If x and y are positive and sqrtx = y, which of the following must be equal 0?
A) x-y
B) x- sqrty
C) y-2x
D) y- x^2
E) y^2 -x
If 13≤31-2x≤39, which of the following represents all possible values of x?
(A) -9≤x≤4
(B) -4≤x≤4
(C) -4≤x≤9
(D) 9≤x≤22
(E) 22≤x≤35
How should I go about doing this question, and what’s the quickest way? Thanks for your help!
Which of the following must be negative whenever x>y>0?
A) x^2 -4xy + y^2
B) x^2 -2xy – y^2
C) x^2 – xy -2y^2
D) y^2 -x^2 -xy
E) y^2 -x^2 +xy
if x^2 – y^2 = x- y and x<y, what is the average (arithmetic mean) of x and y?
A) 0
B) 1/2
C) 1
D) x/2
E) y/2
Which of the following equations, together with 2x + y= 8, results in a system of equations with exactly one solution? A) -2x – y= -8 B) x+2y=0 C)2x+y=0 D) 2x+y=14 E) 4x+2y= 16
College Board released a bunch of sample questions this week for the new PSAT and SAT, which will make their debuts in October 2015 and March 2016, respectively. Over the next few days, I’ll be making posts working through each question, a few at a time, and commenting on them when I feel like I have (more…)
How’s everyone else doing on this quiz? ...
This content is for Members only.
Log In
Buy a Math Guide or Subscribe
Verify your Math Guide ownership
Log In
Buy a Math Guide or Subscribe
Verify your Math Guide ownership
How’s everyone else doing on this quiz?
Thanks to Hurricane Sandy, this has been a rough week for a lot of people. If you’re feeling charitable, please note that I am still giving away Math Guides for donations to the Red Cross. Let me note, before we get into this, that these challenge questions are WAY harder than anything you’d see on (more…)
When a student asks me how to solve a math problem, my default response is to show, if possible, how to solve it by plugging in, backsolving, or guesstimating. I do this because I figure if the “math way” was obvious, the student wouldn’t be asking me for help in the first place. Besides, problem (more…)
…Say what now? This isn’t tested on the SAT all that often, but it has appeared (you’ll find an example in the Blue Book: Test 3 Section 5 Number 8) and I’ve had a bunch of kids tell me lately that they don’t remember ever learning it in school. When you have two polynomials that (more…)
There are two kinds of proportionality (some call these problems “variation” problems, but I’m sticking with proportionality) problems that you might see on the SAT: direct and inverse. I’m going to cover both here since I’m in the business of preparing you for any eventuality, but you should know that the the former is much (more…)
Leonardo da Vinci totally <3’d parabolas. The parabola is actually a hugely important mathematical concept with tons of forms, properties, and even its own history. It can open up, down, left, right, or any other direction. It can be used to graph the trajectory of my last AT&T cell phone that I threw in a (more…)
Not all function questions have weird symbols, some are just vanilla f(x) type things. You’ve probably been working with the f(x) notation in school for some time now, but let’s review some of the things you’ll see over and over again on the SAT: Interpreting function notation One thing you’re definitely going to need to (more…)
source One of the SAT’s most nefarious tricks is the symbol function. That doesn’t mean you should let it intimidate you, though. In fact, symbol functions (and function questions in general) are some of the easiest hard questions you’re going to come across. Which is to say: these questions come late in sections because kids (more…)