@DrSteve Thank you very much!!!
I have problem with the first question (Compare and contrast algebraic and geometric representations). Could someone explain me the solution. http://sat.collegeboard.org/practice/sat-skills-insight/math/band/700/skill/6
The function g has a negative y-intercept and a positive slope that is different from the slope of f. Choice (D) is the only one consistent with these facts.
Note: m and b are positive. It follows that 1/m is positive and -b/m is negative.
Hey @DrSteve ! I still have some problems with these geometric question…
http://f-picture.net/lfp/s018.radikal.ru/i510/1501/ed/21b3ab3f64da.jpg/htm
http://f-picture.net/lfp/s020.radikal.ru/i717/1501/74/910018f089a3.jpg/htm
Could you help me please ?
Here’s a hint for the first one: The diagonals of a rhombus are perpendicular, and in this case 30, 60, 90 triangles are formed (do you see why?).
For the second one, use the following facts:
(1) The figure is drawn to scale (it doesn’t say it’s not)
(2) The diagonals of a rectangle are congruent
(3) The diagonal not shown is a radius of the circle
Technical note: the solution I am suggesting is technically incorrect, but it does give the correct answer! For an extra challenge, see if you can explain why the solution is not quite correct.
Oh yes…I just got the solution of the second question. Firstly, i have to find the circumference of quarter of a circle
2rп=>(2)(6)п=>12п and then devide by 4, so =>3п
Secondly, SA and CT = 2r-8 = 4
and finally, we can just draw another diagonal of rectangle which will be radius of circle = 6
So, 6+4+3п= 10+3п
But, i didnt understand the first one. Ok, the diagonals are perpendicular, but why other two angles are 60 and 30?
It’s because the given diagonal is the same length as a side. So a side of the rhombus is twice the length of half the diagonal. Whenever you have a right triangle with a leg and hypotenuse in the ratio 1:2, you have a 30, 60, 90 triangle.
I should point out that we are also using the fact that the diagonals of a parallelogram (and in particular, a rhombus) bisect each other.
I have just got it! Thank you @MrSteve!
I am terrible at math, got a SAT Math score of 460. Anyone have suggestions on how to improve?
Can anyone explain the difference between Permutations and Combinations? I know one is when order matters, and one is when order doesn’t matter, but what exactly does that mean?
Like for example: You have 4 types of bread, A, B, C, and D. How many combinations of 3 different types of bread can you make?
How would I know if this is a permutation, or if it is a combination?
Basically, a permutation is a rearrangement of elements or objects where the order matters. A combination is similar, but order does not matter. For example, there are 5! permutations of the set {1,2,3,4,5}, but only one combination of 5 (i.e. one way to pick 1,2,3,4,5 with order irrelevant).
In your above question, read again. It says “combinations.”
Note: The word “permutation” might be misleading, because strictly speaking, a permutation of a finite set S is a rearrangement of all elements of S. If we are choosing a sequence of k elements from |S| = n elements, we usually call these the k-permutations of n, in which there are n(n-1)(n-2)…(n-k+1) of them.
Additionally, we use the word “permutation” this way, because the set of all n! permutations of {1,2,…,n} form the symmetric group. Hence, we need a clear definition of a permutation in order to use it.
So would the question on the SAT tell you if it’s a combination or not?
@ThatSpellingGuy111 usually not; you will have to determine yourself.
Use permutations (or k-permutations) when the order of which you select the objects matters.
Examples:
*Selecting president, VP, treasurer, secretary, historian from a class of 15
*Finding the number of 4-digit positive integers with distinct, nonzero digits
Use combinations when the order of which you select the objects does not matter.
Examples:
*Selecting a committee of 5 students from a class of 15
*Finding the number of 4-digit positive integers whose digits are in increasing order (hint: noticing that this is a combination is a bit tricky, but such a problem has appeared on the SAT before)
For practice, can you tell me how many ways you can do each of the above tasks?
Yo, interesting kind of math problem that I’ve seen on a few different practice tests but am pretty clueless on how to solve it. Here’s two versions of the sort of question I mean:
“The c cars in a car service use a total of g gallons of gasoline per week. If each of the cars uses the same amount of gasoline, then, at this rate, which of the following represents the number of gallons used by 5 of the cars in 2 weeks?”
“The price of ground coffee beans is d dollars for 8 ounces and each makes c cups of brewed coffee. In terms o c and d , what in the dollar cost of the ground coffee beans required to make 1 cup of brewed coffee ?”
I’m curious as to how these are supposed to be solved. Is there something I’m missing? Also, are there any prep books that cover this particular sort of problem? I’ve been cycling between Barron’s, Chung’s, Blue Book and CrushTheTest for math but nothing in any of those books have taught me how to solve a problem similar to this.
Much thanks.
@DressingIron These are mostly just basic (but sometimes tricky) algebra questions, and the best way to solve them is by practicing and being able to manipulate variables to achieve what you want to solve. Are you sure none of those prep books have any similar math problems?
For the first one,
Each car uses c/g gallons of gas in 1 week
→ 5 cars use 5c/g gallons of gas in 1 week
→ 5 cars use 2*5c/g = 10c/g gallons of gas in 2 weeks
For the second one, note that it costs $d to make c cups of brewed coffee, so it costs $d/c to make 1 cup. Not sure where the 8 ounces comes into play, but sometimes they throw extra info at you just to try to confuse you. But don’t fall for it!
Note: Another strategy is to just make up numbers to reduce the number of variables (e.g. c = 5, g = 10). But I don’t usually recommend this strategy, for two reasons: 1. It’s usually slow, inefficient, and you have to evaluate the answer choices after solving, and 2. Manipulating variables really isn’t that hard on the SAT. However, it may be a good strategy for someone who is weak at algebra, or simply someone who wants to check their answer by plugging in values.
Most students will want to solve these problems by picking numbers. This is a very basic SAT math strategy. Any decent prep book for weak to average math students will cover this strategy extensively as it can be used on such a large number of SAT math problems.
I have several articles and a video on this strategy, and there is a thread on this forum that I started a while back called “SAT Math Strategies” where I discuss some guidelines for using this strategy. You should be able to find it with a simple search.
@MITer94
On the president, VP, historian, secretary question i got 32760.
On the number of 4-digit positive integers with distinct, nonzero digits, i got 3024.
For the committee one, i got 3003.
For the increasing order question, i got 126.
I think my problem is I don’t know how to tell if it’s a permutation or a combination.
Like if I look at question about committee members, I’d say permutation because it matters which students are on the committee. I’d have done the same for the increasing order question, which is apparently a combination.
Then, for the 4 digit positive integer question with distinct, nonzero digits, I’d have said that is a combination because it doesn’t matter what order they’re in, as long as they don’t have a zero.
I still don’t get how I’m supposed to tell whether it’s a combination or a permutation. The “order matters” and “order doesn’t matter” definitions don’t really make any sense. Is there another way to explain it? Like with the terms: A, B, C, D?
@DrSteve
Do you know a simple way to explain permutation and combination so that it’s a black and white concept, if possible?