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Math Review (Note: An understanding of physics is not necessary to answer the following.) 1. ( 4 2 )( 4 3 ) = 2. (6 2 ) 2 3. Express your results for the following in scientific notation: 1 (2.3x10 20)(3.8x10-15) 8 3 a) b) (2.32x10 ) (8x10 8 ) 4. Evaluate: e 2 .4 5. Find ln(f) given that f I I and I 6I 0 . 0 1 1 2 7 6. Evaluate: a) b) 2 5 5 10 7. An angle is measured to be 2.14 radians , find cos() . 8. For the triangle shown, a=3 and c=5. Find b, sin( ) and tan( ) . c a b 9. For the picture shown below, find and , in terms of . this line is perpendicu lar to the slope dashed line s are parallel 10. How many seconds are in one year? 1 1 1 11. It is known that , given that f 8 cm and s 12 cm, find s. f s s 2 12. For a circle the area is given by A r , where r is the radius. Two circles have different 2 2 radii. A1 r1 6m . Find A2 if r2 2r1 . 13. The earth spins on its axis. How long does it take to spin around once? 14. Several measurements are made of student's heights. What is the average height? What is the standard deviation? (Your calculator can probably do these calculations.) Height (in meters): 1.6, 1.8, 1.75, 2.1, 1.65, 1.8, 1.9. 15. You are given that F 6a 20 and F 8a 0. Find F and a. 16. Find an expression for Fy in terms of M,g, and L. F L MgL/ 2 (2m)gL / 3 0 y 17. Determine an expression for x in terms of M, m, G, and d: Mm Mm G 2 G x (d x)2 jgf 2/6/2016 687286999 1 18. Be able to sketch the following: y(t) 3t 2 (y in meters for t in seconds). 2 19. The relationship between position and time can be of the form x(t) bt . Find b for the data shown below. (Do not forget units.) 20. A drawer contains 9 red socks and 11 blue socks. It is dark and you are trying to grab a matching pair. How many socks do you need to take out to be sure of a matching pair? 21. Some physics and algebra leads to the expression below, find . (You may ignore units.) We mgtan know that q=10-6, L=0.01, m=0.005, g=10, k=10-8, q 2Lsin . k 22. For certain charges the electric field is given by E(x)=b/x2. At the location x0, E(x0)=E0. Find E for x=4x0 in terms of E0. 23. Using Kirchoff's loop and junction rules we obtain these equations for the currents in 2I1 2I2 5 0 different parts of the circuit. Find I1 and I2. I1 4I2 0 24. If you have already had calculus you should be able to do the following: d d (3t 3 4t 5) ? Ax 2 cos(bx) ? (A and b are constants) dt dx jgf 2/6/2016 687286999 2