Here are a couple of examples of problems you might see at the top level of ISEE along with their solutions.
VERBAL
If we continue to use our resources in such large amounts, one day our supply will be ——.
(A) unlimited
(B) infused
(C) enriched
(D) exhausted
This is a sentence completion question that tests vocabulary and the student’s ability to understand the context of sentences. The correct answer is d).
To solve a sentence completion problem, the student needs to use the context of the sentence to deduce the meaning of the missing word; then, the student must use their vocabulary to choose the word from the answer options that has the closest meaning.
The award establishes that we are using our resources in great quantities; furthermore, it says that we are “continuing” to use it in large quantities. Therefore, the logical conclusion would be that one day our supply will run out or run out. The word that means “out of stock” or “out of stock” is exhausted, which is the answer choice (D).
If, by any chance, the student doesn’t 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 don’t make sense. Clearly using large amounts of resources over a period of time won’t cause them to become unlimited, that doesn’t make sense. Infused doesn’t make sense either, and enriched also doesn’t fit the context of the sentence well enough to be a compelling 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 the general formula follows (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 plug x = 9 into the above equation and see what value of y results; however, we quickly see that we don’t know the value of k, so we must find it first. The problem gives us other information that will help us find the value of k. Substituting the other values that the problem gives us (y = 20 when x = 6), we will obtain the following:
y=kx
20 = k*6
We can now 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 x. If x increases by 1, y increases by 10/3; if x increases by 3, y increases by 10. Using our new equation, we can find the answer to the question by substituting x = 9:
y = (10/3)*(9)
y = 30
The answer is 30.