Alternative Solutions: Practice Test #6

DITW = Do it their way

Trial and Error = pick an answer, play with it, see if it fits what they said in the problem…

Back Door = make up numbers for the variables in the problem, work out an answer that is based on the numbers you made up, then put those made up numbers back into the answer choices, ruling out any that don’t produce a matching answer.

More detailed explanations available in the book…


  1. Linear modeling again!  When y=mx + b (or b + mx) the b is the starting value.  In this case, that’s the service fee.
  2. DITW
  3. DITW
  4. You don’t have to FOIL this out all the way.  Just notice that the x^2 term has to be p^2…
  5. Yes, you should be able to match a graph and its equation.  But if you can’t…pick any x value,,,say x=2.  Find the y-value that goes with that x value.  (You get y=-1) .  Then, check which graph contains the point you have just found, (2,-1).
  6. DITW
  7. If you need to, use the back door: make up numbers, then put your numbers into the answer choices to see which one works.
  8. No real trick to this one once you understand what they are asking.   In other words, when you add entry in the second column to the one in third column,  do you get the value in the first column?
  9. Just try the answers…
  10. DITW
  11. Know your basic parabola facts and your shifts…see pages 165-166
  12. They want you to do polynomial division.  But seriously, this one cries out for the back door.  Try letting x=1.  Work out the answer.  Then put x=1 into each answer choice.  It’s much easier my way.
  13. This is actually pretty subtle.  You could try each value and see if it factors (or see if the discriminant is negative). That’s kind of a pain.  There is another way to get the answer but I admit it is sneaky.  Consider the quadratic function y=2x^2-4x-t.  It opens upward.  So if it has no real solutions, if you shift it upward it will still have no real solutions.  But the problem can only have one answer!  So it has to be A.  (If this doesn’t make sense to you, post a question and I will go into it in more detail.  Also, I predict that very few test-takers will get this one right.)
  14. DITW
  15. Try numbers!  I used a=1 and b=4 so I got 9.  But oh, no!  A and D both come out to 9.  No worries – just do it again with new numbers. I tried a=1, b=6 and got 16.  This time, only D worked.
  16. Other than playing around with numbers, how else are you going to do this?
  17. DITW
  18. This is a Pythagorean Theorem question.  But first, when you see this shape you should automatically be on the alert for similar triangles and ratios…
  19. DITW – even I admit that algebra is the fastest way.  But if you are comfortable with the idea of weighted averages and inverse proportions, there is another way to think about this one.

The goal is a 15% solution. Since that is closer to the 10% stuff than it is to the 25% stuff, I expect to need less of the 25% solution than the 3 liters I already have.  In fact, if you look at how far each solution is from the goa, the 10% stuff is 5% away, the 25% stuff is 10% away.  Like weights balancing on a see-saw, the farther away, the greater the effect.  In fact, it is an inverse proportion.  So I know I’ll need half as much of the 25% solution.

OK, I admit that if I were taking this test, I would never have come up with that method on time.  So in this case, do the algebra if you can.  If not, take a guess and move on.

  1. DITW



  1. Combine like terms if you want.  Or try a number!
  2. DITW
  3. You are looking for shallow, then level, then steep.  Slope is rate of change.  Also, the snow was always getting deeper so C and D are silly.
  4. DITW
  5. They are just checking if you know that you can divide both sides of an inequality, in this case by 3.
  6. DITW
  7. It seems from the released tests that the SAT would really like you to know that to make accurate predictions, a survey must involve RA NDOM sampling.
  8. If this is your sixth practice test, then you have seen this before.  But read carefully so you know if they are asking about everybody or just a subset.  This time, they only want to know about vanilla lovers.
  9. DITW
  10. By algebra, if x is the second voyage, then x + x + 43 = 1003.  But why not just try the answer choices?
  11. DITW
  12. You don’t have to calculate the average growth rates to see which is greatest.  Average growth rates are also slopes of the segments that connect the two points.  So draw them and then pick the steepest one.
  13. And here we have yet another linear model: y= mx + b but with some of the letters changed.  The a value is still the rate of change, or in this case, the amount of daily growth.
  14. Pick a value from the graph or chart . For instance, on day 28 the height was 98.  Try t = 28 in each answer choice.  You will see that only one answer is even close.
  15. Really?  The very next question?  I tried x = 4…
  16. These are similar triangles.  It might help you to see that better if you redraw the one on the left, turning it and flipping it so that it is oriented the same way as its neighbor…
  17. Make up a set of numbers so that 2h + d = 25.  Then go to the answers…by now you should know that I call that “the back door play”.  In basketball, the back door play gets you an easy layup.
  18. DITW
  19. Trial and error!  For example, if d=7.2 inches then 2h = 25-7.2=17.8 inches so h=8.9 inches.  No good.  If it had fallen in the right range, we would then check if the number of steps came out odd.  Keep going until you find the one that works…
  20. DITW
  21. DITW
  22. Many people find it helpful to list out the data:

10,10,10,10, 11,11,11,11,12,13,15,15,15,17,20,21,21,27,31,34,55

Once you do that, finding the median is just a matter of finding the middle number.  Also, once you have done a few this way, you won’t need to any more.  You can just think: there are 21 states on the list so 10 of them will be greater than or equal to the median, 10 will be less than or equal to the median and the 11th one will be the median.  Start at the top of the chart and keep a running tally of how many states you have accounted for.  By the fourth row, you will have counted 10 states.  The median will be in the next row.

  1. DITW
  2. You can DITW or you can use trial and error with each answer choice.
  3. Linear functions are “evenly spaced”.  So to start,  figure out what goes between the first row and the second row.  Then you will know how much you have to go up by to get to f(3).
  4. DITW
  5. DITW
  6. This is yet another example where you are better off finding your own answers first and then checking which equation matches them.  Just draw a number line and you can easily see that the two points they are talking about are -1 and -7.  So check each answer to see which one works with both of those values.
  7. Let’s make up numbers again.  For example, if t= 25, then s = 80 and the average speed is 80/25=3.2 inches per second.  Now, it’s off to the answer choices!
  8. Hmm..if we drew a curve through these points it would be a downward parabola.  So you know it is B or D.  When x=4, it looks like y= 800 or so.  Plug in x=4 into B and D.  It won’t be a close call.
  9. Just try numbers…easy numbers.
  10. DITW
  11. DITW…remember the formulas are given in the front of the section
  12. If you don’t want to do the algebra, you can graph both functions on a graphing calculator and then trace along until you come to the intersection point.
  13. DITW
  14. If the average is .1 greater and there are 6 items then the total is .6 greater…
  15. Make a little chart, fill in the 480 dollars at the bottom,  then work your way back up, cutting the value in half each time.
  16. Here’s a hint: the 6 students represent 15% of the committee.  You can set up ratios to find the rest of the committee members.  For example, to find the administrators:  6/15 = x/25


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