### Quiz Bowl

**Number of team members participating:** 8 students

**Length of competition:** 45 minutes

**Materials Needed for Competition at Drexel:**

- pencils
- paper will be provided.
- dry erase board will be provided.
- dry erase marker will be provided.

**Materials Needed at School Prior to Competition:**

- practice problems provided by Philadelphia EMC organizers

All eight students will solve problems as part of a quiz bowl. Students will work together to answer questions and compete head to head against other teams. Teams will be seated at tables. A moderator will ask a question using a microphone. Each team will write an answer to each question on a dry erase board. Team captains will then hold up their boards for the audience and judges to see.

- The team captain should be seated in middle of the team.
- Teams should write answers clearly and neatly so that judges can see answers. Teams with unclear answers will not receive points.
- Time will begin once the moderator finishes reading the question.
- Teams should NOT include computational or scratch work on the board; only answers should be written on the board.
- Once a team holds up a board, the team may NOT change their answer.
- Teams will be provided with scratch paper, two dry erase markers, a board, and an eraser to clear the board.
- NO books, notes, calculators, or electronic devices, such as cell phones, may be used. Cell phones must be turned off.

**General Guidelines for All Answers**

Print answers clearly and legibly. Unclear or illegible answers will not be scored. Do not write decimal approximations to numbers such as π and &sqrt;2. Leave expressions such as π and &sqrt;2 in your answer. Simplify answers as much as possible. For example, 6/4 should be simplified to 3/2, and square roots of integers should not appear in the denominator. Perfect squares should be removed from radicals. Frequently, several equivalent expressions will be considered correct. For example, 3/2, 1 1/2, and 1.5 could be correct.

**Common Core: Standards for Mathematical Practice**

- CCSS.Math.Practice.MP1 Make sense of problems and persevere in solving them.
- CCSS.Math.Practice.MP2 Reason abstractly and quantitatively.
- CCSS.Math.Practice.MP4 Model with mathematics.
- CCSS.Math.Practice.MP5 Use appropriate tools strategically.

**Round 1**

Round 1 will consist of 15 questions. All teams that provide the correct answer to a question posed by a moderator will earn 5 points.

SAMPLE PROBLEM 1

What is the largest 3-digit prime number?

SAMPLE PROBLEM 2

How many integers between 0 and 100 are divisible by 3 or 7?

SAMPLE PROBLEM 3

A license plate is 2 letters followed by 3 digits and none of the digits or letters repeat. How many different license plates are possible?

SAMPLE PROBLEM 4

Jabril currently has enough money to buy 45 books. If the cost of each book was
10 cents less, Jabril could buy 5 more books. How much money does Jabril have
to spend on books?

SAMPLE PROBLEM 5

At a formal dinner, guests were seated around a circular table for six. Before the dinner, the host asked each guest to shake hands (once) with everyone on the
table. How many handshakes were made at the table?

SAMPLE PROBLEM 6

What is the greatest common factor of 42, 126, and 210 ?

SAMPLE PROBLEM 7

What is the value of x when 2x + 3 = 3x – 4 ?

SAMPLE PROBLEM 8

If 40% of a given number is 8, then what is 15% of the given number?

SAMPLE PROBLEM 9

Michaela received a 10% raise each month for 3 consecutive months. What was
her salary after the three raises if her starting salary was $1000 per month?

**Round 2**

Round 2 will consist of 5 questions that each have multiple answers. Each team will earn 1 point for each correct answer and 1 bonus point if the team provides all of the possible answers.

SAMPLE PROBLEM 1

Which two-digit numbers from 10 to 90 have the property that both digits are
perfect squares? For example, 10 is the smallest such number and 90 is the
largest.

SAMPLE PROBLEM 2

List the whole numbers between -3 and 3.

SAMPLE PROBLEM 3

When 2 lines are cut by a transversal name as many as you can of the angle
pairs that are formed.

SAMPLE PROBLEM 4

Name the 6 trigonometric relationships.

SAMPLE PROBLEM 5

List all the perfect cubes between 1 and 1000 inclusive.

SAMPLE PROBLEM 6

List as many Pythagorean triples as you can where the values of all 3 sides are
less than 50.

**Round 3**

Round 3 will consist of 10 questions. The first team with a correct answer will earn 3 points. The first team with the correct answer will then receive a follow-up question for 2 bonus points.

SAMPLE PROBLEM 1

What is the value of any number raised to the power of zero?

SAMPLE FOLLOW-UP TO PROBLEM 1

What is 0! ?

SAMPLE PROBLEM 2

When two exponential expressions with a common base are multiplied together
what operation is done to the exponents to combine the expressions?

SAMPLE FOLLOW-UP TO PROBLEM 2

Simplify: 5x^{7}y^{3} · 9x^{-4}y^{10}