# Acceptable Answers for Math Bowl

## Simplifications

Enforce minimal rules here.

## Be consistent:

If a question has a numerical answer, the number itself must be given rather than an expression for the number. An answer must be exact.

## Examples

UnacceptableAcceptable
2x-x + 14–5 x + 9
152 (numerical) 225
(1/2) / (1/3) 3/2, 1 1/2, 1.5
sqrt(20) 2sqrt(5), 2*5.5
2/6 1/3, ".33 repeating"
1/sqrt(8) 1/(2sqrt(2)), sqrt(2)/4
2x + 9 times x - 4 (2x + 9)(x - 4)

## Be careful here

The answer must be unambiguous and satisfy standard simplification rules. When in doubt about the simplification, accept the answer as long as it satisfies standard conventions unless it violates the table above. Numerical answers are not always what the question is after. For example acceptable answers to: "Give the factorization of 36." are 2x2x3x3 and 22 32 (this is not a numerical question, but rather one about form). On the bowl question sheets, we have tried to list various forms of the correct answers in the not so obvious cases.

## Units

Units are not required. However if they are given, they must be correct. Moderator may ask for units if needed to clarify an answer (e.g. answer supplied is 4 ft. and the student says 48).

## Names

Only last names are required. For example, "Newton" is acceptable even though the answer supplied may be Isaac Newton. If first name is given, it must be correct.

The Moderator.

# Example Round

Moderator: JOHN

Team A: LUCAS, KATE, TARYNE

Team B: JACOB, LAURA, JENNIFER

Timer: JOSH

Commentator: GORDON

Purpose: humorous portrayal of the rules of the bowl.

General description: Moderator reads question, team members work feverishly, think, scratch heads, discuss (quietly). Just try to make sure that your actions are in fitting with the specific script response for the question. The lesson of the response is summarized in the parenthetical expression.

1. The edges of a rectangular box are 3, 4 and 5 inches, respectively. What is the surface area of the box?

LUCAS (A): 5 sec; buzzes and answers, "94".

MODERATOR: "Correct".

(Don't need units.)

2. Factor completely the polynomial 4x2 + x - 3.

JACOB(B): 10 sec; buzzes and answers, "4 x - 3 times x + 1".

MODERATOR: "Wrong". JACOB's team looks angry, knowing JACOB messed up.

TARYNE(A): Buzzes 4 sec later and answers, "The quantity, 4 x - 3, times the quantity, x + 1".

MODERATOR: "Correct".

3. A trapezoid has bases of lengths 4 and 6, respectively. If its height is 5, what is its area?

KATE(A): 5 sec; buzzes and answers, " 52".

LUCAS (A): "No! 25".

MODERATOR: "Wrong"

MODERATOR: "Correct".

(For numerical answer must give the exact value, rather than an expression for the number; 1st answer after buzz counts; only one try.)

4. What is the probability of randomly picking, without replacement, 2 red balls out of a bin of 4 red and 5 white balls?

(Both teams feverishly writing. Then suddenly...)

KATE(A): Blurts out, "4/9 times 3/8, that's 1/6", without buzzing.

JACOB(B): Quickly buzzes and answers, "1/6".

MODERATOR: "Team B Correct."

(Team A must buzz before answer counts.)

5. What is the sum of the odd numbers from 1 to 19, inclusive?

KATE(A): Immediately blurts out, "100".

LUCAS (A): Quickly buzzes and answers "100".

MODERATOR: "Correct".

(Must buzz before answer counts; answers before buzzer are not counted - whether correct or wrong.)

6. (Read a bit slower) What is the highest power of 3 that divides 10 ! ?

TARYNE(A): Buzzes BEFORE Moderator says "factorial".

Moderator stops immediately and does not finish the question.

MODERATOR: "Wrong." Reads the question entirely again. JACOB(B): 10 sec; buzzes and answers, "4".

MODERATOR: "Correct."

(Many questions have surprise endings designed to caution those itchy button fingers.)

7. What is the area of the triangle bounded by the coordinate axes and the line y = x + 4?

JENNIFER(B): 5 sec buzzes. Waits too long.

MODERATOR: after 2 sec "Time delay penalty. Team A?"

LUCAS (A): another 5 sec buzzes and answers "8".

MODERATOR: "Correct."

(If you hesitate more than couple seconds, then you lose the turn.)

8. How many faces has a tetrahedron?

LAURA(B): 5 sec buzzes and answers, "6".

MODERATOR: "Wrong"

KATE(A): 10 sec and discussion buzzes and answers "7".

MODERATOR: "Wrong"

MODERATOR: "Sorry, only one answer allowed."

(Only get one chance.)

9. What is the length of the hypotenuse of the right triangle with legs of length 2 and 4?

TARYNE(A): 3 sec buzzes and answers, "Square root of 20".

MODERATOR: "Wrong"

JENNIFER(B): 5 sec later buzzes and answers, "2 times the square root of 5".

MODERATOR: "Correct."

(Answer must be in a simplified form.)

10. Who is credited with the discovery of gravity?

JACOB(B): 5 sec buzzes and answers, "Newton".

MODERATOR: "Correct."

(Only the last name need be given; but if the first name is given, it must be correct.)

11. Which is larger, 1 1/2, 2e/3, or the square root of 2?

Members of both teams hard at work. 25 sec go by and....

TIMER: "5 seconds left."

LUCAS (A): With 1 sec left, "1 1/2".

TIMER: "Time"

MODERATOR: "Wrong. Team B do you have an answer?"

JENNIFER(B): "Yes, 2e/3";

MODERATOR: "Correct."

(NEW RULE: If time runs out while a team is answering and the answer is wrong, then the other team is given the opportunity to offer quickly an answer.)