ISEE Upper Level Math : ISEE Upper Level (grades 9-12) Mathematics Achievement
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Example Questions
Example Question #4 : Mean
Alice's numeric grade in her physics class is determined by four equally weighted hourly tests and a final, weighted twice as much as an hourly test. The highest score possible on each is 100.
Going into finals week, Alice's hourly test scores are 76, 85, 82, and 87. What must Alice make on her final, at minimum, in order to average 90 or more for the term?
It is impossible for Alice to achieve an average of 90 or better for the term.
It is impossible for Alice to achieve an average of 90 or better for the term.
Alice's grade is a weighted mean in which her hourly tests have weight 1 and her final has weight 2. If we call 
which simplifies to
Since she wants her score to be 90 or better, we solve this inequality:
Since it is established that 100 is the maximum score, Alice cannot achieve an average of 90 or more for the term.
Example Question #5 : How To Find Mean
Eric has taken four tests in his English class. His scores on the tests are 94, 87, 95, and 89. The upcoming final exam will be weighted as much as each of the previous four tests. What is the lowest score Eric can get on the final exam and still have a mean score of no less than 90?
84
85
86
87
85
The first step here, since you're working with the average (or mean), is to determine what is the sum of five test scores that will result in Eric earning at least a mean score of 90.
Start with the fact that he will need to make at least a 90 for his average score. Since you already have the average score, you're working backwards. You need to multiply 90 by 5 for the 5 test scores that will be used to get that average:
This tells you that the five scores - the four test scores and the final exam - will need to add up to at least 450 in total.
You know the four original test scores, so you can add those up:
So you know the four test scores add up to 365. To get an average of at least 90, the fifth score must bring that sum to at least 450. To find the minimum final exam test score, you subtract 365 from 450:
This tells you that Eric must score at least an 85 on the final exam to achieve an overall mean score of 90.
Example Question #4 : Mean
Consider the time Becky spends doing homework each night. What is the average number of hours Becky spends on homework each night (consider only Monday-Thursday)?
Monday: 3.2 hours
Tuesday: 1.1 hours
Wednesday: 2.7 hours
Thursday: 0.9 hours
1.900 hours
1.925 hours
1.975 hours
1.950 hours
1.975 hours
To calculate the average, find the sum of the total hours divided by the number of nights:
Example Question #3 : How To Find Mean
The mean of the following numbers is 
The mean is determined by dividing the sum of the values by the total number of values:
Example Question #611 : Isee Upper Level (Grades 9 12) Mathematics Achievement
What is the mean of the first ten prime numbers?
The first ten primes form the data set:
Add them, and divide by :
Example Question #8 : How To Find Mean
Consider the following set of scores from a math test. If the mean is 
Mean of the scores can be calculated as:
Where:
Example Question #612 : Isee Upper Level (Grades 9 12) Mathematics Achievement
The heights of a football team's members are 
The mean is the sum of all the data values divided by the number of values. So we can write:
Example Question #12 : How To Find Mean
Consider the following set of scores from a physics test. Give the mean of the scores.
The mean of the scores can be calculated as:
Where:
Example Question #64 : Data Analysis
The mean of five numbers is 
The mean of five numbers is equal to their sum divided by 
Where:
Example Question #65 : Data Analysis
The sum of 
The mean of eight numbers is equal to their sum divided by 
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