MTH 1112 | Department of Mathematical and Computer Sciences | MSU Denver

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Khan Academy MTH 1112

This website shows Khan Academy links for most topics in MTH 1112.

First find the chapter you want in the menu below.

Scroll down through each section to see some links to Khan Academy videos and practice problems for topics in this section.

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Chapter 1

**Section 1.1: Making Sense of Data**
Topic	Videos	Practice Problems
Average	Stats Intro: mean, median, and mode	Calculating the mean
Median	Finding mean, median, and mode	Calculating the median

**Section 1.2: Visualizing Relationships in Data**
Topic	Videos	Practice Problems
Relations	Relations and Functions
Domain and Range of a Relation	Domain and range of a relation
Graphing Two-Variable Data	Coordinate plane: graphing points	Graphing points

**Section 1.3: Equations; Describing Relationships in Data**
Topic	Videos	Practice Problems
Making a Linear Model from Data	Determining a linear relationship
First Differences	Recognizing linear functions
Getting Information from a Linear Model	Application problem

**Section 1.4: Functions; Describing Change**
Topic	Videos	Practice Problems
Function Definition	What is a function?
Independent and Dependent Variables	Dependent and independent variables	Dependent and independent variables practice
Deciding whether an equation defines a function	Difference between equations and functions
Vertical Line Test
Four Ways to Represent a Function

**Section 1.5: Function Notation**
Topic	Videos	Practice Problems
Function Notation	Understanding function notation	Functions
Evaluating Functions	Evaluating with function notation	Function notation practice
Domain of a Function	Domain and range of a function given a formula	Domain of a function
Piecewise defined functions	Finding a piecewise function definition from a graph	Graphing piecewise functions

**Section 1.6: Working with Functions; Graphs**
Topic	Videos	Practice Problems
Graphs of Basic Functions	Basic functions Parabolas Radical functions Exponential Functions Absolute value functions	Interpreting graphs of linear and nonlinear functions Graphs of absolute value functions
Graphing with a graphing calculator
Graphing piecewise defined functions	Finding a piecewise function definition from a graph	Graphing piecewise functions

Chapter 2

**Section 2.1: Working with Functions**
Topic	Videos	Practice Problems
Average rate of change of a function	Average rate of change Average rate of change using a table Average rate of change using an equation	Average rate of change
Average speed of a moving object

**Section 2.2: Linear Functions**
Topic	Videos	Practice Problems
Identifying linear functions
Graphing a linear function	Graphs of linear functions
Linear functions and rate of change	Recognizing linear functions
Linear functions and slope	Slope of a line	Slope of a line practice
Finding linear functions from a graph	Constructing equations from graphs

**Section 2.3: Equations of Lines**
Topic	Videos	Practice Problems
Slope-intercept form	Linear equation from a slope and a point
Point-slope form	Linear equations in point-slope form	Point-slope form
Finding the equation of a line	Finding a linear equation given a point and a slope Constructing the equation of a line given two points	Solving for the y-intercept
Horizontal and vertical lines	Slope of a line 3

**Section 2.4: Direct Proportionality**
Topic	Videos	Practice Problems
Parallel lines	Parallel line equation
Perpendicular lines	Perpendicular line slope
Modeling direct proportionality	Direct variation

**Section 2.5: Linear Regression; Fitting Lines to Data**
Topic	Videos	Practice Problems
The line that best fits the data	Fitting a line to data (in excel)
Using the line of best fit for prediction
The correlation coefficient

**Section 2.6: Linear Equations; Getting Info from a Model**
Topic	Videos	Practice Problems
Getting information from a linear model	Constructing linear equations to solve word problems
Models that lead to linear equations	Mixture problems Distance word problem

**Section 2.7: Linear Equations; Where Lines Meet**
Topic	Videos	Practice Problems
Intersection points of linear functions	Solving linear systems by graphing Solving systems	Graphing sstems of equations
Modeling supply and demand

Chapter 3

**Section 3.1: Exponential Growth and Decay**
Topic	Videos	Practice Problems
The growth factor	Exponential growth and decay word problems	Rewriting and interpreting exponential functions
The growth rate	Decay example

**Section 3.2: Exponential Models; Comparing Rates**
Topic	Videos	Practice Problems
Changing the time period
Compound interest	Introduction to compound interest

**Section 3.3: Comparing Linear and Exponential Growth**
Topic	Videos	Practice Problems
Percentage rate of change
Linear growth versus exponential growth	Understanding linear and exponential models	Understanding linear and exponential models practice
Logistic growth: growth with limited resources

**Section 3.4: Graphs of Exponential Functions**
Topic	Videos	Practice Problems
Graphing exponential functions	Graphing exponential functions
The effect of varying a or c
Fitting an exponential function from a graph	Constructing linear and exponential functions from a graph

**Section 3.5: Fitting Exponential Curves to Data**
Topic	Videos	Practice Problems
Fnding exponential models for data	Constructing linear and exponential models from data	Constructing linear and exponential functions
Is an exponential model appropriate?

Chapter 4

**Section 4.1: Logarithmic Functions**
Topic	Videos	Practice Problems
Logarithms base 10
Logarithms base a
Basic properties of logarithms	Introduction to logarithm properties
Logarithmic functions and their graphs	Graphing logarithmic functions	Graphs of exponentials and logarithms

**Section 4.2: Laws of Logarithms**
Topic	Videos	Practice Problems
Laws of logarithms	Logarithm of a power	Logarithms
Expanding and combining logarithmic expressions	Using multiple logarithm properties to simplify
Change of base formula	Change of base formula

**Section 4.3: Logarithmic Scales**
Topic	Videos	Practice Problems
Logarithmic scales	Logarithmic scale
The pH scale
The Decibel scale
The Richter scale	Richter scale

**Section 4.4: The Natural Exponential and Log Functions**
Topic	Videos	Practice Problems
What is the number e?
The natural exponential and logarithmic functions
Graphing exponential functions	Graphing exponential functions
The natural logarithm	Natural logarithm
Continuously compounded interest	Introduction to compound interest and e
Instantaneous rate of growth or decay
Expressing exponential models in terms of e

**Section 4.5: Exponential Equations**
Topic	Videos	Practice Problems
Solving exponential and logarithmic equations	Solving exponential equations Solving logarithmic equations
Getting information from exponential models	Exponential growth and decay word problems
Newton's Law of Cooling
Radiocarbon dating

**Section 4.6: Working with Functions: Composition/Inverse**
Topic	Videos	Practice Problems
Composition of functions	Creating new functions from composition	Functions 3
The inverse of a function	Function inverse example	Inverses of functions
Which functions have inverses?	Function invertibility
Exponential and logarithmic functions as inverse functions	Comparing exponential and logarithmic functions

Chapter 5

**Section 5.1: Working with functions: shifting and scaling**
Topic	Videos	Practice Problems
Shifting graphs up and down	Flipping and shifting functions
Shifting graphs left and right	Shifting functions
Stretching and shrinking graphs vertically	Shifting and reflecting graphs
Reflecting graphs	Shifting and reflecting graphs	Shifting and refecting functions practice

**Section 5.2: Quadratic functions and their graphs**
Topic	Videos	Practice Problems
Quadratic functions in general form	Graphing using roots and vertex	Graphing parabolas 1
Quadratic functions in standard form	Completing the square
Graphing using the standard form	Graphing in vertex form	Graphing parabolas 2

**Section 5.3: Maxima and Minima**
Topic	Videos	Practice Problems
Finding maximum and minimum values	Finding the vertex of a parabola
Modeling with quadratic functions

**Section 5.4: Quadratic Equations**
Topic	Videos	Practice Problems
Solving quadratic equations: factoring	Solving a quadratic equation by factoring	Solving quadratics by factoring
The quadratic formula	How to use the quadratic formula	Quadratic equation
The discriminant	Discriminant of quadratic equations
Modeling with quadratic functions	Quadratic example

**Section 5.5: Fitting curves to data**
Topic	Videos	Practice Problems
Modeling data with quadratic functions

Chapter 6

**Section 6.1: Working with functions; Algebraic operations**
Topic	Videos	Practice Problems
Adding and subtracting functions	Adding and subtracting polynomials
Multiplying and dividing functions	Multiplying polynomials

**Section 6.2: Power functions; Positive powers**
Topic	Videos	Practice Problems
Power functions with positive integer powers
Direct proportionality	Proportionality constant for direct variation
Fractional positive powers
Modeling with power functions

**Section 6.3: Polynomial functions**
Topic	Videos	Practice Problems
Polynomial functions	Terms, coefficients, and exponents in a polynomial
Graphing polynomial functions by factoring
End behavior and the leading term	Polynomial end behavior example	Graphs of polynomials
Modeling with polynomial functions

**Section 6.4: Fitting polynomial and power curves to data**
Topic	Videos	Practice Problems
Fitting power curves to data
A linear, power, or exponential model?	Understanding linear and exponential models Comparing exponential and quadratic models
Fitting polynomial curves to data

**Section 6.5: Power functions; Negative powers**
Topic	Videos	Practice Problems
The reciprocal function
Inverse proportionality	Inverse variation example	Direct and inverse variation

**Section 6.6: Rational functions**
Topic	Videos	Practice Problems
Graphing rational functions	Asymptotes of rational functions

Chapter 7

**Section 7.1: Systems of Linear Equations in Two Variables**
Topic	Videos	Practice Problems
The substitution method	The substitution method	Systems with substitution
The elimination method	Addition elimination method	Systems with elimination
Graphical interpretation: the number of solutions	Consistent and inconsistent systems	Graphical solutions to systems
Applications: mixture problems	Mixture problem 2

**Section 7.2: Systems of Linear Equations in Several Variables**
Topic	Videos	Practice Problems
Solving a triangular system using back-substitution	Systems of three variables
Inconsistent and dependent systems	Independent and dependent systems
Modeling with linear systems	Three equation application problem

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