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AP Physics Review of Mathematics Part 1: Scientific Notation and Dimensional Analysis Many of the constants, speeds, masses, charges, etc … in physics can be very large or very small. For example the Speed of Light is 3x108 m/s, the electron mass is 9.11x10-­‐31 kg. Therefore, scientists express many numbers in terms of scientific notation and you will need to be able to read, simplify and convert to and from and vice versa as needed. Since all multiple-­‐choice portions of the AP exam must be completed WITHOUT a calculator, this is one of several important mathematical skills to be comfortable with. Show ALL work. Review the rules for scientific notation in the Appendix of our text, and/or a good math book. Then express the following numbers in proper scientific notation: 1. 300,000,000 m/s 2. .0000000000667 N m2 3.
kg2 86,400 sec/day In many cases multiple numbers in a problem contain scientific notation and will need to be reduced by hand. Review the rules for exponents in the Appendix of our text, and/or a good math book. Then, using the rules of exponents, (without a calculator) simplify the following numbers in proper scientific notation. 4. (2x106) • (3x104) = ____________________________________________________________________________________ 5. (6x10-­‐3) • (2x105) = ___________________________________________________________________________________ 6. (2.8x107) / (7x103) = _________________________________________________________________________________ 7. (9x109) / (3x1014) = __________________________________________________________________________________ 8. (4x105)3 = ______________________________________________________________________________________________ 9. (2x10-­‐6)2 = _____________________________________________________________________________________________ Fill in the power and the symbol for the following with prefixes. Prefix 10. milli 11. micro 12. kilo 13. Mega 14. Giga Power Symbol Not only is it important to know what the prefixes mean, it is also imperative that you can convert between units, systems, etc. Review the method for converting between units in chapter 1 of our text and then convert the following numbers into the specific unit. Note: Use scientific notation as appropriate. 15. 550 g = ____________________ kg 16. 102.7 MHz = ___________________ Hz 17. 720 ms = __________________ sec 18. 2.34 m = __________________ mm 19. 20 m/s = __________________ mi/hr Part 2: Geometry Review the rules for geometrical relationships in the Appendix of our text, and/or a good math book. Then, with these ideas in mind, calculate the area of the following shapes and determine the various angles as needed. It may be necessary to break up the figure into several shapes that you know as well as employ geometric equivalences. Show ALL work. w = 10 20. w = 20 in 21. h = 10 in h = 10 w = 25 in A 22. B If θ = 30°, what are the values of: A = _______ C D θ= 30° B = _______ C = _______ D = _______ Part 3: Trigonometry Review the rules of trigonometry in the Appendix of our text, and/or a good math book. Then, using these principals, calculate the following unknowns. Show ALL work in simplest radical form and DO NOT use a calculator. 23. 24. 25. θ = 45° 11 m θ = ? θ = 60° 6 in y = _________ hyp = _________ x = _________ θ = _________ x = _________ 8 in y = _________ hyp 5 cm