### All ISEE Upper Level Math Resources

## Example Questions

### Example Question #11 : Data Analysis And Probability

Washington Elementary School has seven eighth-grade teachers; each teacher has the number of boys and girls listed above.

An eighth-grade girl has transferred from another school. It is desired that no teacher have more than thirty students overall or eighteen girls in his or her class. Of the seven teachers, how many could accept the girl into his or her class?

**Possible Answers:**

One

Six

Two

Seven

**Correct answer:**

One

We can eliminate Cermak and Georghiou immediately since each has eighteen girls in his class. Of the other five:

Adams has students;

Boyer has students;

Donovan has students;

Esterhaus has students;

Finnegan has students.

Only Mrs. Finnegan's class could accept the new girl without going against the wishes of the school. The correct response is one.

### 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.

**Possible Answers:**

**Correct answer:**

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 #13 : 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?

**Possible Answers:**

Between Thursday and Friday

Between Wednesday and Thursday

Between Monday and Tuesday

Between Tuesday and Wednesday

**Correct answer:**

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 #14 : 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.

**Possible Answers:**

**Correct answer:**

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).

**Possible Answers:**

**Correct answer:**

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 #22 : 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 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)?

**Possible Answers:**

2.5 degrees per hour

2.1 degrees per hour

1.7 degrees per hour

1.3 degrees per hour

**Correct answer:**

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 #23 : 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.

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.

**Possible Answers:**

**Correct answer:**

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 #24 : Data Analysis And Probability

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?

**Possible Answers:**

**Correct answer:**

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.

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