<p> AP Physics 1 Basic Algebra Review</p><p>The exercises below are a review of the prerequisite math skills that you need to succeed in AP Physics 1. Make sure to read all directions throughout the packet. Final answers can be in fractions and in terms of mathematical constants (, e, i, etc.). Use a math book or internet for reference. No physics is needed for this review. If you have difficulty, please do not hesitate to email me at [email protected] In 2015, the head grader for the AP physics test stated that “Basic algebra was often weak”. These problems are examples of what College Board considers basic algebra, and can be solved with only the knowledge of algebra 1, geometry and chemistry. Very little time will be devoted to reteaching these concepts, so any gaps will have to be covered outside of class during your own time.</p><p>Significant Figures and Scientific Notation Review</p><p>1.) How many significant figures do the following numbers have?</p><p> a.) 6.001 Answer: ______d.) 27.00 Answer: ______</p><p> b.) 0.0080 Answer: ______e.)  Answer: ______</p><p> c.) 206,000 Answer: ______</p><p>Directions: Find the following. Final answers should be in scientific notation with the correct number of significant figures. -8 2 4 3 2.) (5.0 ´10 )(2.9 ´10 ) 3.) (3.25 ´10 + 7.4 ´10 )</p><p>1.00 ´1026 8400 6.000 ´10-11 4.) 2.00 ´107 5.) 1.2 ´107 Unit Conversions Review ( basic stoichiometry) 6.) Finish the SI prefix table below. Follow the example of the centi- prefix. You will need to memorize these. Symbol Name Numerical Equivalent n  m c centi 10-2 k M G</p><p>7.) 16.7 kilograms is how many grams?</p><p>8.) 560 nm is how many meters?</p><p>9.) 15 years is how many seconds?</p><p>10.) 8.99 ´109 seconds is how many years?</p><p>11.) 2.998 ´108 m/s is how many kilometers per hour?</p><p>Trigonometry Review Directions: Use the figure below to answer problems 15-25. Simplify as much as you can.</p><p> c a  b</p><p>12.) Find c if given a and b. 13.) Find a if given b and c.</p><p>14.) Find a if given c and . 15.) Find b if given a and .</p><p>16.) Find c if given b and . 17.) Find  if given b and c.</p><p>18.) Find  if given a and b. 19.) If a = 2.0 and c = 7.0, what is b? 20.) If c = 10.0 and  = 60, what is b? 21.) If a = 12.0 and  = 30, what is b?</p><p>Algebra Review Directions: Solve the following equations for the given variable and conditions. Simplify if needed.</p><p>Example: 2x + xy = z. Solve for x. x(2 + y) = z z x = 2 + y</p><p> v 22.) v + v = 0. Solve for v1. a = . Solve for t. 1 2 23.) t</p><p>2 2 24.) v f = vi + 2ad A.) Solve for vi. B.) Solve for d.</p><p>1 d = d + v t + at 2 25.) f i o 2 A.) Solve for vo. B.) Solve for t, if vo = 0.</p><p>C.) Solve for t, if di = df.</p><p> v - v F = m f i 26.) t f - ti</p><p>A.) Solve for vf, if ti = 0. B.) Solve for tf, if vf = 0 and ti = 0.</p><p> v 2 Solve for v. . Solve for θ. a = mgsinq = mmgcosq 27.) c r . 35.) </p><p>1 1 mv 2 + mgh = mv 2 + mgh 28.) 2 f f 2 i i A.) Solve for hf, if hi = 0 and vf = 0. B.) Solve for vf, if hf = 0.</p><p>Ft mv mv . Solve for vf. m v m v (m m )v . Solve for vi,2. 29.) = f - i 38.) 1 i,1 + 2 i,2 = 1 + 2 f</p><p> m v m v m v m v . Solve for vf,2 if vi,1 = 0. 30.) 1 i,1 + 2 i,2 = 1 f ,1 + 2 f ,2</p><p>. Solve for r2. 31.) (F1 sinq)r1 + (-F2 sinf)r2 = 0</p><p> m m 32.) -kx + m(-g) = 0. Solve for m. F = G 1 2 . Solve for r. 33.) g r2</p><p> v2 L - L cosq = 34.) 2 Solve for L. mv 2 Mm. Solve for v. L . Solve for g. = G T = 2p 35.) R R2 36.) g</p><p>1 1 1 mv 2 + kx 2 = mv 2 + mgh . Solve for x if vf = 0. 37.) 2 f 2 2 i i</p><p>1 1 1 38.) = + . Solve for RT. RT R1 R2</p><p>Miscellaneous Directions: Simplify without using a calculator. Remember to show all of your work. 1 1 1 1 39.) + 40.) + 4 6 3 18 x s2 41.) Consider z = , c = ab, l = m - n, or r = . y t 2 a.) As x increases and y stays constant, z ______.</p><p> b.) As y increases and x stays constant, z ______.</p><p> c.) As x increases and z stays constant, y ______.</p><p> d.) As a increases and c stays constant, b ______.</p><p> e.) As c increases and b stays constant, a ______.</p><p> f.) As b increases and a stays constant, c ______.</p><p> g.) As n increases and m stays constant, l ______.</p><p> h.) As l increases and n stays constant, m ______.</p><p> i.) If s is tripled and t stays constant, r is multiplied by ______.</p><p> j.) If t is doubled and s stays constant, r is multiplied by ______.</p><p>Systems of equations Conceptual Question: 42.) How many equations are needed to solve… a.) for 1 unknown variable? ______b.) for 2 unknown variables? ______c.) for 3 unknown variables? ______</p><p>Use the equations in each problem to solve for the specified variable in the given terms. Simplify.</p><p>43.) Ff = mFN and FN = mgcosq. Solve for  in terms of Ff, m, g, and .</p><p>44.) F1 + F2 = FT and F1× d1 = F2 × d2. Solve for F1 in terms of FT, d1, and d2. </p><p> v 2 45.) Fc = mac and a = . Solve for r in terms of Fc, m, and v. c r</p><p>L 1 46.) T = 2p and T = . Solve for L in terms of , g, and f. g f</p><p>Graphing Equations</p><p>47.) If r = c – x*t was graphed on an r vs. t graph, what would the following be? Slope: ______y-intercept: ______</p><p>48.) On the y vs. x graphs below, sketch the relationships given.</p><p> a.) y = mx + b, if m > 0 and b = 0. b.) y = mx + b, if m < 0 and b > 0. c.) y = x2 d.) y = x</p><p> e.) y = 1/x f.) y = 1/x2</p><p>1 g.) y = h.) y = sin(x) x Marbles in Cylinder Lab</p><p>You received a graduated cylinder with three identical marbles and an unknown amount of water already in it. You placed extra identical marbles in the cylinder and obtained the data below. Use the data to graph a best-fit line showing the relationship between the water level and the number of marbles. The y-intercept should be visible on the graph. Label your axes and include units. From the graph, determine a mathematical formula for the water level for any number of marbles. Lastly, give an explanation of your formula in words. Make sure to give an explanation of the slope and y-intercept of your formula. 49.) Graph below Number of Marbles Water level (mL) in Water 3 58 4 61 5 63 6 65 7 68</p><p>50.) Formula: ______51.) Explanation of the formula in words: (Include the meaning of the slope and y-intercept.)</p>