Pre-MBA preparation is very important for many students because many:

- Have not had exposure to quantitative topics during prior academic programs; or
- Have been out of school for many years and so feel the need to get a refresher on the basic quantitative skills prior to starting the MBA program; or
- Do not have any prior business background.

Our graduate tutors run a variety of pre-MBA boot camps to assist MBA students to be better prepared for their MBA programs. For those who prefer to study by themselves, Professor Alan Anderson has shortlisted Khan Academy videos to get you a good quantitative base for your MBA program. You can watch these videos at your own leisure.

**Professor Anderson’s Selected Khan Academy Videos**

**Other Pre-MBA Topics**

## Algebra for an MBA Student

Khanacademy.org offers a huge array of videos in quantitative subjects, such as statistics, algebra, geometry, calculus, differential equations, etc. The following discussion details the videos that cover the most important concepts in algebra. These videos are found under the heading “Algebra” under the category “Math by Subject.”

### 1) Foundations

This section covers the properties of the real numbers, including negative values, exponents, fractions and decimals.

- Intro to Negative Numbers
- Ordering Negative Numbers
- Adding and Subtracting Negative Numbers
- Multiplying Positive and Negative Numbers
- Dividing Positive and Negative Numbers
- Absolute Value and Number Lines
- Intro to Exponents
- Exponent Example 1
- Exponent Example 2
- The 0 and 1st Power
- Powers of Fractions
- Powers of Zero
- Understanding Square Roots
- Intro to Order of Operations
- Order of Operations Example
- Adding Fractions Word Problem: Paint
- Adding Fractions with Different Signs
- Multiplying Positive and Negative Fractions
- Dividing Negative Fractions
- Ordering Decimals 1
- Fraction to Decimal with Rounding
- Rewriting Decimals as Fractions
- Finding a Percent
- Adding Decimals
- Subtracting Decimals
- Multiplying Decimals Example
- Dividing Decimals with Hundredths
- Introduction to Negative Exponents
- Exponent Properties with Products
- Exponent Properties with Quotients
- Exponent Properties with Parentheses
- Exponent Properties 1
- Exponent Properties 2
- Exponent Properties 3
- Exponent Properties 4

### 2) Algebraic Expressions

This section introduces complex algebraic expressions, including variables, constants, exponents and operators. Techniques for manipulating expressions into a more useful form are covered in detail.

- What is a Variable?
- Expressions with Two Variables
- Example: Evaluating Expressions with Two Variables
- Intro to Combining Like Terms
- Simplifying Expressions
- How to Expand an Expression Using the Distributive Property
- The Distributive Property with Variables
- Equivalent Forms of Expressions
- Intro to Adding Rational Expressions with Unlike Denominators

### 3) Linear Equations and Systems of Equations

This section introduces the concept of linear functions and shows how to solve for variables with linear equations. There is also a discussion on solving systems of linear equations.

- One-Step Division Equations
- One-Step Multiplication Equations
- One-Step Subtraction Equations
- Simple Equations: Examples Solving a Variety of Forms
- Two-Step Equations Intuition
- Two-Step Equations with Decimals and Fractions 2
- Two-Step Equation Word Problems: Oranges
- Intro to Equations with Variables on Both Sides
- Writing Proportions Example
- Solving Proportions Example
- Systems of Equations with Graphing
- Solving Linear Systems by Substitution
- Systems of Equations with Elimination: Apples and Oranges

### 4) Quadratics and Polynomials

This section introduces more complex expressions, known as polynomials. A quadratic equation is one that contains at least one squared term. Techniques for solving quadratic equations are covered, along with techniques for performing algebraic operations on quadratic equations.

- Factoring with the Distributive Property
- Multiplying Binomials and Polynomials
- Squaring a Binomial
- Factoring Quadratics as (x+a)(x+b)
- Solving Quadratics by Factoring
- Adding and Subtracting Polynomials
- More Examples of Adding and Subtracting Polynomials
- The Parts of Polynomial Expressions
- Simplifying Polynomials

## Pre-MBA Finance Preparation

The following discussion shows several of the most important topics that are required knowledge for all finance students, along with the most relevant videos from Khan Academy. These can be found under the category “Finance and Capital Markets” under the Subject tab on the website’s home page.

1) Computing Interest

The following videos introduce students to techniques for computing interest rates and understanding the relationship between different definitions of interest rates. These are found under the category “Interest and Debt.”

- Introduction to Interest
- Interest (Part 2)
- Compound Interest Introduction
- The Rule of 72 for Compound Interest
- Annual percentage rate (APR) and effective annual rate (EAR)

The first video explores the concept of interest rates, showing how it applies to many aspects of our daily lives. The video provides a brief introduction to the concepts of present and future value. The second video introduces the formulas used to compute present and future value. The next video discusses the impact of different compounding conventions on interest rates. The Rule of 72 video introduces a useful rule of thumb that can be used to quickly determine how long it takes to double a sum of money with a specified interest rate, or what rate of interest is required to double a sum of money within a specified time frame. The last video discusses two alternative methods for expressing interest rates: annual percentage rate (APR) and effective annual rate (EAR). APR reflects simple interest only, while EAR reflects both simple and compound interest.

2) Time Value of Money

The time value of money is one of the most important concepts in finance. For example, the value of all securities in the marketplace is determined by time value of money concepts. The capital budgeting process, through which corporations choose investment projects, is also based on time value of money principles. The following videos are found under the heading “Interest and Debt.”

The first video explains how time value of money concepts can be used to determine the value of cash flows received at different points in time. The remaining videos show in detail how to use algebraic formulas to compute the present value for a variety of different situations.

3) Bond Pricing

Bonds are debt instruments that are issued by borrowers to raise funds. Corporations and governments are major issuers of bonds. The following videos explain the features of bonds, and show how bonds are priced using present value concepts. They also explain how bond cash flows are discounted using a measure of interest rates known as “yield to maturity” or “yield”; yields are based on the prices of Treasury securities. These videos are found in the section “Interest and Debt.”

- Introduction to Bonds
- Introduction to the Yield Curve
- Relationship Between Bond Prices and Interest Rates
- Treasury Bond Prices and Yields

4) Stock Pricing

A share of stock represents partial ownership, or equity in a corporation. Stocks are issued in order to raise capital. The following videos provide an introduction to the basic features of stocks and a comparison of their features with bonds. These videos are found in the section “Stocks and Bonds.”

5) Options and Futures

Options, forwards and futures are three examples of derivative securities, which are extremely powerful hedging tools. The pricing of these securities can be highly complex, especially for options. These videos are found in the section “Options, Swaps, Futures, MBSs, CDOs,…”

- Forward Contract Introduction
- Futures Introduction
- American Call Options
- American Put Options
- Call Payoff Diagram
- Put Payoff Diagram
- Call Writer Payoff Diagram
- Put Writer Payoff Diagram
- Introduction to the Black-Scholes Formula
- Put-Call Parity Arbitrage I
- Put-Call Parity Arbitrage II

The first two videos discuss the basic features of forward and futures contracts, which are very similar and can be used to lock in the price at which an asset may be bought or sold in the future. The remaining videos introduce the key features of options. A call option enables the owner to buy an asset in the future at a predetermined price, while a put option enables the owner to sell an asset in the future at a predetermined price. American-style options can be “exercised” at any time up to the maturity date, while European-style options can only be exercised at maturity. Payoff diagrams can be used to illustrate the relationship between the cash flows to an option and the price of the underlying asset.

One of the most important differences between forward/futures and options is that the buyer of an option must pay a price, or a premium. Option pricing models are extremely sophisticated. The first option pricing model was the Black-Scholes model, which is used to price European-style options; the developers of this model were awarded the Nobel Prize in Economics in 1997. The prices of European-style puts can be derived from the corresponding calls through a relationship known as Put-Call Parity.

This should give you a strong pre-MBA foundation on which to build your success in the MBA program. Good luck with your MBA program. If we can be of assistance, please do not hesitate to give us a shout.

## Pre-MBA Economics Preparation

The following discussion shows several of the most important topics that are required knowledge for all economics students, along with the most relevant videos from Khan Academy. These can be found under the categories “Macroeconomics” and “Microeconomics” under the Subject tab on the website’s home page.

**1) Introduction to Economics**

This section provides an overview of the field of economics with an introduction to the classic work by Adam Smith, “The Wealth of Nations.”

**2) GDP – Measuring National Income**

This section introduces the concept of Gross Domestic Product and how it is computed. The different components of GDP are analyzed, and the circular flow model of economic activity is explained. The key distinction between real and nominal GDP is also covered.

- Circular Flow of Income and Expenditures
- Investment and Consumption
- Income and Expenditures Views of GDP
- Components of GDP
- Real and Nominal GDP
- GDP Deflator
- Example Calculating Real GDP with a Deflator

**3) Supply and Demand**

This section introduces the most important concepts in economics: supply and demand. The law of supply and law of demand are analyzed in detail, showing the resulting supply and demand curves and how equilibrium is determined in the marketplace. The factors that determine supply and demand are also explored.

- Law of Demand
- Prices of Related Products and Demand
- Changes in Expected Future Prices and Demand
- Changes in Income, Population or Preferences
- Normal and Inferior Goods
- What Factors Change Demand?
- Law of Supply
- Factors Affecting Supply
- What Factors Change Supply?
- Market Equilibrium
- Changes in Market Equilibrium

**4) Elasticity**

This section covers a key concept in economics: elasticity. This refers to the sensitivity of one variable to a change in another variable. Elasticity is used to determine how sensitive consumers and producers are to changes in prices. Elasticity can also be used to determine the optimal output of a business enterprise. Other useful types of elasticity are also defined; these can be used to determine how consumer spending patterns change as incomes rise, or how the change in the price of a good can impact the quantity purchased of other goods.

- Price Elasticity of Demand
- More on Elasticity of Demand
- Constant Unit Elasticity
- Total Revenue and Elasticity
- More on Total Revenue and Elasticity
- Cross Elasticity of Demand
- Elasticity of Supply

**5) Market Structures**

This section covers several important types of market structures, including perfect competition, monopoly, oligopoly and monopolistic competition. Many industries exhibit characteristics of one or more of these market structures; their pricing and output decisions will depend on the type of market structure in which they operate.

- Perfect Competition
- Monopoly Basics
- Monopolist Optimizing Price: Total Revenue
- Monopolist Optimizing Price: Marginal Revenue
- Oligopolies and Monopolistic Competition

## Pre-MBA Statistics Preparation

The following discussion details the videos that cover the most important concepts in statistics. These videos are found under the heading “Probability and Statistics” under the category “Math by Subject.”

**1) Descriptive Statistics**

This section provides an introduction to several measures that can be used to describe the key properties of populations and samples. These include measures of central tendency and measures of spread or dispersion.

- Statistics Intro: Mean, Median and Mode
- Mean, Median and Mode Example
- Inferring Population Mean from Sample Mean
- Measures of Spread: Range, Variance and Standard Deviation
- Variance of a Population
- Sample Variance
- Population Standard Deviation
- Sample Standard Deviation and Bias

**2) Probability**

This section introduces the foundations of probability theory and defines the concept of the event. The notion of independence is covered in detail; there is also a review of basic set theory.

- Introduction to Theoretical Probability
- Probability: The Basics
- Simple Probability: Yellow Marble
- Simple Probability: Non-Blue Marble
- Probability with Venn Diagrams
- Addition Rule for Probability
- Compound Probability of Independent Events
- Coin Flipping Probability
- Die Rolling Probability
- Dependent Probability Introduction
- Dependent Probability: Coins
- Independent and Dependent Probability
- Dependent Probability
- Calculating Conditional Probability
- Intersection and Union of Sets
- Relative Complement or Difference Between Sets
- Universal Set and Absolute Complement
- Subset, Strict Subset and Superset
- Bringing the Set Operations Together

**3) Random Variables and Probability Distributions**

This section introduces the concept of a random variable, which is a function that assigns values to the outcomes of a random experiment. Using a random variable as a starting point, any number of probability distributions may be defined; these assign probabilities to the values of a random variable. Many probability distributions are especially useful in finance, including the binomial and normal distributions. This section also explains the concept of moments, which are summary measures of the properties of a random variable.

- Random Variables
- Discrete and Continuous Random Variables
- Constructing a Probability Distribution for a Random Variable
- Getting Data From Expected Value
- Binomial Distribution
- Visualizing a Binomial Distribution
- Binomial Probability Example
- Expected Value of Binomial Distribution
- Introduction to the Normal Distribution

**4) Sampling Distributions and Confidence Intervals**

This section introduces the concepts of sampling distributions and confidence intervals. A sampling distribution is a probability distribution that describes the properties of a sample statistic, such as the sample mean. A confidence interval is a type of interval estimate; it provides an estimated range of values for a population value such as the mean.

- Central Limit Theorem
- Sampling Distribution of the Sample Mean
- Sampling Distribution of the Sample Mean 2
- Standard Error of the Mean
- Confidence Interval 1
- Small Sample Size Confidence Intervals

**5) Hypothesis Testing**

This section covers the key concept of hypothesis testing. A hypothesis test is a series of steps designed to test whether or not there is sufficient evidence to reject a specified proposition. Hypothesis testing is used in a wide variety of applications throughout statistics, and is especially important for financial applications.

- Hypothesis Testing and p-Values
- One-Tailed and Two-Tailed Tests
- Type 1 Errors
- Z-Statistics vs. T-Statistics
- Small Sample Hypothesis Test

**6) Regression Analysis**

Regression analysis is one of the most important tools of statistics; it can be used to test the strength and direction of the relationship between different variables. Regression analysis is heavily used in economics and finance.

- Scatter Plots: Studying, Shoe Size and Test Scores
- Correlation and Causality
- Fitting a Line to Data
- Fitting the Line of Best Fit Exercise
- Squared Error of Regression Line
- Regression Line Example
- R-Squared or Coefficient of Determination
- Calculating R-Squared
- Introduction to Residuals

**Pre-MBA Accounting Preparation**

**1) Financial Statements**

The following videos are found under the category “Accounting and Financial Statements.” There are several sections dedicated to accounting; of particular interest to finance students is the discussion of financial statements analysis. The financial condition of a corporation can be found in its financial statements, especially the balance sheet and income statement.

- Balance Sheet and Income Statement Relationship
- Interpreting the Balance Sheet
- Interpreting the Income Statement
- Basic Cash Flow Statement

The first video introduces the balance sheet and income statement, showing what items are listed on them. The next two videos provide students with an opportunity to get some practice with financial statements; there is an embedded calculator that enables students to attempt to answer a series of questions about a fictional balance sheet and financial statement. The last video explores the items that appear on a cash flow statement, taken from the information found on the balance sheet and the income statement. Another view of these financial statements can be had here at:

- Learn how to read an income statement;
- Learn how to read a balance Sheet;
- Learn how to read a cash flow statement; and
- Learn how to understand and interpret percentage statements.

**Other Topics**

**Other Pre-MBA Resources**

- Basic math: MathPage & Interactive Math
- Microsoft Excel from Edx: Introduction to Data Analysis using Excel and deskbright.com
- HBS Pre-MBA course module (expensive!)
- MBA reading list from the Financial Times
- Core Curriculum Reading list from Harvard (just FYI)

**For those who prefer to study by themselves, Professor Alan Anderson has picked the above Khan Academy Videos to get you a good quantitative base for your MBA program. If you do not have so much time, please feel free to call, email or contact us using the signup forms on the side bar or at the bottom of this page so we can help you decide the best option for you.**