Summer Assignment for AP Physics 1
Why Math?
Physics is the reason you had those math classes. In fact much of mathematics was developed to solve and understand physics situations. Sometimes mathematical theory leads to new possibilities and insights for physics to explore. Physics uses the language of mathematics. If you are not reasonably versed in the language and techniques of mathematics, you will have trouble understanding the concepts of physics, which of themselves have not always been apparent even to bright people, for example, Aristotle.
You will be given a math placement test upon entering AP Physics 1. You will not be asked anything beyond what you should have already reasonably mastered in your math classes to date. However, some students are rusty and some students never really mastered the material. Accordingly, you need to do the following documents/links below to review the basics and to become more proficient. The vast majority of these links contain only a few problems.
Do not assume you know how to do the problems because you recognize the title of the problem set. Try at least a few of each type to ensure you can apply the math concepts to new situations -- you will constantly be doing that in Honors Physics class. OUR EXPERIENCE INDICATES THAT EVEN SOME STUDENTS WHO GET A FOR SEMESTER GRADES IN MATH ARE OFTEN WEAK IN SOME ESSENTIAL SKILLS NECESSARY FOR PHYSICS. Errors involving relatively simple math skills often lead to poor understanding of physics concepts and underperformance on AP Physics 1 tests and quizzes.
There may be a few problems here and there in this material that we would not generally include or de-emphasize, but vast majority of this material is representative of basic math skills. (This is also good review for SAT.) Do not panic if you have trouble; just continue working on examples where you are weak until you succeed.
Near the bottom are some additional links that you must also explore. They are good tutorials on graphs and data analysis.
- Parallel Lines and Angles
- Parallel Lines and Angles Problems
- Triangles
- Right Triangle: Perimeter and Area
- Triangle Problems
- Triangle Given Its Perimeter, Altitute and Angle
- Find Angles in Regular Shapes (2 small worksheets) (Typo on 1st sheet for Right & Similar Triangle Problem- 1; top apex angle should be 7y not 4y and <BCA =45°)
- Find Angles in Irregular Shapes (3 small worksheets)
- Volume (V) and Surface Area (SA) Formulas
- Practice with Volume and Surface Area
- Multiple Choice Practice - Pythagorean Theorem & Trigonometric Functions
Algebra
- Basic Rules and Properties of Algebra
- ALGEBRA TUTORIAL
- simplifying polynomials
- intermediate algebra problems
- intermediate algebra problems #3
- Multiple Choice Practice - Variables and Expressions
- intermediate algebra questions #1
exponential and logarithmic
- exponential and logarithmic expressions
- Exponential and Logarithmic Equations
- Exponential Equations
- Logarithmic Equations
- Practice with Exponents Algebraic
- Practice with Dividing Polynomials
- Practice with Multiplying and Dividing Algebraic Fractions
- Practice with Solving Algebraic Equations
- More Practice with Algebraic Fractions
Equation of Lines
- slopes and equations of lines
- Slope of a Line Tutorial
- Equation of a line Tutorial
- Equations of Lines
- Equations of Straight Lines
- Practice with Graphs and Equations of Lines
fractions and percents:
- http://www.analyzemath.com/fractions/addition.html
- http://www.analyzemath.com/fractions/multiplication.html
- http://www.analyzemath.com/fractions/division.html
- Percent Math Problems
- fractions and mixed numbers
- Simplifying Complex Fractions (Simplifying the Numerator and Denominator)
- Simplifying Complex Fractions (Multiplying by a Common Denominator)
Algebra and basic equations
- Equations
- Substituting Values Into Algebraic Expressions
- Quadratic Equations
- Simplify
- Practice with Solving Quadratic Equations 1
- Practice with Solving Quadratic Equations 2
- Solving/isolating for one variable
- Solve Equations With Square Root
- Solving Linear Equations
- Solve Equations of the Quadratic Form
- Solve Equations with Absolute Value
- Grade 8 algebra questions
- Grade 9 Algebra Questions
- Grade 11 algebra questions
- Equations with Rational Expressions - Tutorial
solving systems of equations
- Solve Systems of Equations - Tutorial
- Solve Equations by Substitution
- Practice with Linear Quadratic Systems
- Solving Linear Systems Algebraically Using Substitution
- Solving Linear Systems Algebraically Using Elimination/Linear Combination (Addition/Subtraction)
- Practice with Solving Linear Systems Graphically
- Applied Practice with Systems of Linear Equations
Word Problems:
- Grade 6 Math word Problems
- Grade 7 Math word Problems
- Grade 9 Math Word Problems
- Ratio Word Problems with Answers - Grade 9
- Grade 10 Math word Problems
- Rate, Time Distance Problems
- Problem Solving: Distance, Rate, Time
- Work Rate Problems with Solutions
converting units:
- converting units and dimensional analysis
- Convert Units of Lengths
- Convert Units of Velocity
- Practice with Metric/English Conversions and Rates
- The Metric System of Measurement
- Practice with Scientific Notation
- Scientific Notation II
multiple skills:
- Error in Measurement
- Rounding and Error in Measurement
- Error in Differing Dimensions - Area, Volume
- Practice with Error in Measurement
- Multiple Choice Practice - Measurement
- Slope and Rate of Change
- Introductory Math Problems
- Math Worksheet - Algebra and Substitution
- Powers of 10 & Scientific Notation
- General Guidelines for operations in Scientific Notation
- Applied Practice with Scientific Notation
It would be good if you familiarize yourself with the basic trig functions sine, cosine, and tangent
the following are tutorials on graphs and data analysis
- Common Graph Forms in Physics
- Building the Perfect Graph
- Best Fits to Data/Curve Fitting
- Scatter Plots and Line of Best Fit
- Power versus Exponential Except for radioactive decay, most non-linear graphs in AP Physics 1 are Power Laws. In AP physics C, exponential functions appear in damped oscillators and circuits.
- Inverse Variation
Evaluating Information -- Applying the CRAPP Test
Geometry
A nice resource for many subject reviews