Math Counts Warm-Up #5-6 2017-2018

Front

A pencil and 5 paper clips weigh the same as 2 erasers. A pencil weighs the same as 29 paper clips. How many paper clips weigh the same as an eraser?

Back

17

Front

How many pairs of numbers (a, b) satisfy the following rules: I. a = 0 or b = −1 or b = 1; II. a = −1 or a = 1 or b = 0?

Back

5

Front

A certain sphere has a volume that is numerically equal to three times its surface area. What is the radius of this sphere?

Back

9

Front

A family farm is equally divided among three heirs: Jim, Jan, and John. What portion of the proceeds from the most recent sale should Jim receive if John's share is divided among his three heirs?

Back

3/8

Front

What is the maximum area of a rectangle with a diagonal of length 16 units?

Back

128

Front

What is the formula for the volume of a sphere?

Back

V = (4/3)πr³

Front

What is the formula for the surface area of a sphere?

Back

SA = 4πr²

Front

What is the relationship between the sides of a right triangle and its diagonal (hypotenuse)?

Back

a² + b² = c² (Pythagorean theorem) where c is the hypotenuse.

Front

How do you find the area of a rectangle?

Back

Area = length × width.

Front

What is a common fraction?

Back

A fraction where the numerator and denominator are both integers.