Mathletes Pre-Competition Jeopardy

Arithmetic

300

The first thirty-three numbers in the sequence 3, 33, 333, 3333, 33333, 333333, ... are added together. What is the digit in the hundreds place in their sum?

3

500

Ian, Lucas, and Angela climb the famous staircase at UCLA, which has 87 steps. Ian climbs 1 step at a time. Lucas climbs 2 steps at a time. Angela climbs 3 steps at a time. What is the total number of steps used by exactly two people?

44 steps

Trigonometry

300

Find the exact value of sin²75^o + cos²105^o

1

500

A triangle is inscribed in a semicircle of radius 1. The area of the triangle is one half of the area of the semicircle. What is the measure of the smallest angle in the triangle? Answer to the nearest tenth of a degree.

25.9^o

Geometry

300

A and B lie on the diameter of the circle. Point C lies on the circle and is 6 inches away from A and 8 inches away from B. What is the radius of the circle?

5 inches

500

If the length of a rectangle is increased by 30 percent while its width is decreased by 20 percent, what happens to the area? Your answer needs to include both of the following:

a. Did the area increase, decrease, or stay the same?

b. State the percent change.

Increased by 4%

Algebra

300

If x can be any real number, what is the minimum possible value of the following expression: Give your answer as a reduced fraction. 4x² – 6x + 2

-¼

500

At his birthday party, Mr. Green would not directly tell how old he was. He said, “If you add the year of my birth to this year, subtract the year of my tenth birthday and the year of my fiftieth birthday, and then add my present age, the result is eighty.” How old was Mr. Green?

70

Group

1000

There are four statements, A, B, C, and D. Each of the four statements is either true or false. Two students, Aaron and Anthony, each make three claims about the four statements.

Aaron claims:

1. Of the three statements A, B, and C, exactly one is true.

2. Of the three statements B, C, and D, exactly one is true.

3. Of the two statements A and D, exactly one is true.

Anthony claims:

1. Of the three statements A, B, and C, exactly one is true.

2. Of the three statements B, C, and D, exactly one is true.

3. Of the three statements A, C, and D, exactly one is true.

Either Aaron or Anthony is telling the truth, and the other lies at least once. Of the statements, A, B, C, and D, which are true?

C