-(2 x+4)$

Julie Silva

Numerade Educator

Problem 89

Subtract the given polynomials.
$\left(x^2-3 x+1\right)-\left(-5 x^2+2 x-4\right)$

Julie Silva

Numerade Educator

Problem 90

Subtract the given polynomials.
$\left(8 x^3+5 x^2-3 x+2\right)-\left(4 x^3+5 x-12\right)$

James Kiss

Numerade Educator

Problem 91

subtract the given polynomials.
$(x+3)-\left(x^2+3 x-4\right)-\left(-3 x^2-5 x+6\right)$

James Kiss

Numerade Educator

Problem 92

Subtract the given polynomials.
$\left(10 x^4-6 x^3+x^2+6\right)-\left(x^3+10 x^2+8 x-4\right)$

Julie Silva

Numerade Educator

Problem 93

Multiply the given polynomials.
$5 x^2(x-3)$

Maninder Singh

Numerade Educator

Problem 94

Multiply the given polynomials.
$(x+4)(3 x-5)$

Adithya Ramanujam

Adithya Ramanujam

Numerade Educator

Problem 95

Multiply the given polynomials.
$(x-y+6)(x y)$

Julie Silva

Numerade Educator

Problem 96

Multiply the given polynomials.
$(2 x-1)\left(x^2-x+4\right)$

Grace Muhihu

Numerade Educator

Problem 98

use polynomial long division to divide.
$\frac{x^2+4 x+6}{x-2}$

James Kiss

Numerade Educator

Problem 99

Use polynomial long division to divide.
. $\frac{2 x^2-3 x+8}{x+4}$

James Kiss

Numerade Educator

Problem 100

se polynomial long division to divide.
$\frac{x^3-2 x+6}{x-3}$

AG

Ankit Gupta

Numerade Educator

Problem 101

Use polynomial long division to divide.
$\frac{3 x^5+4 x^4-x^2+1}{x^2+5}$

Farnood Ensan

Numerade Educator

Problem 102

Use polynomial long division to divide.
$\frac{3 x^6-2 x^5-x^4+x^3+2}{x^3+2 x^2+4}$

Farnood Ensan

Numerade Educator