# If x and y are positive and sqrtx = y, which of the following must be equal 0?

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?

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?

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?

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

# In a certain apartment building, residents are allowed to own exactly one dog, exactly one cat, or one dog and one cat…

In a certain apartment building, residents are allowed to own exactly one dog, exactly one cat, or one dog and one cat. No other pets are allowed. There are 22 cats and 17 dogs in the building. If there are 25 apartments that contain only one dog or one cat, how many apartments, in total, contain pets?

(A) 27
(B) 32
(C) 35
(D) 39
(E) 42

Thank you. 🙂

# Which of the following equations, together with 2x + y= 8, results in a system of equations with exactly one solution?

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

# New sample questions: Math part 6

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…)

# A little algebra practice for y’all

How’s everyone else doing on this quiz?

# Weekend Challenge – Epic playlist

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…)

# “Is there a math way?”

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…)

# Corresponding coefficients in equivalent polynomials

…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…)

# Direct and Inverse Proportionality (Variation)

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…)

# Parabola Schmarabola

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…)

# Plain-old (non-symbol) function questions

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…)