Math Olympiad

Algebra Antics

100

Solve for x: 2x+7=15

x=4

200

Factor completely: x²-9

(x+3)(x-3) 

300

Simplify: 6x²y/3xy²

2x/y

400

Solve: x²+5x+6=0

x=-2 or x=-3 

500

Solve: 2/x-1 = 3/x+2

x=7

Geo Galore

100

Find the area of a triangle with base 10 and height 6

30

200

What is the sum of the interior angles of a pentagon

(n-2)(180) = 540 degrees

300

A circle has a radius of 7. What is its circumference in terms of pi? 

14pi

400

A right triangle has legs of length 8 and 15. Find the hypotenuse. 

17

500

A square has an area of 98. What is the length of its diagonal in simplest radical form. 

14

Tricky Trig

100

What is sin(30°)? 

1/2

200

What is cos(60°)? 

1/2

300

If tanθ = 3/4 , what is the value of sinθ? 

3/5

400

Simplify: tan²θ + 1? 

sec²θ 

500

Solve for x such that 0°<x<360° : sinx = sqrt(3) / 2

x=60° or x=120° 

Calculus Corner

100

What is the derivative of x²

2x

200

What is the indefinite integral of 3x² dx

x³ + c

300

Evaluate the limit as x approaches 0 of sinx / x

1

400

The velocity of a particle is given by v(t)=3t²+2t. At t=2, is the particle speeding up or slowing down? 

Speeding up

500

What is the area under the curve of f(x)=2x from 0 to 3. 

9

Stats

100

If a coin is flipped, what is the probability of landing on heads? 

0.5 / 50%

200

A dice is rolled, what is the probability of rolling a number greater than 4? 

1/3 or 0.33 or 33%

300

There are 4 red marbles, 3 blue marbles, and 3 green marbles. If you randomly draw one marble, what is the probability it is not red? 

3/5 or 0.6 or 60%

400

The numbers 2, 4, 5, 7, and x have a mean of 6. What is the value of x? 

12

500

A factory produces 100 widgets on day 1. Each day it produces 20 more widgets than the previous day. How many widgets does it produce on day 5? 

180