MathCounts Practice - 3 Feb

Front

What is the formula for calculating the perimeter of a polygon?

Back

The perimeter of a polygon is the sum of the lengths of all its sides.

Front

How do you find the perimeter of a hexagon with vertices A(0, 0), B(4, 0), C(4, 2), D(2, 2), E(2, 4), and F(0, 4)?

Back

Calculate the distance between each pair of consecutive vertices and sum them up. The perimeter is 16 units.

Front

What is a congruent triangle?

Back

Congruent triangles are triangles that are identical in shape and size, meaning their corresponding sides and angles are equal.

Front

What is the area of a right triangle?

Back

The area of a right triangle is given by the formula: Area = (base × height) / 2.

Front

What does it mean for a circle to be tangent to a line?

Back

A circle is tangent to a line if it touches the line at exactly one point.

Front

How do you find the coordinates of a point on a circle given its center and radius?

Back

Use the equation of the circle: (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.

Front

What is the relationship between the sides of a right triangle?

Back

In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides (Pythagorean theorem).

Front

How do you solve a system of equations with two variables?

Back

You can use substitution or elimination methods to find the values of the variables that satisfy both equations.

Front

What is a checkerboard and how does movement work on it?

Back

A checkerboard is an 8x8 grid where pieces move diagonally. Each piece can only move to adjacent squares of the opposite color.

Front

What is the significance of the coordinates (6, 6) in the context of a circle?

Back

The point (6, 6) lies on the circle, meaning it satisfies the circle's equation.