ISEE Upper Level Math : ISEE Upper Level (grades 9-12) Mathematics Achievement
Study concepts, example questions & explanations for ISEE Upper Level Math
All ISEE Upper Level Math Resources
Example Questions
Example Question #1 : How To Find The Missing Part Of A List
A pair of fair dice are tossed. What is the probability that the product of the numbers of the faces is greater than or equal to ?
Out of a possible thirty-six rolls, the following result in a product of twenty or greater:
This is eight out of thirty-six, making the probability
Example Question #1 : Sets
Ten students are running for student council; each member of the student body will choose four.
Two of the candidates are Kevin's brothers, Mickey and Steve. Kevin wants to vote for one, but not both, of his brothers. How many ways can Kevin fill out his ballot so that he can vote for exactly one of his brothers?
Kevin will choose three students from the eight who are not his brothers, and will do so without respect to order. This is the number of combinations of three from eight:
Kevin will also choose one of his two brothers. By the multiplication principle, Kevin has 
Example Question #691 : Isee Upper Level (Grades 9 12) Mathematics Achievement
Define
What is the natural domain of 
The only possible restriction of the domain here is the denominator 
This has no real solution, so the domain is the set of all real numbers, 
Example Question #5 : How To Find The Missing Part Of A List
Nine students are running for student council; each member of the student body will choose four.
The candidates include two of Eileen's sisters, Maureen and Colleen. Eileen wants to vote for one or both of them. How many ways can Eileen fill out her ballot so that one or both of her sisters is among her choices?
If Eileen wants to choose both sisters, then she will choose two out of the other seven candidates. This is the number of combinations of two out of seven:
If Eileen wants to choose one sister, then she will choose three out of the other eight candidates. This is the number of combinations of three out of eight:
Since there are also two ways Eileen can choose one sister, by the multiplication principle, she can fill out the ballot 
Add these two:
Example Question #2 : Sets
Define
What is the range of
Since 
The range is therefore
Example Question #7 : How To Find The Missing Part Of A List
The Department of Motor Vehicles wants to make all of the state's license numbers conform to two rules:
Rule 1: The number must comprise two letters (A-Z) followed by four numerals (0-9).
Rule 2: Numerals can be repeated but not letters.
Which of the following expressions is equal to the number of possible license numbers that would conform to this rule?
The first letter can be any one of the 26 letters, but after this choice is made, since the letter cannot be repeated, there are 25 choices for the second letter. Each of the next four characters can each be one of the 10 numerals, with repetition allowed. By the multiplication principle, the number of possible license numbers is
Example Question #6 : Sets
The Department of Motor Vehicles wants to make all of the state's license numbers conform to two rules:
Rule 1: The number must comprise two letters (A-Z) followed by four numerals (0-9).
Rule 2: Repeats are allowed, but neither of the letters can be an "O" or an "I".
Which of the following expressions is equal to the number of possible license numbers that would conform to this rule?
Repeats are allowed, so the first character can be one of the 24 allowed letters (26 minus the "I" and the "O"), as can the second; each of the next four characters can each be one of the 10 numerals. By the multiplication principle, the number of possible license plate numbers is:
Example Question #692 : Isee Upper Level (Grades 9 12) Mathematics Achievement
Find the missing part of the list:
The sequence pattern follows the rule:
Therefore,
Example Question #693 : Isee Upper Level (Grades 9 12) Mathematics Achievement
Which of the following can be the next number after 47 in the sequence below?
Each number in the set is the value of the preceding number multiplied by 2, plus 1:
Therefore, the next number in the set will be 47 times 2, plus 1. This gives us:
Example Question #694 : Isee Upper Level (Grades 9 12) Mathematics Achievement
Jack noticed that a group of prime numbers followed a pattern in which they increased by 2, then 4, in an alternating pattern:
(11 plus 2 is 13, 13 plus 4 is 17, 17 plus 2 is 19, 19 plus 4 is 23.)
Jack believes that this pattern applies for all prime numbers, not just this group.
Which of the following is the best counter argument to his belief?
7 is 4 less than 11.
Jack made a mistake on some of the addition in the set.
The next prime number, 29, breaks the pattern because it is 6 greater than 23.
19 is not a prime number.
The next prime number, 29, breaks the pattern because it is 6 greater than 23.
While Jack's pattern applies to the group of number that he selected, it will not apply for the next prime number, 29, because it is 6 greater than the previous prime number of 23. Therefore, the correct answer is:
The next prime number, 29, breaks the pattern because it is 6 greater than 23.
All ISEE Upper Level Math Resources
