Posts tagged with: Blue Book

Explanation for Pg 543 question 2 of blue book. Thanks.

Read up on symbol functions here.

If k* = k(k – 1) for all k integers k, then 5* = 5(5 – 1) = 5(4) = 20.

Can you solve #11 on p.455 in the blue book?

Read the graph carefully. If you write down the coordinates of the given points, you get ordered pairs (1, 10), (3, 30), (5, 50), etc.  If you remember that your axes are L on the x-axis and W on the y-axis, then you see that those ordered pairs correspond to L = 10W.

Can you please answer question #8 on page 454 in the blue book for test #2?

You can break that into a 2\times 2 square and a4\times 6 rectangle.2\times 2=4 and4\times 6=24, so the total area of the figure is 28.

On page 452 in the blue book for question number 2 can you help me solve? I know it is a easier question.

5 minutes is 5/60 = 1/12 of an hour. So if the machine can fill 24 cartons in an hour, then it can fill (1/12)24 = 2 cartons in 5 minutes.

Hello , I have question on blue book page 406 number 24 (critical reading section) the answer is (E)emphasize the author’s position but can answer also be (d) suggest a focus fr further research ??

That last paragraph says: “So let me state this explicitly: A city is a natural system, and we can study it in the same way we study other natural systems and how they got to be the way they are.

The italics provide the emphasis, and the fact that what is italicized is the main idea of the passage makes E the perfect choice. There’s no suggestion there. He says “we can,” not “somebody should.” That’s a statement of possibility, not a suggestion.

I’ve touched upon inference questions in an earlier post (remember: ask yourself WHY something was written, not just WHAT is written). But logic-based inference questions get their own special article because they are a more specialized and advanced subcategory of inference questions. These questions truly test if you know WHY something was written. They don’t just ask what can be inferred or what a particular sentence suggests; those are reserved for the normal, easier inference questions.

These logic questions ask for things such as which of the following is most analogous or best represents the issue/event/phenomenon described in the passage. They require you to fully understand both the meaning and purpose of the passage, then apply that understanding to hypothetical situations. The SAT is checking whether you can accurately judge situations not discussed in the passage based upon logic directly derived from the passage.

Let’s take a look at a question from the OSSG (Official SAT Study Guide) 2nd Edition.

EXAMPLE — Logic-Based Inference Question
OSSG 2nd Edition
pg. 592 #20

The example passage is about bats. First off, notice what the question is asking: which of the following LEAST detracts. The ETS has been kind enough to capitalize that keyword for you, yet so many simply overlook it. Be very careful around LEAST, EXCEPT, and NOT questions. The right answer is the one that answers the question correctly, not necessarily the one that matches what the passage says.

So the first thing you need to do is to straighten out the question itself, figure out what it’s truly asking for. In other words, ask yourself what would something that detracts very little from the author’s argument look like? Probably something that firmly supports the author. If none of the choices directly support the author, then look for the second best thing: the choice that doesn’t oppose the author, basically a choice that bears no relationship to the author’s argument. And if all choices oppose the author, then look for the third best thing: the choice that opposes the author to the least extent or degree.

Of course to answer the question, you first have to understand what the author’s argument is. Let’s go to the passage for that, pg. 591. Read lines 25-42 carefully.

Again, there are two levels of understanding:
1.WHAT something says (superficial first level)
2.WHY something was said (deeper second level)

WHAT is said:

  • Typically humans sleep at night.
  • Our “normal” time is daytime, when we are awake.
  • Anything that doesn’t follow our “normal” schedule is up to no good…scary…make us feel vulnerable & defenseless.
  • Bats operate outside our “normal” schedule because they are awake at night.
  • This makes bats frightening to humans.

WHY it is said:

  • To provide the logical framework we need to answer the question.
  • The logic of the author’s argument is simple:
    • “Normal” daytime hours = humans feel safe
    • Abnormal nighttime hours = humans feel threatened

So look at the answer choices and see if any support the logic above. Anything? Sadly no.

A)WRONG. If many people work at night, then by the author’s logic, these people would scare most other people. But we all know some night owl folks and probably aren’t scared of them. You may even be a night owl yourself, studying for the SAT late into the night. Are you scary? Probably not. So this definitely opposes the author’s logic that night dwellers are scary.

B)WRONG. The author says night animals are scary. Yet, the choice says owls (nocturnal animals) don’t cause fear. This is the opposite of the author’s claim/logic, so B is wrong.

C)WRONG. The author says daytime animals are nice and safe. Predators are pretty scary stuff, yet they are awake during the day? Da hell? Opposes author’s logic, so C is wrong.

D)WRONG. Bats have positive qualities?! Not according to the author’s logic that bats = nighttime = negative/threatening. So this is wrong too.

E)RIGHT. Okay, who cares if our dreams come from our personal lives? That doesn’t have anything to do with the author’s claim that day = nice/safe and night = bad/scary. Sure, this choice doesn’t support the author’s claim, but it also doesn’t detract. Since all of the other choices heavily detract, E is the best choice as the only answer that doesn’t detract.

EXAMPLE — Logic-Based Inference Question
OSSG 2nd Edition
pg. 579 #17

This example is about the decreasing involvement of women in business. The question asks which of the following would most directly support the author’s viewpoint (that women are becoming less and less involved in business).

Try it out yourself first, then check out the explanations below.

A)WRONG. Both raising status and assuming greater responsibilities have nothing to do with women becoming less involved in business. Note: “greater responsibilities” by itself doesn’t specify greater responsibilities in business. Since this choice is unrelated, it does not support the author.

B)WRONG. Writing novels has nothing to do with running businesses, so this choice doesn’t support the author’s claim.

C)WRONG. Working in factories shows MORE involvement in business, not less. Definitely does not support author; in fact, this choice directly opposes the author’s view.

D)RIGHT. If married couples aren’t running business together (jointly) anymore, then either the men or the women are becoming less involved in business. While the choice doesn’t specify if women are the ones becoming less involved, this is the only choice that presents the possibility of women retreating from business.

E)WRONG. Academic institutions have nothing to do with running businesses. This is unrelated, hence unsupportive. Not detracting, but not supportive either.

-Peter

Peter Peng is a SAT/ACT tutor and college admissions essay consultant based in the greater Los Angeles area. He is currently working on a book entitled The SAT Decoded and can be reached at peter@pwnthesat.com.

Special nerd note: #20 in Section 4 is pretty much
my favorite
 Guesstimate question of all time.

The College Board’s latest The Official SAT Study Guide with DVD is exactly the same as the 2nd edition, except that it comes with a DVD containing a bit of extra content. I can see the utility in the SAT timer it includes, but otherwise the only content of value on the DVD is one additional test—the January 2008 QAS. I went through that test yesterday so I could update the Blue Book Breakdown in my Math Guide (I’m calling it Test 11). A PDF of that page (with page number references, etc.) is available here for book owners. For everyone else, below is an HTML version of that table with links to some important strategies.

§
p
#
Techniques and concepts
Diff.
3
8
1
Factoring
1
3
8
2
You could plug in here, ya know.
1
3
9
3
In a parallelogram, as in a rectangle, opposite sides are equal. Fill in all given lengths.
2
3
9
4
Read the graphs carefully
2
3
10
5
3
3
10
6
3
3
10
7
3
3
10
8
4
3
11
9
Uh…subtraction?
1
3
11
10
2
3
12
11
2
3
12
12
Inequalities
3
3
12
13
Draw it. (5, 0) is on the circle, so the distance to (13, 0) is 8.
3
3
12
14
At 5 feet you have 2 posts. At 10 feet you have 3 posts. The number of posts is 500/5 + 1.
4
3
13
15
3
3
13
16
3
3
13
17
4
3
13
18
The key here is to figure out the total journey’s time, which is 30 min + 15 min.
5
4
14
1
1
4
14
2
Plug in to clarify the relationship if you want.
1
4
15
3
Draw it, and then maybe backsolve if the answer doesn’t jump out at you.
2
4
15
4
1
4
15
5
You’ll probably just use your head, but your calculator’s fraction function is a safety net.
2
4
15
6
Read the graph carefully. Note that the bars add up to more than 100%.
3
4
15
7
Backsolve, or just do the algebra: x + 1 = 2x – 1
2
4
16
8
For Pete’s sake, just list them!
2
4
16
9
2
4
16
10
3
4
16
11
Logic. You don’t know anything about I or II, but if Greta never goes to mysteries, III is true.
3
4
17
12
3
4
17
13
The ones on the ends add 4 to the perimeter. The others add 3.
3
4
17
14
You probably should just do the algebra here. Combine like terms and you get 2x < 0.
3
4
18
15
4
4
18
16
Read carefully! Wednesday doesn’t work because Anna didn’t hit the 5 total servings goal.
4
4
18
17
3
4
18
18
The surface area of the big cube is 6. The surface area of a small cube is 6/4.
4
4
19
19
5
4
19
20
Guesstimate, or connect big circle centers to make isosceles right triangles.
5
8
32
1
2
8
32
2
1
8
33
3
3
8
33
4
2
8
33
5
Draw the square and the other diagonal, then draw the points.
2
8
33
6
Plug in, saying the original quantity was 100. You eat questions like this for breakfast.
2
8
34
7
2
8
34
8
Shortcut: write out all of set T, then look for multiples of 6 in it.
2
8
34
9
3
8
34
10
This is a rare instance of “It cannot be determined.” Could have 14 to 26 oatmeal cookies.
1
8
35
11
4
8
35
12
4
8
35
13
4
8
36
14
2 is the additional height you get each time a pail is added.
4
8
36
15
Know the properties of even and odd numbers, or plug in a bunch of possibilities.
5
8
36
16
Quick and dirty: Graph (or look at the table of values) on your calculator. 
5

This breakdown is meant to help you analyze and categorize your mistakes after you’ve taken Practice Test 3 in the Blue Book. The whole idea is that the best thing you can do to improve your score is to understand your weaknesses, and then drill the hell out of them to make them strengths. Click to see similar breakdowns for Blue Book Tests 1 and 2.

§
p
#
Techniques and concepts
Diff.
2
514
1
I suppose you could backsolve if you wanted to.
1
2
514
2
1
2
515
3
Spatial reasoning is fun!
1
2
515
4
25% is a quarter. A quarter of a circle is a right angle. Which angles are acute?
2
2
515
5
2
2
516
6
2
2
516
7
2
2
516
8
If you’re not immediately sure what (–0.5)2 is, just put it in your calculator..
2
2
516
9
3
2
517
10
3
2
517
11
3
2
517
12
Read the Venn diagram carefully. It might help you to darken the boundaries of A and B.
3
2
517
13
Percents, Backsolve 
3
2
518
14
3
2
518
15
Percents
3
2
518
16
4
2
518
17
4
2
519
18
Draw them and count.
4
2
519
19
4
2
519
20
5
5
525
1
1
5
525
2
1
5
526
3
1
5
526
4
Read the question carefully.
1
5
526
5
4
5
527
6
3
5
527
7
Draw it carefully.
4
5
527
8
FOIL it. Corresponding coefficients will be equal, so (–8 – k) = –5k and m = 8k.
5
5
528
9
1
5
528
10
2
5
529
11
2
5
529
12
3
5
529
13
This is a tricky graph. Read it carefully.
2
5
529
14
Write the equation: 5n = n + 5. Solve for n.
3
5
530
15
4
5
530
16
4
5
530
17
For every 4 inches of strip, there are 5 inches of edge. Use ratios.
4
5
530
18
Square’s side = 8, so R is (4, 8). Plug into the equation to solve for a. Parabolas.
4
8
543
1
Do the algebra: (3/4)n = 18.
1
8
543
2
2
8
544
3
Read the graph carefully.
1
8
544
4
Read the question carefully.
2
8
544
5
2
8
545
6
2
8
545
7
2
8
545
8
2
8
545
9
3
8
546
10
3
8
546
11
Do the algebra.
3
8
547
12
Reasoning: Can they all be negative? No. All but one? Yes, if the one is big enough.
3
8
547
13
List the combinations methodically.
4
8
547
14
Graph amplification 
3
8
548
15
Follow the pattern remembering that all negative values are less than 100.
4
8
548
16
5

This is straight out of the PWN the SAT Math Guide, except I’ve deleted the page number references and inserted links to certain techniques. View the breakdown of Blue Book Test 1 here.

§
p
#
Techniques and concepts
Diff.
2
452
1
Patterns
1
2
452
2
1
2
453
3
Read the graph and the question carefully.
1
2
453
4
3
2
453
5
Actually turn the book on your desk and see what the shape looks like when rotated.
2
2
454
6
Do the algebra: 2x + 3 = 10, what is 4x?
2
2
454
7
2
2
454
8
Break it into two rectangles.
2
2
454
9
Do the algebra carefully.
2
2
455
10
3
2
455
11
First, read the graph carefully: the scales on the axes are different! Lines.
2
2
455
12
3
2
455
13
Read the Venn diagram carefully. It might help to darken the boundaries of Y and Z.
3
2
456
14
3
2
456
15
4
2
456
16
3
2
456
17
3
2
457
18
4
2
457
19
This one is a pain, but backsolving works if you don’t want to do algebra.
4
2
457
20
5
5
463
1
Well, x must be 0, right?
1
5
463
2
1
5
464
3
Plug in, Sets 
2
5
464
4
2
5
464
5
2
5
464
6
3
5
465
7
Graph amplification, or just plug in and graph if your calculator can.
3
5
465
8
4
5
466
9
Do the algebra: 2x + 5 = 14, solve for x.
2
5
466
10
3
5
467
11
How many times does 0.25 fit into 8?
2
5
467
12
4
5
467
13
3
5
467
14
3
5
468
15
Just walk through each choice keeping the goal in mind (and write everything down).
3
5
468
16
4
5
468
17
Do the algebra: 1 + 0.07(t – 20) = 0.06t, solve for t.
4
5
468
18
Tricky (but fun!): p = 16k (count carefully) and a = 10k2. Set them equal and solve for k.
5
8
481
1
Simplifying fractions?
1
8
481
2
1
8
482
3
1
8
482
4
2
8
482
5
2
8
483
6
2
8
483
7
It might help to plug in, but make sure your numbers make sense on the diagram.
3
8
483
8
3
8
484
9
Graph reflection 
2
8
484
10
3
8
484
11
Inequalities 
3
8
485
12
Picture that circle as a wheel rolling along. Those rectangles could be at any orientation.
4
8
485
13
4
8
485
14
5
8
486
15
Figure out what Tom paid for the room using percents, then multiply that by 4.
5
8
486
16
5

I broke down every Blue Book test when I wrote the Math Guide. In the book there are page numbers instead of links, obviously.

The idea here is that you can take a test, and use the results from that test to really identify some weaknesses. Then you drill those weaknesses before taking another test. Awesome, right?

I’m running a promotion throughout February that will give away some free copies of the book. Want in? The details are here.

§
p
#
Techniques and concepts
Diff.
3
396
1
Try every answer choice.
1
3
396
2
Read the question carefully.
1
3
397
3
1
3
397
4
Read the graphs and question carefully.
2
3
397
5
Read the graph and question carefully.
1
3
397
6
Read the graph and question carefully.
2
3
398
7
2
3
398
8
2
3
398
9
3
3
398
10
2
3
399
11
3
3
399
12
Read the graphs and question carefully.
3
3
399
13
Just list out the pattern terms.
3
3
399
14
3
3
400
15
3
3
400
16
3
3
400
17
4
3
400
18
4
3
401
19
5
3
401
20
Percents 
5
7
413
1
Read the graph carefully.
1
7
413
2
1
7
414
3
2
7
414
4
Plug in for m if you’re stuck.
2
7
414
5
3
7
415
6
3
7
415
7
3
7
415
8
5
7
416
9
Do the algebra.
1
7
416
10
Um…rounding?
2
7
417
11
2
7
417
12
Draw it carefully, then guess and check.
3
7
417
13
There are 30 days in April and you’re told what happens every 5 days. Use ratios.
3
7
417
14
Figure out the difference between each term (it’s 20). Take no prisoners.
4
7
418
15
3
7
418
16
Be super careful and use trial and error. Starting point: X is the biggest.
4
7
418
17
4
7
418
18
Don’t be fooled, this question is easy as long as you can read function notation.
5
8
419
1
Read the graph carefully. Boy, there sure are a lot of these in this test!
1
8
419
2
1
8
420
3
1
8
420
4
Draw it. The sides of the square are 4.
2
8
420
5
Make four blanks, and fill them in based on what the question says.
1
8
421
6
3
8
421
7
3
8
422
8
3
8
422
9
3
8
422
10
3
8
423
11
3
8
423
12
4
8
423
13
3
8
424
14
4
8
424
15
5
8
424
16
4

I designed the Math Guide to be read (and worked through) cover-to-cover alongside the Blue Book, but it’s never been my philosophy that test prep is a one-size-fits-all kind of thing. You don’t have to work through the book linearly to have a successful experience with it. Jump all over the place, if that suits you. Like so:

  1. Take Blue Book Practice Test #1. Correct and score it. That score is your baseline.
    1. In the breakdown in the back of my book for Test #1 (sample of Test #3’s page here), highlight every question you got wrong, and write down the techniques and relevant page numbers.
    2. Work through every chapter (sample chapter) that you’ve written down more than once.
    3. Do the short drills at the end of each chapter. Use my handwritten solutions to understand any mistakes you make.
    4. THIS IS IMPORTANT: Go back to the Blue Book now, and redo every question in the test you got wrong, making efforts to apply the concepts you read about in the book. New techniques won’t be easy or feel natural the first time, but if you want to change your scores, you’re going to have to change your approach.
  2. Read the Strategies chapter in my book. It’ll give you something as you do all the actual math work. You need to know how the test is designed, and how to use that to your advantage, and how not to fall into some of the most common traps. 
  3. Take Blue Book Practice Test #4. Yes, I know this is out of order. Only tests #1-3 have fully accurate scoring tables, so save #2 and #3 for the end of your prep. For this test, record your score as the exact middle of the range of scores you get from the scoring table. Repeat steps A-D for Test #4.
  4. Do Diagnostic Drill #1 in my book.
    1. Use the answer key and technique guide at the end of the drill. Make special note of problem types you’ve been missing over and over again. At this point, it’s safe to call those weaknesses.
    2. Reread the chapters corresponding to your weaknesses again, and use the guides at the end of each chapter to do all the problems contained in Blue Book Tests #7-10 that require those techniques.
  5. Take Blue Book Test #5. Again, record your score as the middle of the range. Repeat steps A-D.
  6. Do Diagnostic Drill #2 in my book. Repeat steps a and b above.
  7. Take Blue Book Test #6. Repeat steps A-D, recording your score as the middle of the range. Take note of any weaknesses that persist. Use the guides at the end of each chapter aimed at your weakness to revisit EVERY question from Test #1 and Tests #4-10.
  8. Take Blue Book Test #2. You’re back to real, previously administered tests now, with accurate scoring tables. Take note of your improvement from the first test you took, and highlight any areas that still require attention. Reread the chapters for any remaining weaknesses AGAIN (yes, I know you’re rereading them over and over again) and revisit the relevant questions in every test except Test #3.
  9. OPTIONAL: Take Diagnostic Drills #3 and #4 in my book. These drills are hard, so if you’re not shooting for super-high scores, you needn’t drive yourself crazy here.
  10. Take Blue Book Test #3. Time it so that you’re doing this a few days (NOT the day before) your SAT. You want this to be an accurate prediction of your score on test day. Think of it like your dress rehearsal.
  11. Get in there and PWN the SAT for real. Do it.

 

Some notes
  • There are 6 full tests in this plan. It’s not something you can do overnight. If you want to do well on the SAT, you need to devote significant time to the task. I think 2 months is the minimum amount of time you should spend on the process.
  • This is obviously just a plan for the math section. You might want to devise a similar plan for the other two sections, using resources like The Ultimate Guide to SAT Grammar, which contains a similar blue book breakdown for writing questions.
  • As I said above, I don’t believe in a one-size-fits-all approach. If this seems a bit too chaotic and unfocused for you, that’s OK. I think this plan will work well for some people.
  • If you have questions as you go, ask me, or check the Blue Book Solutions list to see if there’s already a good explanation for your question available.
  • I might edit this page now and then, based on feedback I get from readers (both tutors and students). So if you think I’m missing something, comment away!

In the Blue Book, about this common:

Screengrab from the PWN the SAT Math Guide

I’m not saying you need to plug in numbers for each (or even most) of these. But I am saying you should be aware of how often you have the option.

I recommend anyone who’s planning to prepare for the SAT purchase The Official SAT Study Guide (you’ll see me refer to it a lot on this site simply as the Blue Book), but that doesn’t mean I think it’s the world’s greatest prep book. In fact, I find the whole first half of it to be pretty weak.

It makes sense that it would be, if you think about it. The College Board wants to sell books, but at the same time prop up their test as the go-to exam for college admissions. They can’t very well sell you a book that’s going to reveal every strategy necessary to ace the test, they’d be putting themselves out of business. So they sell you a book full of very good practice tests, and very mediocre strategies.

They know that the back cover of their book (you’ll see it when you buy it – it insists that there are no tricks to help you get a better score) is baloney. They know that the first half of the book isn’t that helpful. But they need to prop up the myth that their exam is a pure measure of your academic prowess. They can’t very well admit that it’s susceptible to test-specific strategies and tricks, and that kids who prep with someone who knows them have a huge advantage!

So buy the book, and do ALL the tests. They’re written by the same people who write the SAT, and in fact the first three tests in the 2nd edition were real SATs (they’re the October 2006, January 2007, and May 2007 (Saturday version) tests, respectively). But don’t take the back cover, or the first half of the book, too seriously.