Grade 8

Directions: Using the digits 1 to 9 at most twice each, make the sum of the four expressions the greatest possible value. Source: Catriona Shearer

Directions: Using the integers -9 to 9 (excluding 0) at most one time each, fill in the blanks to create two distinct perpendicular lines. Source: Louise Pepper with answers from the students of Kings College Alicante, Spain

Directions: Using the digits 1 to 9, at most one time each, fill in the boxes to make a product that equals 800,000,000. Source: Robert Kaplinsky

Directions: Given the point (3,5), use digits 1-9, at most one time, to find a point (__, __) that minimizes the slope of the line that passes through the two points. The slope cannot be undefined. Source: Nanette Johnson (Problem Based on Andrew Constantinescu’s Problem) and Andrew Constantinescu

Directions: Given the point (3,5), use digits 1-9, at most one time, to find a point (__, __) that maximizes the slope of the line that passes through the two points. The slope cannot be undefined. Source: Andrew Constantinescu

Directions: Using the digits 1 to 9, at most one time each, fill in the boxes to make the following expression as close to 0 as possible. Source: Erick Lee

Directions: Using the digits 1-9 at most one time each, fill in the blanks so that when you solve for x, it is a whole number. Source: Franco D. Adkins

Directions: Using the digits 1- 9, at most one time each, to fill in the boxes to make each expression evaluate to a perfect square number. Extension/Challenge: What is the largest/smallest square number you can make? How many different perfect square numbers could be made? Source: Erick Lee

Directions: Using the digits 1 to 9, at most one time each, fill in the boxes to make a true statement. Source: Ryun Deckert and Brock Montgomery

Directions: Using the digits 1 to 9, find one pair of digits to fill in the boxes to create expressions that produce one rational root and three irrational roots. Source: Norma Gordon