Math Review for Physics 2 2014 The following is meant to brush off your math skills. It also will inform you of what math skills I expect you to have coming into physics. You should be enrolled in Algebra II or have already completed it. Do not leave your answers in fractions, or a radical sign, or with a Π in them, give me a numerical answer. 1. Find the following without the use of a calculator: a. z3 and z5 for z = 2 b. 107 x 10-3 c. (4 x 104)/(2 x 10-6) d. (2.5 x 10-6)(4x106) e. (1.6 x 10-19)2 f. (6 x 106)(4 x10-5)4 2. Express the following as powers of 10 (i.e., scientific notation) a. 32,600 b. 0.831 c. 0.0002 d. 186,000 e. 1006 f. 0.000000000019 3. Given the following equations, solve for the indicated unknown. (a) 3t2 = 5t + 2: find t (b) 50 = 10 + 5a : find a (c) vf2 = vo2 + (1/2)at2 : find a if vf = 0, vo = 20, and t = 4 (d) F = mv2/r : find r if F = 455, m = 94, and v = 22 4. a. What is the area of a circle in meters squared with a diameter of 8 cm? b. What is the circumference of the circle above in meters? c. What is the surface area of a sphere with a radius of 5 cm - express the answer in square meters. (4Πr2 is surface area) d. What is the volume of a cube with an edge length of 2 cm in meters cubed? e. What is the surface area of the above cube in meters squared? f. What is the volume of a sphere with diameter of 1.5 m (4/3*Π*r3) 5. Ratios and fraction math is something we will use a lot in physics. So, let’s see if you remember how to do these: a) 1/5 + 1/6 + 1/9= 1/x b) Divide x2/4 by x4/9 solve for x c) You have two sets of equations. The m variable has the same value for both equations. Solve for the ratio r2/r1 Equation 1: 4m/r1=20 Equation 2: 7m/r2=55 Velocity versus time Velocity (m/s) 25 20 15 10 5 0 1 2 3 4 5 6 7 8 9 10 11 time (seconds) 6. On the graph above, what is the slope: a. From time=1 to time=4 seconds? b. From time=4 to time=6 seconds? c. From time=7 to time=10 seconds? d. From time=10 to 11 seconds? 7. Time for a little trig! SOH CAH TOA a. What is the cosine of 30°? ( We will always use degrees, not radians in physics) b. If the tangent of an angle is .789, what is the angle? c. If an angle in an right triangle has a sine of 0.75, and the hypotenuse is 1.5 m, what is the length of the opposite side? 8. Do the following unit conversions. Conversion factors are in your planner or the inside front cover of your physics textbook. a) Convert 100 km to miles b) Convert 5.5 hours to seconds c) Convert 1 m2 to cm2 d) Convert 67 km/hr to meters/seconds e) Convert 45 mm/sec to meters/hour 9. You remember the Ideal Gas Law, don’t you? PV=nRT. If T is held constant and of course n and R are constant for a sample of gas, how are P and V related? Sketch a graph of P vs. V below (that means P is on the y axis, and V is on the x axis). 10.0 Set up a system of equations for this word problem and solve it. There is no “guess and check” in physics, I expect you to set up algebra expressions. The admission fee at a small fair is$1.50 for children and $4.00 for adults. On a certain day, 2200 people enter the fair and $5050 is collected. How many children and how many adults attended?