Commonwealth Education - The SAT Companion: Math

The SAT Companion:
Complete Answer Explanations to All Math Test Problems in The Official SAT Study Guide, 2nd Edition TM : Verbal

Written, edited, and published by, and under the direction of
Commonwealth Education.

Contributing Author: Ryan Garton

Copyeditor: Mrs. Sally Nyland

Cover Design: Mrs. Lisa Moroni-Hall

eBook Formatting: Robby Charters

Commonwealth Education

Commonwealth Education is a leading provider of tutoring and test preparation for students of all ages based in Falls Church, Virginia, USA.

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ISBN: 978-0-9859835-0-5

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Dear Future University Student:

Thank you for purchasing The SAT Companion: MATH. We know how daunting the SAT test is, and we hope you find our companion guide to The Official SAT Study Guide, 2nd Edition TM useful as you prepare for your test day. To use this book effectively to help you perform well on the SAT, we suggest the following steps:

1. Buy The Official SAT Study Guide, 2nd Edition TM . The authors of this book are the creators of the test, and you will get no better practice than by doing these problems.

2. Review/Skim the subject chapters in The Official SAT Study Guide, 2nd Edition TM . The information in here should not be new, but it will be a good refresher.

3. Do problems, problems, and more problems!! Time yourself and take it seriously. Dont look at the answers until you have completed the section. Dont cheat yourself! Did we mention do problems?

4. Use The SAT Companion : MATH as a reference. Again, dont cheat yourself by reading a problem in the book and then going right to the Companion explanation! Try these problems first, give yourself a real shot at completing them, and then while reviewing your score refer to the Companion to provide a detailed explanation.

5. Study frequently, in smaller chunks of time as opposed to one big block of time. Lets say you have 2.5 hours per week to study for the SAT. If you commit to 30 minutes, 5 times a week, your resulting progress will be much better than if you spent 2.5 hours in one session. SAT practice is all about frequent exposure to problems. Note: 2.5 hours IS NOT our guidance on how much you should study per week. If you can study 5, 10, or 20+ hours a week, do it.

Weve written explanations in an easy-to-understand voice, and laid out the steps for each problem. We have not cut corners; the easy problems (is there really such a thing?) have explanations that are just as thorough as the hard problems.

The SAT Companion : MATH is a comprehensive reference guide. Whether you are reviewing this material with a Commonwealth Education tutor, in an SAT class, or by yourself, you will always be a click away from a complete explanation of the solution to a problem.

There are many ways to complete math problems; our method is surely not the only one! We have chosen our explanations as they make the most sense to us, but if you get to the same answer as we do by another method, please feel free to share it with us! We may not be students anymore, but we are always learning and looking for better ways to answer problems and provide a great product.

We wish you the best of luck, and please tell us how you did when your results come in! If you have any questions or comments, please do not hesitate to contact us at SAT@commonwealthedu.com.

• Test 1 Section 3 Question 1
  Algebra to start with.
  • i
    Lets write our given: x = 4
  • ii
    What are we looking for? The answer that has the greatest value.
  • iii
    There are two ways to do this, the first being:
    Work every possible answer by inputting 4 for x:
    • (4+1)(4+2) = (5)*(6)=30 (answer)
    • (4+1)(4-1) = (5)*(3)=15
    • (4-2)(4+2) = (2)*(6)=12
    • (4-2)(4+1) = (2)*(5)=10
    • (4-4)(4+4) = (0)*(8)=0
  • iv
    Or logic it out:
    • Cross out (E) because (4-4) = 0. Any number times 0 is 0, so thats out.
    • Now look at (C) and (D). We are subtracting 2 from x . If x were really large, this might not matter, but x is 4, so taking 2 away from it reduces it by 50%. (C) and (D) are gone.
    • Were left with (A) and (B). They both have (x+1) in them, so just look where they differ. Is there any way (x+2) can be smaller than (x-1)? No way. (B) is gone.
• 
  A is the correct answer.
  
• 
  Test 1 Section 3 Question 2
  
  Variable Problem
  • i
    What are we looking for? What speed C is traveling when Bs speed is 7 mph (so B=7 is a given).
    The table reflects the speeds we will find.
    
    
  • ii
    We have 3 variables here, so this usually means a two-stepper. Lets use our variables and givens to translate the math speak into equations.
    • Train As speed is times Train B s speed.
      A = X B
      A =3B Equation 1
    • Train Cs speed is twice Train As speed.
      C = A
      C =2A Equation 2
  • iii
    Now weve got two equations, so lets use em. What are we looking for again? Cs speed, thats right.
    B =7 (Given)
    A =3 B
    A=3(7) = 21
    C =2 A
    C=2(21) = 42
    
  
  E is the correct answer.
  
• 
  Test 1 Section 3 Question 3
  
  Average Problem
  • i
    Know that average and mean are the same. Average = Sum of the terms / # of terms.
  • ii
    Lets write our givens:
    • Terms: x, 5x, 6x
    • Number of Terms: 3
    • Average of terms: 8
  • iii
    What are we looking for? The value of x
  • iv
    AVERAGE= Term 1 + Term 2++ Term n *
    n*
    
    * n just means total number of terms. If there were 5 terms in the sequence, n = 5. Dont let variables scare you. Make them your friends (we refer to them as such through this text)!

• • v
    Now plug in given information.
    • x + 5x + 6x = 8
      3
    • 12x = 8
      3
    • Multiply both sides by 3:
      12x = 8 3
      
    • Simplify fraction:
      12x = 24
      3 The 3s cancel each other out.
    • Divide by 12:
      12x = 24
      12 12
    • Simplify fraction:
      12x =
      12 12
      The 12s on the left side cancel out and were left with 24/12.
    • Finish up!
      x = 2
  
  B is the Correct Answer
  
• 
  Test 1 Section 3 Question 4
  
  Graphing Question. There will be many. Own them.
  • i
    What are we looking for? The graph that agrees with the statement, No two points on the graph have the same x- coordinate.
  • ii
    Know the rules of a function: Every x value of a function has only ONE UNIQUE y value. Isnt that the same thing as the statement in the question? Yes.