The Must Know SAT Math Words

When I took the math portion of the SAT, there was one type of question I was not looking forward to—the word problems. With symbols, numbers, variables, equations, and words all combined into one, these problems were stacked with different types of information so much so that my head would literally burst trying to figure what the question was even asking me. It wasn't until grinding problem after problem that I began seeing a pattern and figuring out a strategy in getting these word problems correct.

The Strategy that Helped me:

The best strategy that helped me was translating key words into math. When I cyphered though a word problem, I would cross of the key terms I knew referenced a math concept, and replace it with a math symbol I was aware of. That way, I was sort of condensing this long, verbose word problem into this pseudo-algebraic statement that I could understand.

Math Keyword List:

So here is a comprehensive list of the most important SAT key words that I created to get the math word problems under check. I formed the list based on the 8 SAT practice tests and almost all the old math SAT practice exams that I had took in order to provide a comprehensive list to help you conquer the SAT math word problems.

Practice Problem Set 1

$1$.
Suppose John has only green and red apples in his grocery bag. If the ratio of the number of green to red apples in his bag is $(k - 5)$ to $(k - 3)$ where $k$ is an integer greater than $4$, what's the probability John will randomly pick a red apple from the bag in terms of $k$?

(a) $\frac{k - 3}{2(k - 4)}$

(b) $\frac{k - 3}{k - 4}$

(c) $\frac{k-3}{4}$

(d) $\frac{k - 5}{2k - 8}$

$2$.
If $(2n + 1) > (5n + 1)$, then what can we say about $n$?

(a) $n < 0$

(b) $n > 0$

(c) $n = 0$

(d) None of the above

$3$.
Suppose $k$ is an integer such that $x = 2k$ and $y = 2k + 1$. What might $k$ be such that $\frac{y}{x}$ is an integer?

(a) $\frac{1}{2}$

(b) $1$

(c) $0$

(d) None of the above

$4$.
For what value(s) of $n$ is $n^2$ not equal to $2n$?

(a) $n = 0$

(b) $n = 2$

(c) both (a) and (b)

(d) None of the above

$5$.
Given the expressions below, what is the numerical value of $x$?
   (i)   $4$ of $x$ is $5$ more than $y$

   (ii)  $z$ divided by $y$ is $2$ less than $2$ of $y$

   (iii) $y$ divides $z$ is $2$ fewer than the second largest factor of $12$

(a) $x = 1$

(b) $x = 2$

(c) $x = 3$

(d) $x = 4$

For numbers $6$ and $7$ please refer to the description below:

There are $500$ students at the prestigious Redacted University. Recently the flu has been circulating around the area causing many people to get sick. Suppose that $\frac{1}{5}$ of all students are sick due to the flu at school today and the rest are healthy. The next day, a staggering $\frac{3}{5}$ of healthy students become sick and only $\frac{1}{5}$ of sick students become healthy.

$6$.
What is the proportion of all students who are healthy the next day?

(a) $\frac{1}{25}$

(b) $\frac{8}{25}$

(c) $\frac{9}{25}$

(d) $\frac{16}{25}$

$7$.
Exactly how many students are healthy the next day?

(a) $20$ students

(b) $160$ students

(c) $180$ students

(d) $320$ students

$8$.
What answer choice is equivalent to the expression $x^3 - 64$?

(a) $(x - 4)(x^2 + 4x + 16)$

(b) $(x - 4)(x^2 - 4x + 16)$

(c) $(x - 4)^3$

(d) None of the above

$9$.
What answer choice is equivalent to the expression $x^3+ 2x^2 - 4x - 8$?

(a) $(x - 2)(x^2 + 4)$

(b) $(x^2 + 4)(x + 2)$

(c) $(x^2 - 4)(x^2 + 4)$

(d) $(x-2)(x + 2)^2$

Challenge Problem:

$10$.
Suppose k is an integer such that $x = 2k$ and $y = 2k + 1$. What can we say about $x + y$?

(a) $x + y$ is always even

(b) $x + y$ is always odd

(c) Can be both even or odd

(d) Neither even nor odd

Answer key:

1.   a
2.   a
3.   d
4.   d
5.   b
6.   c
7.   c
8.   a
9.   d
10. b