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Other algebra prompts

These prompts have been used, to our knowledge, only rarely or not at all in classrooms. If you do use one with your class, please contact us and let us know your experiences.
  
Solving quadratic equations
ax2 + bx + c = 0 (a, b, c are integers) always has two solutions for x.
   
Quadratics with all odd coefficients never have integer solutions.
  
Calculus (differentiation)
Billy Adamson (Head of Mathematics at Thurston Community College, Bury St Edmunds, UK) designed the prompt and posted these pictures on social media of his students' questions and observations.