Mathematics Contest Worksheet - Bluffton - 2009 printable pdf download

Mathematics Contest Worksheet - Bluffton - 2009

MATHEMATICS CONTEST 2009

SOLUTIONS

PART I: 30 Minutes; NO CALCULATORS

Section A. Each correct answer is worth 1 point.

1. List all the prime numbers between 20 and 30.

Solution: Recall that n is a prime number if it has exactly two factors: 1 and n. There is only

one even prime (2), and of the odd numbers between 20 and 30, 21 = 3 × 7, 25 = 5 × 5, and

27 = 3 × 9. That leaves 23 and 29.

2. Perimeter is to square as

is to circle.

Solution: Perimeter is the distance around a square (or any polygon); circumference is the name

we give to the distance around a circle.

3. Find the sum: 1 + 1 + 2 + 6 + 11 + 20 + 37 + 68 + (−58) + (−27) + (−10) + (−1)

Solution: The ﬁrst four numbers sum to 10. Of those that are left, each of the four positive

numbers pairs with one of the four negative numbers to give 10—for example, 11 + (−1) = 10,

20 + (−10) = 10, etc. That gives ﬁve 10s, or 50.

4. Which of the following capital letters appear to have a horizontal line of symmetry?

A C D F G

I J L M N O P

Solution: A horizontal line of symmetry means that the bottom half is a mirror image of the top

B C D E H I K O

half. That describes the letters

5. If a Sunday falls on the 24th of the month, what is the probability that the next Sunday will fall

on the 31st of that month? Express your answer as a fraction or ratio in simplest form.

Solution: Seven months (January, March, May, July, August, October, and December) have 31

days, so this probability is 7/12.

6. Darryl scored 36 points. Steve scored 12 points more than did Don, who had 1/4 as many

points as did Darryl. How many total points did all three players score?

× 36 = 9 points, and Steve had 9 + 12 = 21 points,

Solution: Darryl had 36 points, Don had

giving a total of 66 points.

+ 2009

−

7. Evaluate: 2009

1/3

+ 2009

−

= 2009 + 1 + 90 =1920.

Solution: 2009

1/3

Mathematics Contest Worksheet - Bluffton - 2009