math.docx - MCAT EXCELERATOR Copyright 1998 2002 Richard...

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MCAT EXCELERATOR Copyright ç 1998 , 2002 Richard Hochstim. All rights reserved. MCAT is a registered trademark of the Association of American Medical Colleges. “Excelerator” is a trademark of Richard Hochstim. < > Chapter 2 MCAT Quantitative Skills The bad news is that you can’t use a calculator on the MCAT. The good news is you won’t need to. Almost all questions are conceptual, and those that do require computation, don’t require much. So how much math do you need? Some basic quantitative skills, an understanding of units, a bit of geometry, and a healthy helping of trigonometry. Enjoy… ^ ü ∏–)]. 2.1 Mathematics A. Magnitude «The magnitude (size) of a number increases as one moves from left to right below: -3 -2 -1 0 +1 +2 +3 assignment » Which of these two half reactions has the larger standard reduction potential? Fe¤± + 2e— ÿ˘ Fe EÎ = -0.040 volts Al‹± + 3e— ÿ˘ Al EÎ = -1.706 volts solution: The first reaction does because -0.040 > -1.706 assignment » List the following compounds in order of increasing solubility (as K͘ in- creases, solubility increases). Ag„CrO K͘ = 9.0 ´—⁄¤ AgSCN K͘ = 1.0´—⁄¤ ®
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ZnCO‰ K͘ = 1.5´—⁄⁄
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2 » M CAT E XCELERATOR C HAPTER 2 solution: AgSCN < Ag„CrO < ZnCO‰ . Recall that 10—⁄¤ < 10—⁄⁄ «When working in scientific notation, if the number to the left of the ´ exp gets smaller, the exp onent gets larger. assignment » Convert the wavelength of red light (700 nm) to meters using scientific notation (1 nm = 10—· m). solution : n 700 nm = 700´—· m = 7.00´—‡ m «When a unit becomes larger, the number attached to that unit becomes smaller, and visa versa. assignment » How many cubic centimeters are there in 7.5 liters? One cc is equal to one milliliter. The prefix "milli" means one over a thousand. solution : Since the unit of measurement is getting smaller by 1/1000, (liter to milliliter), the number attached to the unit milliliter must get larger by a thousand. Thus there are 7.5 x 1000, or 7500 mL in 7.5 L. 7.5 L / x 1000 m L L / = 7500 mL B. Algebra assignment » What is the sum of 1.5´—‹ + 5.0´—›? solution : First convert the exponent of the smaller number to equal the exponent of the larger number. Then add. 1.5´—‹ + 0.50´—‹ = 2.0´—‹ assignment » Solve for ÎC in the equation: ÎF = 9 ÎC + 32 . 5 {
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solution : First subtract 32 from both sides of the equation to yield Î F - 32 = 9 ÎC . 5 Next divide both sides of the equation by 9/5 to give 5 (Î F - 32) = Î C . 9 example » 1 1 1 Solve for RŒ in the equation, = R‰ + R„ , in terms of R„ and R‰. solution : •The first step is to isolate RŒ from the other variables. This may be done 1 1 1 by subtracting 1/R„ from both sides to give, = - . R‰ R„ • The next step is to multiply the terms on the right hand side of the equation by R„/R„ and R‰/R‰ respectively, so as to obtain a common de- nominator of R„R‰.
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