# Ch 1: Mathematics of Physics

### About This Chapter

## Mathematics of Physics - Chapter Summary

Refresh your skills in problem solving using linear equations, and remind yourself how to add vectors through this chapter on the mathematics of physics. Our brief but comprehensive video lessons provide a review of metric system units and conversion, as well as calculations with ratios and proportions. You'll also reexamine sines and cosines, as well as trigonometry and the Pythagorean theorem. Other topics addressed in this chapter include the following:

- Unit conversion and dimensional analysis
- Significant figures and scientific notation
- Understanding vector and scalar quantities
- Combining vectors using graphic and trigonometric methods
- Products of vectors: Dot products and cross products
- Standard units of measure: Newtons, kilowatt-hours, teslas, electron volts and more
- Temperature units: Converting between kelvins and Celsius
- Orders of magnitude
- Slopes and tangents on a graph

If you're a New York high school student, use these video lessons to help you prepare for the Physics Regents Exam. These video presentations were crafted by a team of experienced professional educators, and they typically can be viewed in less than 10 minutes. Each video is accompanied by a self-assessment quiz that can help you measure your mastery of the mathematics of physics.

### Physics Regents Exam Objectives

To earn a New York State Regents Diploma, and thus qualify for high school graduation, you need to pass one of four science exams. You can choose from chemistry, earth science, living environment and physics. The Regents Physics Exam contains 85 questions, which are a mix of multiple-choice and written-response.

### 1. Problem solving using Linear Equations

From sale prices to trip distances, many real life problems can be solved using linear equations. In this lesson, we'll practice translating word problems into linear equations, then solving the problems.

### 2. Calculations with Ratios and Proportions

Even if only 99 out of 100 people need to know how to work with ratios, the odds that they'll be useful to you are very high. In this lesson, we'll practice performing calculations with ratios and proportions.

### 3. The Metric System: Units and Conversion

Just like you and your friend communicate using the same language, scientists all over the world need to use the same language when reporting the measurements they make. This language is called the metric system. In this lesson we will cover the metric units for length, mass, volume, density and temperature, and also discuss how to convert among them.

### 4. Unit Conversion and Dimensional Analysis

How is solving a chemistry problem like playing dominoes? Watch this lesson to find out how you can use your domino skills to solve almost any chemistry problem.

### 5. Significant Figures and Scientific Notation

Are 7.5 grams and 7.50 grams the same? How do scientists represent very large and very small quantities? Find out the answers to these questions in this video.

### 6. Trigonometry: Sine and Cosine

Learn an easy trick to help you solve trigonometry problems, including problems with sine, cosine and inverse trig functions. At the end of this lesson, you'll know what SohCahToa means and how to use it.

### 7. Trigonometry and the Pythagorean Theorem

Explore how the Pythagorean Theorem can be used in conjunction with trigonometric functions. In this lesson, take an inverse trigonometric function, and define all three sides of a right triangle.

### 8. Vector Addition (Geometric Approach): Explanation & Examples

After watching this video, you will be able to explain why we might need to add two vectors and, given magnitudes and directions, add two vectors using geometric methods. A short quiz will follow.

### 9. Temperature Units: Converting Between Kelvin and Celsius

Have you ever wondered what the lowest possible temperature is? In this lesson, you will learn what temperature measures. You will also be introduced to the Kelvin scale (an absolute scale) and learn how it relates to the Celsius scale.

### 10. Slopes and Tangents on a Graph

Hit the slopes and learn how the steepness of a line is calculated. Calculate the slopes between points and draw the tangents of curves on graphs in this lesson.

### Earning College Credit

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### Transferring credit to the school of your choice

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### Other Chapters

Other chapters within the NY Regents Exam - Physics: Test Prep & Practice course