Notes, summaries, assignments, exams, and problems for Mathematics

Loan Amortization and EAR: You want to buy a car, and a local bank will lend you $40,000. The loan will be fully amortized over 5 years (60 months), and the nominal interest rate will be 8% with interest paid monthly. What will be the monthly loan payment? What will be the loan’s EAR?

Using a financial calculator: N=60, I/YR=8/12=0.6667, PV=-40,000, FV=0. Solve for PMT: $811.06.

To calculate the EAR: EAR = (1 + nominal rate/m)^m - 1. In this case, EAR = (1 + 0.08/12)^12 - 1.0 = (1.00667)^12 - 1.0 = 8.30%.

Loan Amortization Example: Jan sold her house on December 31 and took a $10,000 mortgage as part of the payment. The 10-year mortgage has a 10% nominal interest rate, with semiannual payments beginning next June 30. Next year, Jan must report...

Market Value Performance Measures

• Market Value Added (MVA): Market Capitalization (Number of shares × Price per share) - Equity.
• Market-to-Book Ratio: Measures value added per dollar invested by shareholders. Calculated as: Market Value of Equity / Book Value of Equity (Total Shareholders' Equity).

Measuring Profitability

• Economic Value Added (EVA): Profit after deducting all costs, including the cost of capital. Formula: [After-tax operating income] - [Cost of Capital × Total Capitalization at start of year (Long-term debt + Total equity)].
• Return on Equity (ROE): Net Income / Equity (start of year).
• Return on Assets (ROA): [(1 - Tax Rate) × Interest Expense + Net Income] / Total Assets (start of year).
• Return on Capital (ROC): [(1 - Tax Rate)

Statistics: The Science of Organizing Data

Statistics is the science of organizing data to draw conclusions or answer questions.

Descriptive Statistics

Descriptive statistics describe data through numerical summaries and graphs.

Variables

Variables are characteristics of individuals within the population.

Discrete and Continuous Variables

Discrete variables are counted, while continuous variables are measured.

Nominal and Ordinal Variables

Nominal variables are named, while ordinal variables are ranked or ordered.

Interval and Ratio Variables

Interval variables have no meaningful zero and equal intervals between values, while ratio variables have a meaningful zero.

Types of Variables in a Study

The response variable is what is being studied, the explanatory...

10 reasons to use games in language teaching

1.Games create a context for meaningful communication. 2. This meaningful communication serves as a basis for comprehensible input. 3. Games add interest to what learners find boring. 4. Games can be used with all language skills. 5. Games offer a fun experience. 6. Games encourage participation from all learners. 7. Games are learner-centered activities. 8. Games work outside of class. 9. Games promote cooperative learning. 10. Games fit into multiple intelligence theory.

Using Games in Teaching English to Young Learners: How to Choose a Game

Students may wish to play games purely for fun. Teachers need more convincing reasons. The key to a successful language game is that the rules are clear. The...

Key Trends in Educational Outcomes (2009-2012)

• Equity in education outcomes deteriorated between 2009 and 2012.

Gender Differences in Academic Performance

• In 2012, girls outperformed boys in reading by an average of 29 score points.
• In 2012, boys outperformed girls by 16 score points in mathematics, a 7-point larger gender gap than seen in 2003.
• Across OECD countries, 42% of students (64% of girls) believe their failure in mathematics is due to a lack of ability. In Spain, this figure rises to 74% of students (80% of girls).

Socioeconomic Origin and Academic Performance

• In 2012, socioeconomically advantaged students outperformed less-advantaged students by 34 score points in mathematics.

Ethnicity and Academic Performance

• The immigrant student population

Map Generalization

Types of Symbols

• Line Symbols: Represent real-life objects with a linear path.
• Point Symbols: Represent objects occurring at a single point on Earth's surface using a dot.
• Area (Polygon) Symbols: Represent real-life objects spread over Earth's surface using geometric shapes.

Generalization Techniques

Reality contains too much information for a single 2D map. Generalized geometry and content make a map useful. A good map suppresses less important information to highlight what needs to be seen.

• Selection: Only relevant line, point, and area features are chosen.
• Classification: Grouping similar features and using a common symbol to represent them.
• Simplification: Reduction of unnecessary detail.
• Smoothing: Smoothing out abruptly joined

Food and Nutrition

Food is the act of providing sustenance to the human body, while nutrition encompasses the physiological processes by which the body receives, transforms, and utilizes the chemical components in food.

Inherited Diseases

• Hemophilia
• Huntington's disease
• Cystic fibrosis
• Color blindness
• Phenylketonuria

Measures of Dispersion

Measures of dispersion indicate how close the data are to the average.

Vaccines

Vaccines are preparations containing killed or attenuated microorganisms. They are introduced into our bodies to produce antibodies that kill the organism, providing immunity.

Common Pathogens

Pathogens such as bacteria and fungi are the most common causes of infectious diseases.

Health and Disease

Health is a state of complete physical, mental,...

Gantt Charts and Project Status

Gantt charts are bar graphs that immediately show the status of implementation within a project, identifying any delays or advances. They attempt to represent the duration of each of the activities into which the project is divided. A drawback to their use is that they do not permit cross-connections showing directly how one activity depends on or influences another.

CPM / PERT Terminology Definitions

Activity

Each element of the project or program represented by an arc in CPM. This arc sometimes represents a time duration or a connection between two events of the graph. An activity cannot begin while the preceding event has not occurred.

Event

An event in the project or CPM that marks the beginning or end of an activity....

B. Changes in Inventories

The company must make an inventory of the stocks it has, doing a physical count of them and checking the result with the information recorded in the book balance. After verifying this data and correcting any differences, it is necessary to stabilize stock accounts; that is, to correct the accounting balance of these accounts to reflect reality.

C. Verification of Accounting Data

Before determining the result of the accounting fiscal year, the company must verify accounting data by checking, on the one hand, that there are no mistakes in arithmetic or transcription and, on the other, contrasting it with the economic reality. To do this, perform the following inventories and balances:

• Trial Balance: Its purpose is to check

Case Study 1: Sales Team Head Settlement

Employee Details & Salary Structure

Settlement Calculation Steps

Unpaid Salary

• Period: November 1 - November 3 (3 days)

Monthly Salary = 1,090 + 320 + 90 = 1,500 Euros/month

Unpaid Salary for 3 days = (1,500 / 30) * 3 = 150 Euros

Pro-rata