2024 2025 CATEGORY 3 DECEMBER BENCHMARK

Front

What is the algebraic representation for a dilation that transforms (x, y) to (4x, 4y)?

Back

A dilation by a scale factor of 4.

Front

What is the relationship between the areas of the squares in a right triangle according to the Pythagorean theorem?

Back

The area of the two smaller squares is equal to the area of the largest square.

Front

What is the formula for the volume of a cone?

Back

Volume = (1/3)πr²h, where r is the radius and h is the height.

Front

If a cone has a volume of 100π cubic centimeters and a height of 12 centimeters, what is the radius?

Back

5 cm.

Front

What is the Pythagorean theorem?

Back

In a right triangle, a² + b² = c², where c is the hypotenuse.

Front

What does dilation mean in geometry?

Back

Dilation is a transformation that alters the size of a figure but not its shape.

Front

What is the scale factor in a dilation?

Back

The scale factor is the ratio of the length of a side of the image to the length of the corresponding side of the original figure.

Front

How do you find the distance between two points (x1, y1) and (x2, y2)?

Back

Distance = √((x2 - x1)² + (y2 - y1)²).

Front

What is the area of a square with side length s?

Back

Area = s².

Front

What is the relationship between the sides of a right triangle and the squares of their lengths?

Back

The sum of the squares of the lengths of the two legs equals the square of the length of the hypotenuse.