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Physics Study Sheet for Math pre-test You will have a test on these – NO CALCULATOR. Why Learn Physics? Three reasons: 1) learn how the world around you works 2) You might find a career idea in it 3) The more education you have, on average the money you can earn Statistics show that students have a better chance to graduate from college if they go to a fouryear university than of they begin at a two-year college. Algebra Skills 1. Solve an equation for any variable. Here are some examples, make sure you can solve them for x. See answers on last page. a) v + w = x2yz c) 2 1 1 x 3 2 b) d) a y b x 2 1 y x 3 2 2. Be able to reduce fractions containing powers of ten, for example: a) 102 104 3 10 b) 103 106 3. Be able to take a multiplicative expression to a power, for example: a) 2 x x2 b) 3 y 3 2 PP means Practice Problem, the solutions to odd ones are in the back of the book. 2 Science Skills 4. Convert a number into scientific notation in standard form, and from scientific notation. This includes both large numbers (> 1,000) and small numbers (< 0.01). Try these examples (answers at end): a) 12,345 b) 15000000 c) 1/100 d) 2/10,000 5. Unit pre-fixes: Find Table 1-2 on p. 6. Memorize the multipliers for the following: nano, micro, milli, centi, kilo, mega, giga. You do not need to memorize other prefixes. Try this: 2,000 mockingbirds = 2 ___________. 1 x 106 phones = ______ Invent others. 6. Significant figures. Know how to find the number of sig figs in a value. PP 9, 11. Try these (answers at end): a) 123 b) 1.23 c) 12,300 d) 0.0123 e) 1.230 x 10-4 7. Unit conversion: Be able to use the factor-label method. A conversion factor is a multiplier that is equal to one. For example, 1 foot = 12 inches, so 1 foot 1 . If we want to convert 12inches 113.2 inches to feet, we multiply by the conversion factor: 113.2inches 1 foot 113.2 inches 1 foot 113.2 feet 9.433 feet 12inches 1 12 12 inches a) 13.4 inches to feet b) 4.31 feet to inches 8. Arithmetic operations in scientific notation. For addition and subtraction, the operands must all be expressed in the same powers of ten. For multiplication and division, the exponents are also involved in the operation. Appendix A, p. 842, PP #13. a) 435 + 2.7x102 b) 4.35 + 2.7 x 10-1 c) 4.35 x 2.7x10-2 d) 540 2.7 102 Geometry and right-angle Trigonometry 9. Know sin, cos, tan (memorize SOH CAH TOA) and how to apply them to find the side of a right triangle. Appendix A. a) Find sin, cos, and tan of θ. b) Suppose θ = 50°, sin 50 = 0.766, cos 50 = 0.643, & c = 9. Find a & b. a Sin-1 (0.5) can be read as “the angle whose sin is 0.5”. c Similarly for tan-1 and cos-1 θ b 10. Know sin-1, cos-1, tan-1 and how to apply them to find the angle in a right triangle Appendix A p. 856. Find the value of θ in the triangle above if a = 57.3 and c = 100. Know the Pythagorean theorem, be able to use it to find the third side of a right triangle when the other two sides are given. Do not apply any of the three laws stated above to triangles that are not right triangles. 11. Understanding Ratios. The ratio or fraction 465 signifies the number of times 23 is 23 contained in 465 – the number of successive subtractions of 23 from 465. The result of the division tells us how much of the numerator is associated with one of the denominator. a) How much will one pound cost if we paid $5.00 for 3 pounds? b) If the ratio of girls to boys is 5 to 3, how many girls are there if there are 9 boys? c) If the ratio of length to width is 1.33, what will be the width if the length is 7? ---------------------------------------------------------------------------- See Ch 1 in your book for problems and solutions related to scientific notation and significant figures. vw yz 1. a) x d) 2. a) 12 b) x 5 c) x y b a 2 1 y 2 3y x 6 12 x x 3 2 6 2 2 3y 2 3y 102 104 109 3 10 3. a) 2 x b) 103 103 6 10 2 3 2 4 x x2 x4 b) 3 6 y y 6 4. a) 12,345 = 1.2345 x 104 c) 1/100 = 0.01 or 1 x 10-2 b) 15000000 = 1.5 x 107 d) 2/10,000 = 2 x 10-4 6. a), b) & c) 3 sig figs; d) 4 sig figs 7. a) 40 in 1 ft 3.33 ft 12 in 8. a) 435 + 270 = 705 9. a) & b) sin tan b) 4.31 4.3 ft b) 4.35 + 0.27 = 4.62 12in 51.6in ft c) 4.35 x 0.027 = 4.377 opp a a 0.766 a 6.89 hyp c 9 cos d) 540 2 270 adj b b 0.643 b 5.79 hyp c 9 opp a adj b 57.3 10. sin 1 35 Questions 9 & 10 are not numerically consistent with one another. 100 11. . a) c) 5.26 cost 5 cost 1.67 pound 3 one pound b) girls 5 girls = =1.67= girls = 1.67 × boys=15.0 boys 3 boys