Yeah, this is true. Although you have to sketch pretty carefully here, which I can see why some might dislike this question. But if you sketch it well enough or if you check the answer choices, this problem is pretty simple.
It’s simple for someone like YOU. 
I would hope! But objectively speaking, not many steps are needed.
I’d be interested in seeing them, if you have more examples.
It is going to take me a little time to go through the material I have collected from Khan Academy. Also I did not keep copies of all the questions I did, so I will have to go back to the website and collect more.
Here is one that bothered me, but for completely different reasons than those I discussed above:
There are multiple grammar errors in the wording of this question, and the diction is all wrong. It is written by someone who does not know how to write correctly in English.
The question begins:
“People start waiting in line for the release of the newest cell phone at 5 A.M.”
This sentence means that the newest cell phone was released at 5 AM, not that the people started to get on line at 5 AM. Misplaced modifier.
And the question continues:
“Assume that 6 AM is when time h=1.”
Wow. I don’t even want to get started on all the errors in the above sentence. College Board would never write a sentence like that. This is egregious.
And then the kicker:
“What does the 23 mean in the above equation?”
“the 23” ??? As in “the number 23”?
Compare “What does the 23 mean in the above equation?” to the language in the College Board question:
“Which of the following best explains how the number 61 in the equation relates to the scatterplot?”
Khan Academy questions are written in engineering-speak. If you can’t tell the difference, good luck to you on the writing section.
I find this really interesting. CB and Khan worked together on the online test prep in some way. I would think CB would have blessed the online material. It wasn’t done in a vacuum.
I am sure they blessed it. I am not sure whether they checked it first.
@Plotinus ah, yeah I agree with you on this one. It is worded quite awkwardly, and there are a couple other issues here, in addition to the ones you mentioned.
- Misplaced modifier, as you stated earlier. It likely means "People start waiting in line at 5 a.m. for the release..."
- h isn't really well-defined until we read the next sentence. We are also forced to assume that h increments (e.g. h=2 at 7 a.m.). Perhaps h could be the number of hours until 7 a.m., or until 11 a.m.
- "Assume that 6 a.m. is when h = 1" should probably be worded something like "Assume that when it is 6 a.m., the value of h is 1" (I could put "Assume that when it is 6 a.m., h = 1" but it is not generally good writing practice to mix variables with commas and other symbols).
Of course, the question is still solvable (answer A) but the wording seems awkward to me as well.
Just to show that there are widespread English mistakes in the Khan Academy math problems, here is another example:
The first sentence of this problem reads:
“The table above gives data about a group of students by whether or not they enrolled in college in the year following high school graduation and whether they were the first, second, or third child born in their family.”
“gives data by whether or not” ???
Ok. Maybe the math question writers would do well to spend a little time working through the verbal portion of the Khan Academy prep site?
I don’t think this is just nitpicking because one of the most challenging aspects of SAT math questions is their unusual wording. SAT math is not just about numbers and equations: it is also about language. Students need to practice with the same type of language they will face on the real test.
@Plotinus you’re right. However I don’t know if “gives data by whether or not” is actually grammatically incorrect, or is just a phrase that could be reworded slightly better. But there seem to be bigger issues at play here.
First off, the question should state that the students were from a random sample.
The question should also state “About how many students…” If 849 or 860 first-born students attend college immediately after graduation, this would not be enough evidence to reject the null hypothesis. Since 850 is the “best” answer, we are forced to select it.
I agree with you; good English is important for SAT math questions. It would be odd to even have an English section when they can’t firmly get the wording of other questions.
When writing mathematics, good English becomes even more crucial, as there are other rules and guidelines that should be adhered to when communicating math. The following proof of Fermat’s little theorem, while “technically” correct, would be a headache for me to read:
Modulo p, {1,2,3,…,p-1} is a residue system, so {a,2a,…,a(p-1)} is also a residue system. We know that (p-1)! ≡ a^(p-1) (p-1)! (mod p) because both sets are residue systems and therefore, their products are congruent mod p. Cancel out the (p-1)! to get a^(p-1) ≡ 1 (mod p).
These are fair objections you are raising. One hallmark of real SAT questions over the years is that they can be counted on to be written in meticulously correct manner. No grammar errors, no odd wordings, just consistently careful and concise problem statements. This has been so reliably true that I could train my students to trust the words they were reading. I doubt that the new test will abandon that standard but @Plotinus is presenting examples that show that the Khan material does not always clear the bar.
If this is pervasive, then Khan will move into the same category as all of the other fake tests. But they will have the benefit of being the official CB designee.
I don’t work for Khan. I can’t imagine that they had anything to do with the way questions were worded, or that CB did not have ample time to review and approve it all. Pretty sure they were fed the questions from CB. I definitely could be wrong, but it’s not the way I would have done business if I were CB.
I posted a tweet on the College Board Twitter site asking who writes the practice questions for the Khan Academy SAT prep, and here is the answer I received:
“All of the SAT-format practice questions have either been written and/or approved by the College Board.”
I take this to be a grudging admission that at least SOME of the questions were NOT written by College Board.
I am really curious to know what the approval process was for those questions.
On second thought, if College Board is writing “either …and/or” maybe it DID have a hand in those Khan Academy grammar mistakes!
I found some other questions whose number-crunching requirements seemed unSAT-like, but I don’t want to beat a dead horse. If people are still interested, I will post them tomorrow.
Or maybe not all of the Khan Academy practice is “SAT-format”?
@Plotinus my best guess is that they had someone test-solve them and just check that the question is okay.
I’m wouldn’t be surprised if some test prep material wasn’t test-solved at all - I remember our class taking an AP Calc BC practice test (since we had a sub teacher that day) and the test was full of mistakes and badly-worded questions to the point where some of us refused to do it.
For your guess to be correct MITer94, there would have to have been a very significant change in the meaning of the word “official” in the phrase “Official SAT Test Prep”.
The old meaning was: “written by the same people who write the real test”.
The new meaning would be: “the answers to the questions are checked for accuracy by the same people who check the answers of the real test for accuracy.”
This would be a pretty low bar to clear to make practice material “official”. There would be no one checking whether the questions had the same style, content, and language as the questions of the real test.
Here are some more illustrative questions:
One College Board and one Khan Academy Table Data question:
One more Khan Academy Table Data question:
I would like to note that I usually do not use a calculator to do SAT math questions. Of course a calculator is allowed, and of course most students do use their calculators a lot. I don’t think there is anything wrong with that given that a calculator is allowed by the rules. However, my default instrument for SAT math is a pencil. I only pick up my calculator when I encounter some “bad” numbers. If the numbers are easy, I am faster with a pencil. My calculator is usually just resting while I am doing SAT math. I NOTICE when I pick up my calculator.
When I started to do the Khan Academy Redesigned SAT practice, I noticed that I was reaching for my calculator very frequently. It got so that I was holding the calculator in my hand almost constantly. I was working through many-step problems on the calculator instead of on paper.
Ok, I thought. The Khan practice is for the redesigned SAT. Maybe this is how the redesigned SAT is: you have to do most of the arithmetic on the calculator.
So then I looked again at the CB Official Redesigned SAT practice tests. I have to admit that I have not worked through every math question of all four tests, but I have the general impression that I would use the calculator only a little more than I do during the old SAT, and much less than I do during the Khan SAT practice. It seems to me that the Khan problems have much more “bad number arithmetic” that do the new CB problems.
So the Khan problems are numerically harder. At the same time, it seems to me that they are conceptually and linguistically easier than are the hard CB SAT math problems. The Khan problems seem like “cookbook” problems with bad numbers. They don’t have those creative oddball twists and turns that we find on the harder CB problems. They don’t have unpredictable combinations of multiple skills from completely different areas. They also don’t have that very peculiar language of almost all CB problems. Some of them remind me of GMAT problems.
To come to the case in point, consider the College Board problem I have linked above.
This problem is very unusual in its wording. I think many students will have difficulty even understanding the language well enough to set up a strategy
The solution requires skills in four different areas: table data, ratio’s, systems of linear equations, conditional probability.
However, once you have understood the problem well, the solution requires only minimal calculations. I did only one operation on my calculator as I solved it, and only at very the end. The numbers are good except for one or two very short calculations.
I solved the problem as follows:
Step 1 In the first line of table, I wrote: f 5f
In the second line, I wrote: m 9m
18 122
Step 2: I wrote two linear equations using the table data: f+m = 18, 5f+9m=122
Step 3: I solved the system for f and m by elimination:
I multiplied the first equation by 5 and subtracted it from the second equation:
5f+9m=122
5f+5m=90
4m=32
m=8
f=18-m=18-8=10
Step 4: The last step is to calculate the probability that a right-handed student is female.
number of right-handed females=5f=50
number of right-handed students=122
Probability=50/122 (here I used my calculator – the only time)=.409836 rounded to .410
I tried to find a “hard” Khan probability table data problem to compare. Since the Khan problems are not numbered, it is difficult to say whether the sugar data problem is supposed to be at exactly the same level as the CB left-handed/right-handed problem. All I can say is that the Khan problem came up on a level 4 practice set, and level 4 is the highest level available.
Let me make some observations about the way the Khan question is formulated:
The English is pretty bad, although not as egregious as were the two early examples I posted. However, this is definitely not CB SAT language.
The table has 16 entries with 4 blank lines. All the numbers have decimal points. I haven’t seen CB table probability problems with numbers like these.
The question part refers to a percentage change of 11.4%. Really? We are supposed to use the percentage change formula with 11.4%? I haven’t seen that in CB either.
OK, TIME TO GET OUT THE CALCULATOR I think, even before I have finished reading the question.
Step 1:Disambiguate wording of the problem.
In setting up the solution, first I had to get past an ambiguity in the wording, “increase in sugar consumption.” Does “sugar consumption” mean “sucrose consumption” or consumption of all the different kinds of sugar? The table heading says “sugars” not “sugar” when referring to all the different kinds of sugar. But since the sucrose data lines were all filled in, I supposed "sugar consumption " meant consumption of all the things listed in the table.
Step 2:
There is a 11.4% increase between 1990 and 2000 of the bottom line of the table. So first we have to add up the last column to get the total in 2000.
Let f= high-fructose sugar consumption in 2000, t= total consumption in 2000.
Then the last column of the table becomes
29.8
9.9
f
t
where t=f+29.8+9.9 (here I used the calculator)=f+39.7
Step 3:
Total consumption in 2000 represented an 11.4% increase over the total consumption in 1990. From the table, total consumption in 1990 was 61.6. I hate the percentage change formula, so I used a shortcut.
(f+39.7)=(1.114)(61.6) At this point I put down my pencil and solved the remainder of the problem by calculator.
f+39.7=68.6
f=28.9
Step 3:
The relative frequency of high-fructose corn syrup in 2000 = f/t=28.9/68.6 (luckily I was still holding my calculator in my hand from step 3)=0.42=42%
I used the calculator for 3 operations in this problem. That’s triple the number of calculator operations that there were in the CB problem.
There are a few different areas combined in this problem: table data, percentage change, relative frequency. But this combination is very standard and not creative. It looks to me like a cookbook number-cruncher.
In sum, we have at least three major differences:
- Different language
- Different use of numbers
- Different way of combining diverse areas.
Here is my analysis of the second Khan table data problem posted at:
I am including a second problem as evidence that the differences I am discussing are not limited to one problem.
Language Comment:
The English of the problem is again pretty bad. There are at least three clear grammar errors:
“Irma conducts a survey comparing… versus…” The correct preposition with “comparing” is “to” not “versus”.
It would also be better to write “comparing the kinds of gifts mothers wanted to receive to the kinds of gifts they in fact received”
rather than “what kind of gifts mothers wanted versus what mothers actually received”.
2). On the second page, we have “The incomplete table at left”. This should be “The incomplete table to THE left”
3) On the second page, we have “the mothers that received flowers”. This should be, “the mothers WHO received flowers.”
Table Structure Comment:
We have a 5x5 table with 25 entires and two blank lines. I have not seen any tables like this in the CB material.
You can’t easily add up the lines to determine the missing information because there are too many numbers and the numbers are not round.
Solution:
Step 1: 10% of the mothers who received flowers actually wanted them.
Let x= the number of mothers who both received and wanted flowers (the first blank line in the table).
Since by now I have seen this type of problem several times, and I know I have to use my calculator, and I prefer not to have to pick up and put down my calculator constantly, I found a shortcut to do the calculation on the calculator in one step:
the ratio of the mothers who wanted and received flowers (x) to the mothers who received but did not want flowers (the sum of all the numbers in the received flowers column) is 1:9, so x is the sum of the other numbers in that column divided by 9
x=(65+33+30+59)/9 (here I used the calculator)=21 (rounded off).
Step 2: What percentage of mothers wanted flowers?
This is the number of mothers who wanted flowers divided by 800, the total number of mothers.
We have to add all the numbers in the Wanted Flowers row and divide by 800. Unfortunately, I had put down my calculator to write down 21 from the last step. I should have just continued the problem with calculator in my hand.
(11+21+20+26+26)/800=0.13=13%
The thing that really bothered me about this problem was that I had to add up a TWO LISTS of 5 TWO-DIGIT NUMBERS. I have never seen an CB SAT problem that requires adding up two lists of 5 two-digit numbers.
Adding up 5 two-digit numbers is very time-consuming and subject to data-entry errors, especially under test conditions. You have to be super-careful that you copy the numbers correctly into the calculator. So to me this looks like a problem that is also testing calculator data-entry skills, the kind of skills that data-entry clerks need. Is that what CB wants to test on the SAT?
I would like to raise another question about a Khan Academy problem I discussed earlier:
This problem is a standard independence problem. College enrollment is independent of being a first born iff the rate at which first borns go to college is the same as the rate at which the general population goes to college, i.e.,
x/ 1290 = 2268/3441
This is only one of many questions about independence that came up during my Khan Academy practice.
However, I never saw a question about independence on the old SAT. So I checked carefully through the 4 Official Redesigned SAT tests, and I could not find a single question about independence in them.
Does this mean that there are entire subject areas of math that will be tested by the SAT but that are not represented on the 4 Official Redesigned Practice Tests? And we have to go to Khan Academy to learn what these missing subject areas are?
Or does it mean that Khan Academy has thrown in some additional areas, just for good measure?
Will independence be tested on the SAT or not?
I think students would like to know.
Following…