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Grade 8

Minimize Slope

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

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Maximize Slope

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

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Square Root Expression

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

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Triangle Sum Theorem

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

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Perfect Squares

Directions: Use 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

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Cubed Roots

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

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Rational and Irrational Roots 7

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

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Rational and Irrational Roots 6

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

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Rational and Irrational Roots 5

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

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Rational and Irrational Roots 4

Directions: Directions: Using the digits 2 – 9, find a unique pair that when used to fill in the boxes, create expressions that produce two rational roots and two irrational roots. Source: Norma Gordon

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