Elementary & Middle School

  • CalcuSolve is a competition that tests students’ problem-solving skills related to mathematics. Students participate both individually and as part of a 4-member team. During the course of the event, there will be two (2) team problems and seven (7) individual problems.

    Team Problems (#1 and #9): Problems #1 and #9 will be solved by the team. Teams will go into a breakout room for 10 minutes to work on the problem. Within 10 minutes, they will need to submit their response via a provided electronic form. All groups will be required to include a picture of their work.

    Individual Problems (#2 – #8): The problem will be shared with all participating students. After the problem is shared, students will have 5 minutes to work on the problem. After 5 minutes, a hint will be shared and then students will have an additional 3 minutes to work on the problem and submit their response. All students must upload a picture of their work with their response.

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Contact Us

  • Diane Thomson
  • 484-237-5017

Grade Levels

  • Grades 5 -6

    Grades 7 - 8 (recommended for students enrolled in Algebra I or above)

    Grades 9 - 12 (recommended for students enrolled in Algebra II or above)

Agenda

  • The event will take place from 9am – 11:30am virtually via the Zoom platform.

    • Below is a general timeline of the event:
      • 9am – 9:15am: Welcome and tournament guidelines
      • 9:15am – 9:25am: Team Problem #1
      • 9:25 – 10:45: Individual Problems (there will be a brief break included during this time)
      • 10:45 – 10:55: Team Problem #2
      • 10:55 – 11:00: Wrap-up
      • 11:00 – 11:30: “Overflow” time if needed

Cost

  • There will be a participating fee of $20 per team.

Sample Problems

  • There is a wide range of content that will be covered and your students may be presented with questions on content they may not have been exposed to yet. See below types of questions asked in previous tournaments.

    For example: CalcuSolve 2019 Grades 7-8 Questions


    Question: If a regular octagon is created by removing an equilateral right triangle from each corner of a square with sides of length 𝐿 then what is the perimeter of the octagon in terms of 𝐿?
    Answer: 𝐿√2+2
    Note: This was a team question.

    Question: Find the equation of a parabola which goes through the points (0,2), (1,1) and (2,-1).
    Hint (given after 5 minutes): 𝑦=𝑎𝑥2+𝑏𝑥+𝑐)
    Answer: 𝑦=−12𝑥2−12𝑥+2

    Question: Jim takes 4 hours to mow 3 acres of grass and Jane can mow 2.5 acres of grass in 2 hours. A 6 acre field needs to be mowed and Jim and Jane will work together. Assuming they will work at their normal rate without interfering with each other then how long will it take them to mow the grass in this field together?
    Hint (given after 5 minutes): Think acres per hour
    Answer: 3 hours

    Question: For what values of 𝑘 will the graph of 𝑦=𝑥2+(3−𝑘)𝑥+1 touch the 𝑥-axis at exactly one point?
    Hint (given after 5 minutes): Use the discriminant.
    Answer: 𝑘=1 and 𝑘=5.

    Question: Find the points where the circles 𝑥2+𝑦2=4 and (𝑥−2)2+𝑦2=9 intersect.
    Hint (given after 5 minutes): What can you easily eliminate with these two equations?
    Answer: (−14,√634) and (−14,−√634)

    Question: If 6 gallons of a saltwater solution with a concentration of 0.2 grams of salt per gallon is mixed with 10 gallons of another saltwater solution with an unknown concentration. If the resulting mixture is 16 gallons of a saltwater solution with a concentration of 0.35 grams of salt per gallon then how much salt was in the solution with unknown concentration?
    Hint (given after 5 minutes): The answer is an amount of salt not a concentration of salt.
    Answer: 4.4 grams

    Questions: If a car starts down a straight road at a constant speed of 50 miles per hour and a truck starts at the same position 15 minutes later going the same direction at 65 miles per hour then how long will the car and truck have travelled the same distance?
    Hint (given after 5 minutes): Distance=RatexTime
    Answer: 1 hour and five minutes

    Question: Assume a black circle with diameter of 0.5 meters is painted within a circular dart board with diameter 1 meter. If a dart hits the board at a random location then what is the probability it hits the black circle?
    Hint (given after 5 minutes): 𝐴=𝜋𝑟2
    Answer: 14

    Question: By what percentage would you need to decrease the radius of a sphere in order to decrease its volume by 93.6 percent?
    Answer: 60%
    NOTE: This was a team question.

Technical Details

  • 1. All participating students will need an internet connected device (computer or cell phone) to access the Zoom platform.

    2. A device capable of taking photos, as students will be required to submit a picture of their work with all submissions.

    3. The event will not being recorded. In addition, students will not be required to have their camera on.

    4. Students are permitted to use calculators during the event. The use of any problem solving apps (e.g. Photomath) is not permitted.

Scoring

  • There are two scoring categories – Individual and Team.

    • Individual scoring: There are seven (7) individual problems and each is worth a maximum of 5 points. Students will earn 5 points if they answer correctly prior to a hint being shared and 3 points if they answer correctly after a hint has been shared. A hint will be given after students have had 5 minutes to work on the problem. After the hint is given, they will have an additional 3 minutes to work on the problem. Students can earn a maximum of 35 points on the individual problems. 
    • Team scoring: There are two team problems worth a maximum of 10 points each. Teams have 10 minutes to work on the team problems. A correct answer will result in 10 points being awarded. No hints are provided for team questions.
    • Final scoring: The individual total from each team member (from the individual problems) will be added to the the team points earned to determine the overall score. Assuming a team has a full roster of 4 team members, the maximum team score is 160 points.