Thank you guys so much for coming to the Fall JAMAC! We had a blast and look forward to seeing you all in the spring! Information on the Spring JAMAC will be available here when we've worked out the details.
JAMAC (Junior Albemarle MAth Competition) is a low-stakes, fun mathematics competition for middle schoolers in the Albemarle region, organized by the Albemarle High School Math Club and Math Honor Society. The competition takes place at Albemarle High School, usually on a weekend, and lasts 5-7 hours. The competition consists of individual and team events whose problems tend to get harder. More specific information is available below:
15 questions, 30 minutes
Problems consist of functions, equations, and algebraic manipulation involving one or more variables, that require converting problems into math equations.
"Algebra round" is a rather ambiguous term, as all rounds require the use of algebra (to some extent). As such, the Algebra round doesn't require outside knowledge of topics like combinatorics or geometry; just algebraic/graphical topics and a general understanding of numbers and the real world.
Easy: Reed selects a three-digit number and subtracts it from \(1000.\) After, the result is doubled. Once it has been doubled, he adds \(7\) to the result. What is the largest number Reed can get? (2024 Algebra Round, #1)
Medium: Vivian can make a paper ring in \(4\) hours. Weining can make a paper ring in \(6\) hours. Amy can make a paper ring in \(8\) hours. If all \(3\) are making paper rings together, how many hours will it take them to make \(13\) paper rings? (2021 Algebra Round, #2)
Hard: What is the remainder when \(7^{100}\) is divided by \(3?\) (2024 Algebra Round, #10)
15 questions, 30 minutes
Problems require using algebraic problem-solving skills to find areas, volumes, and side lengths of various 2d and 3d shapes.
The Geometry round is the harder of the three individual topics, as problems in this round are not as intuitive as in other rounds, requiring more complete knowledge of Geometry and more intuitive problem-solving skills. As such, the scores in this round tend to drop faster than in other rounds.
Easy: Mark Watney is stranded on Mars. His greenhouse has a ceiling consisting of triangular glass panes. One of the equilateral triangles has all sides equal to \(4.\) What is the triangle's area? (2024 Geometry Round, #1)
Medium: On Coney Island there is a circular Ferris Wheel that is \(100\) feet tall. It takes \(120\) seconds for the Ferris Wheel to make a complete revolution. When Taylor Swift is sitting on a bench at ground level she sees that Selena Gomez is \(30\) feet in the air. What is the sum of the two possible times it takes for Selena to reach the ground? (2021 Geometry Round, #4)
Hard: Captain Picard's new combadge is pictured in the figure shown. Point \(D\) is the center of the circle. \(\angle{ABD}\) and \(\angle{ACD}\) are \(20^\circ .\) What is the value of \(x\)? See picture here (2024 Geometry Round, #9)
15 questions, 30 minutes
Problems on numeric manipulation and knowledge of geometric and arithmetic sequences and summations. Counting and probability is also included in this section.
Formerly the General Round (considered too vague of a name), this round has more practical applications of math in the real world, like probability, counting, and other data-related topics.
Easy: On Cornelia Street there are \(1,313\) apartments. \(871\) apartments are painted blue, \(351\) apartments have new Maseratis, and \(329\) apartments are not blue nor have new Maseratis. How many apartments are painted blue AND have new Maseratis? (2021 General, #2)
Medium: The amount of messages in a bottle that Taylor Swift has can be expressed as the value of \((2+4+6+8+...+2022)\)\(-(1+3+5+7+...+2021).\) How many messages in a bottle does Taylor Swift have? (2021 General, #8)
Hard: Each term in a sequence after the second is defined by \(t_{n} = 2\cdot t_{n-1} \cdot t_{n-2}.\) If \(t_{5} = 1152,\) find \(t_{1}.\)
10 questions, 15 minutes
Problems on a wide variety of math-related topics, fairly hard but designed to be solved by a team of four people. Teams have to decide how to split up problems, as problem difficulty increases rapidly from problems 1 to 10.
This round requires background knowledge, problem-solving, leadership, and team cooperation. As there is so little time, teams have to efficiently distribute problems to give them the maximum time on each question.
Easy: Wall-E usually leaves his battery on. If his battery is on, but he is not using it, it will last for \(24\) hours. If he is using it constantly, the battery will only last for \(3\) hours. Since his last recharge, Wall-E has been on for \(9\) hours, and during that time he has used energy for \(60\) minutes. If he continues to leave his battery on, how many more hours will his battery last? (2024 Team Round, #2)
Medium: Marjorie is firing a cannon at a yacht. She has a \(25\%\) chance of hitting the yacht on each fire. If she fires the cannon \(4\) times, what is the probability she'll hit the yacht exactly twice? Answer in a fraction in simplest form. (2021 Team Round, #4)
Hard: Jake has \(7\) car keys numbered \(1\textnormal{-}7.\) He randomly tosses Taylor \(3\) car keys. What is the probability that the numbers on the car keys tossed are consecutive and in ascending order? (2021 Team Round, #9)
30 questions, 30 minutes
Guts round (also on various math-related topics) is a fast-paced, chaotic team event featuring live scoring and problem drip-feeding.
In this event, teams start with one sheet of paper with three problems. Once a team believes their answers are good enough, they turn that sheet of paper in and receive the next three. In total, there are ten sets of problems, with each set being harder than the last. Grading is done by multiplying the set number and the amount of correct answers. For example, if a team turns in their 6th set and they get two problems right, 12 is added to their score. Live grading is done for the first five sets.
Easy: The TARDIS is a rectangular prism with a height of \(10\) ft, a width and depth of \(5\) ft, and a volume of \(1250\) ft. What is its surface area? (2024 Guts Round, Round 1, #3)
Medium: At Albemarle High, there are \(498\) students in 9th grade. There are \(188\) students in "Saving the Turtles Club" and \(63\) students in the "VSCO Girl Club". \(197\) students aren't in either club. How many 9th graders are in both clubs? (2020 Guts Round, Round 5, #1)
Hard: Two squares are chosen at random on a chessboard \((8\times 8)\). What is the probability that they share a side? (2020 Guts Round, Round 10, #2)
During the Finals Round, we host a game of 24 for the non-finalists, a game about using different arithmetic operations on four numbers to create 24. Towards the end of the event, we host a Quiz Bowl for everyone, where we read out a paragraph of information about some topic. Each progressive sentence will be more specific than the last, and the first participant to shout out the topic the paragraph is about gets a point. After 10 rounds, we will eliminate half of the participants with the lowest points. The Bowl continues until there is one left standing, who will be the winner.
We offer bronze medals, silver medals, and gold (colored) trophies to the three highest scorers of the Algebra and Number Theory rounds. We offer a bronze medal, small plaque, and large plaque for the overall individual award, given to the three individuals with the highest sum of scores from the three individual events.
Similarly, we offer awards to the teams with the highest scores in each team event; Team Round and Guts Round.
With the low amount of questions in each category, there is a high likelihood of two or three-way ties occurring in all events. JAMAC has a Tiebreak Round to decide rankings, designed to eliminate ties fairly.
Mathletes will be given 3 questions to solve, whose topics will depend on which event we are breaking a tie for. For example, a tie for first in the Algebra Round would mean tiebreak problems are algebra-related. There is a seven-minute time limit, but contestants can submit the problems anytime before the time limit. We grade accuracy OVER time. For example, if one contestant submits before a second, and the second gets a perfect score and the first makes a mistake, the second contestant will be ranked higher. On the other hand, if both contestants have the same score, the first contestant will be ranked higher.
We only break ties if an award can be given to multiple people (the overall individual tiebreak will have problems from all rounds). Ties in team rounds are resolved by averaging individual scores within a team. For example, if Team A's average overall individual score is 10, but Team B's is 5, Team A will rank higher. Like individual rounds, team round ties below the podium will not be resolved.