You can often find uploaded PDFs of past National competitions, such as the 2021 National Problems with Answers . Sample National Sprint Level Problems
Let’s examine problems modeled on real past National Sprint Rounds. We’ll categorize them by topic and provide step-by-step solutions. Mathcounts National Sprint Round Problems And Solutions
n3+100n+10=(n3+1000)−900n+10the fraction with numerator n cubed plus 100 and denominator n plus 10 end-fraction equals the fraction with numerator open paren n cubed plus 1000 close paren minus 900 and denominator n plus 10 end-fraction You can often find uploaded PDFs of past
Scratch paper and a writing utensil only. Calculators are strictly prohibited. Find the ratio of their areas, or the
Ep(x!)=∑k=1∞⌊xpk⌋cap E sub p open paren x exclamation mark close paren equals sum from k equals 1 to infinity of the floor of the fraction with numerator x and denominator p to the k-th power end-fraction end-floor
A regular hexagon is inscribed in a circle, and another is circumscribed. Find the ratio of their areas, or the area of an overlapping region formed by rotating one of the shapes.