High School: Functions

Directions: Using the digits 1 to 9, at most one time each, place a digit in each box to create two different quadratic equations that have a root at 4 and a maximum value of 4. You may reuse all the digits for each equation. Source: Robert Kaplinsky in Open Middle Math

Directions: Using the digits 1 to 9, at most one time each, place a digit in each box to complete the first three terms of the arithmetic and geometric sequences. What sequences result in the greatest sum of their second terms? (e.g. 3, 5, 7 and 2, 6, 18 would result in a sum of 5 + 6 = 11). …

Directions: Using the digits 1 to 9, at most one time each, place a digit in each box to make three true statements. Source: Zack Miller

Directions: Using the digits 0 to 9, at most one time each, place a digit in each box to make one function have no real roots, another function have one real root, and the last function have two real roots. Source: Lynda Chung

Directions: Using the digits 1 to 9, at most one time each, place a digit in each box to find the function’s greatest possible value. Source: Robert Kaplinsky

Directions: Using the digits 1 to 9, at most one time each, place a digit in each box and make two true number sentences. Source: Robert Kaplinsky

Directions: Using the digits 1 to 9, at most one time each, place a digit in each box to make the trigonometric equation true. Source: Kevin Rees

Directions: Using the digits 0 to 9, at most one time each, place a digit in each box so that the values of each expression increases from least to greatest. Each number may only be used once. Source: John Rowe

Directions: Using the digits 1 to 9, at most one time each, find the equation whose solution is the largest value of x (from 0 to 360, or 0 to 2π). Source: Mishaal Surti

Directions: Using the digits 1 to 9, at most one time each, place a digit in each box so that the values of the two functions are equivalent. Source: Steven Midzak