Here are a couple of sample problems that you can see in the top-level ISEE along with their solutions.

VERBAL

If we continue to use our resources in such large quantities, one day our supply will be ——.

(A) unlimited

(B) infused

(C) enriched

(D) out of stock

This is a question to complete a sentence that assesses the vocabulary and the ability of the student to understand the context of the sentence. The correct answer is d).

To solve a sentence completion problem, the student must use the context of the sentence to deduce the meaning of the missing word; then the student must use his vocabulary to choose the word from the answer options that has the closest meaning.

The sentence says that we are using our resources in large quantities; In addition, it says that we are “continuing” to use it in large quantities. So the logical conclusion would be that one day our supply will run out or run out. The word that means “exhausted” or “exhausted” is exhausted, which is the answer choice (D).

If, by chance, the student does not know the definition of “exhausted” but knows the definitions of the other three words, it is still possible to answer the question by eliminating the rest of the answers because they do not make sense. Clearly, using large amounts of resources over a period of time will not make them unlimited, that does not make sense. Infused doesn’t make sense either, and enriched also doesn’t fit the context of the sentence well enough to be an attractive answer.

MATH

If y is directly proportional to x, and if y = 20 when x = 6, what is the value of y when x = 9?

This problem is an algebra problem that tests the student’s knowledge of direct variation. If one variable is directly proportional to another, then it follows the general formula (by definition):

y = kx

This means: as x increases, y increases at a rate proportional to k times x, where k is a constant real number. The problem asks us to find y for a certain value of x. To do this, we would insert x = 9 in the previous equation and we would see what value of y is; however, we quickly see that we do not know the value of k, so we have to find it first. The problem gives us other information that will help us find the value of k. Replacing the other values ​​that the problem gives us (y = 20 when x = 6), we will obtain the following:

y = kx

20 = k * 6

Now we can solve for k by dividing both sides of the equation by 6:

k = 20/6 = 10/3

Now that we know k, we know that the general equation is:

y = (10/3) x

This means that as x increases, y increases at a rate proportional to 10/3 of that of x. If x increases by 1, y increases by 10/3; if x increases by 3, and increases by 10. Using our new equation, we can find the answer to the question by plugging in x = 9:

y = (10/3) * (9)

y = 30

The answer is 30.