Who wants to practice for the SAT on a hot summer day in New York?
I know, SAT math seems like the last thing on your mind when there’s a summer barbeque and a cool dip in the swimming pool to pass the time. But the school year is so busy that the summer, without the hours of homework and extracurricular activities, is actually the perfect time to start preparing for the SAT. So we at Cambridge Coaching are here to help you begin thinking about the SAT and wiping any rust that might have accumulated on your math skills.
Okay, so what SAT Math tips do you have?
While there are certainly strategies for SAT math problems, you can’t get an 800 on the math section simply by learning a few gimmicks. Acing the section requires a healthy dose of practice, and that means solving a lot of problems. So without further ado, let’s jump into an SAT math question.
The square of x is equal to 4 times the square of y. If x is 1 more than twice y, what is the value of x ?
(A) -4
(B) -1/2
(C) -1/4
(D) 1/4
(E) 1/2
Looks like this problem might require some algebra. How do we start?
You’re right, this is algebra, but it’s not as hard as you think. In the last Mechanic post on the SAT, the necessary equations were provided to you. Perhaps the most difficult – and most important – part of this problem is turning the words in the question into equations, or what the SAT calls “direct translation into mathematical expressions.” Re-reading the question, you can translate the two statements made into the following equations:
(1) The square of x is equal to 4 times the square of y: x2 = 4y2
(2) x is 1 more than twice y: x = 1 + 2y
Since we need to solve for x, we need to rewrite the first and second equations to substitute for y. Let’s make the following changes to each equation:
(1) Re-write 4 as 22 and re-arrange the right side of the equation so there’s only one squared term: x2 = (2y)2
(2) Subtract 1 from each side of the equation: x - 1 = 2y
Now we can substitute the 2y from equation 2 into equation 1 and solve for x: x2 = (2y)2 becomes x2 = (x-1)2. Calculating the square of x-1 yields x2 = x2 - 2x + 1, and x2 on each side cancels to create 0 = -2x + 1. From there, just a little arithmetic results in x = 1/2. The correct answer is E.
How did we know how to re-arrange equations 1 and 2 on this math problem?
This is the challenge with any problem with two or more algebraic equations. You should look at the equations and ask yourself first, what do you need to solve for, and second, what are the common terms that can be substituted for one another. Though I knew we needed to solve for x, my initial instinct was to re-arrange equation 2 to be equal to y. But taking a second look at the problem revealed that both equations could be re-written to isolate 2y and that this would create an easy arithmetic exercise. As I wrote earlier, there’s no easy trick that helps you do this, but more practice will help you identify the common terms.
Tune in again soon for the next installment of the Math Mechanic.
Comments