All ISEE Upper Level Math Resources
Example Questions
Example Question #12 : Data Analysis And Probability
A popular word game uses one hundred tiles, each of which is marked with a letter or a blank. The distribution of the tiles is shown above, with each letter paired with the number of tiles marked with that letter. Notice that there are two blank tiles.
What percent of the tiles are marked with consonants?
Note: for purposes of this question, "Y" is a consonant.
Counting the number of tiles with vowels is much easier.
Out of the 100 tiles, there are nine "A" tiles, twelve "E" tiles, nine "I" tiles, eight "O" tiles, and four "U" tiles. This is a total of
tiles out of 100.
There are also two blanks, so the number of tiles marked with consonants is
56 out of 100 is 56%.
Example Question #11 : Data Analysis And Probability
Refer to the above graph, which shows the high and low temperatures for Kingdom City over a one-week period.
Between which two consecutive days did the high temperature show an increase?
Between Monday and Tuesday
Between Tuesday and Wednesday
Between Wednesday and Thursday
Between Thursday and Friday
Between Monday and Tuesday
Examining the high temperature line, it can be seen that, among the four choices given, only the segment connecting Monday to Tuesday has a positive slope (lower left to upper right).
Therefore, of the four choices, Monday to Tuesday is correct.
Example Question #16 : Data Analysis And Probability
A popular word game uses one hundred tiles, each of which is marked with a letter or a blank. The distribution of the tiles is shown above, with each letter paired with the number of tiles marked with that letter. Notice that there are two blank tiles.
What percent of the vowel tiles are marked with an "A"? (Nearest whole percent).
Note: for purposes of this question, "Y" is a consonant.
There are nine "A" tiles, twelve "E" tiles, nine "I" tiles, eight "O" tiles, and four "U" tiles. This is a total of
vowel tiles.
Out of these tiles, 9 are marked with an "E"; this is
.
This rounds to 21%.
Example Question #21 : Data Analysis And Probability
Refer to the above graph, which shows the high and low temperatures for Kingdom City over a one-week period. The temperatures at left are given in degrees Fahrenheit.
Temperatures given in degrees Fahrenheit can be converted to the Celsius scale using the formula
Express the highest temperature of the week in degrees Celsius (nearest whole degree).
As can be seen below, the highest temperature for the week was 78 degrees Fahrenheit, on Tuesday.
To convert this to degrees Celsius, set and substitute in the given formula:
. The correct choice is .
Example Question #13 : Tables
Refer to the above graph, which shows the high and low temperatures for Kingdom City over a one-week period.
The high temperature on Wednesday occurred at 1:00 PM; the low temperature, at the end of the day (midnight). The temperature drop was steady. What was the average drop in temperature per hour between 1:00 PM and midnight (nearest tenth of a second)?
1.7 degrees per hour
2.1 degrees per hour
1.3 degrees per hour
2.5 degrees per hour
1.3 degrees per hour
As can be seen in the diagram below, the high and low temperatures on Wednesday were, respectively, 74 and 60 degrees, for a drop of degrees.
This drop occurred over a period of hours, for an average drop of
degrees per hour. The quotient of this is seen below:
This rounds to 1.3 seconds.
Example Question #571 : Isee Upper Level (Grades 9 12) Mathematics Achievement
A popular word game uses one hundred tiles, each of which is marked with a letter or a blank. The distribution of the tiles is shown above, with each letter paired with the number of tiles marked with that letter. Notice that there are two blank tiles.
All of the consonant tiles are placed in a box. It is desired to place just enough of the vowel tiles so that the probability of drawing a vowel is . How many vowels must be placed in the box?
Note: for purposes of this question, "Y" is a consonant.
There are nine "A" tiles, twelve "E" tiles, nine "I" tiles, eight "O" tiles, and four "U" tiles. This is a total of
There are also two blanks, so the number of tiles marked with consonants is
.
For the probability of drawing a vowel tile to be , the ratio of consonant tiles to vowel tiles must be
- that is, 2 to 1.
If we let stand for the number of vowel tiles to be added, then
vowel tiles.
Example Question #12 : Tables
In a class of students, a poll was taken to see how many siblings students had. The results in the poll were then made into a table.
Number of Siblings | Number of Students with the Specific Number of Siblings |
0 | 5 |
1 | 9 |
2 | 4 |
3 | 2 |
What is the mode for the number of siblings for this class?
Recall that the mode is the number that appears most often in a data set.
For this class, students only have sibling. Thus, appears the most often in this data set.
Example Question #572 : Isee Upper Level (Grades 9 12) Mathematics Achievement
The following are the scores from a math test in a given classroom. What is the median score?
To find the median you need to arrange the values in numerical order.
Starting with this:
Rearrange to look like this:
If there are an odd number of values, the median is the middle value. In this case there are 8 values so the median is the average (or mean) of the two middle values.
Example Question #573 : Isee Upper Level (Grades 9 12) Mathematics Achievement
The median of nine consecutive integers is 604. What is the greatest integer?
The median of nine (an odd number) integers is the one in the middle when the numbers are arranged in ascending order; in this case, it is the fifth lowest. Since the nine integers are consecutive, the greatest integer is four more than the median, or .
Example Question #574 : Isee Upper Level (Grades 9 12) Mathematics Achievement
The median of consecutive integers in a set of data is . What is the smallest integer in the set of data?
We know that the numbers should be arranged in ascending order to find the median. When the number of values is odd, the median is the single middle value. In this question we have consecutive integers with the median of . So the median is the number in the rearranged data set. Since the integers are consecutive, the smallest integer is five less than the median or it is equal to .