High school research projects and journals that accept papers from high school students in mathematical science.
High school research projects and journals that accept papers from high school students in mathematical science.
Part I Problem 1 Let \(XZ\) be a diameter of circle \(\omega\). Let Y be a point on \(XZ\) such that \(XY=7\) and \(YZ=1\). Let W be a point on \(\omega\) such that \(WY\) is perpendicular to \(XZ\). What is the square of the length of the line segment \(WY\) ? (a) 7(b) 8(c) 10(d) […]
PART I Problem 1 Answer: A Problem 2 Answer: D Problem 3 Answer: D Problem 4 Answer: A Problem 5 Answer: D Problem 6 Answer: D Problem 7 Answer: D Problem 8 Answer: C Problem 9 Answer: B Problem 10 For positive real numbers a and b, the minimum value of\( \left18 a+\frac{1}{3 b}\right\left3 b+\frac{1}{8 […]
Problem 1 Let $\mathbb{N}$ be the set of all positive integers and $S=\left\{(a, b, c, d) \in \mathbb{N}^4: a^2+b^2+c^2=d^2\right\}$. Find the largest positive integer $m$ such that $m$ divides $a b c d$ for all $(a, b, c, d) \in S$. Solution Notice that $(2, 2, 1, 3)\in S\Rightarrow m$ is a divisor of $12 […]
Try this ISI BStat - BMath Entrance 2023, Problem no. 2 with hints and final solution.
In the math world, a unique challenge emerges, combining algebra and number theory. The goal: show that specific equation solutions aren't simple fractions. We reveal a key insight about b² - 4ac: it's always a distinct odd perfect square. Using "parity check," No matter the numbers, the left side remains even, while the right side stays odd. The result: these solutions differ from simple fractions, highlighting math's power in problem-solving.
In 2023, the following Cheenta students are successful for Indian Statistical Institute's B.Stat Entrance and Chennai Mathematical Institute's B.Sc. Math Entrance. They ranked within the first 100 in the entire country in these entrances. Most of these students attended the problem solving workshops regularly, which happen 5 times every week. CMI B.Sc. Math Entrance I.S.I. […]
The leaders in the IOQM, ISI Entrance, American Math Competitions and Math Kangaroo mock contests in Cheenta
Please use the following form to contribute problems of CMI BSc Math Entrance 2023. We will work on the solutions. Also come back to this page to see the updates on Problems and Solutions of CMI BSc Math Entrance 2023. B1. Let \( n \) be an odd positive number greater than 1. We have […]
Question 1 What is \(100(100-3)-(100 \cdot 100-3)\) ? (a) \(-20,000\) (b) \(-10,000\) (c) -297 (d) -6 (e) 0 Question 2 Makayla attended two meetings during her 9 -hour work day. The first meeting took 45 minutes and the second meeting took twice as long. What percent of her work day was spent attending meetings? (a) […]
Question 1 What is \[ \frac{2+4+6}{1+3+5}-\frac{1+3+5}{2+4+6}? \] (a) \(-1\) (b) \(\frac{5}{36}\) (c) \(\frac{7}{12}\) (d) \(\frac{147}{60}\) (e) \(\frac{43}{3}\) Question 2 Josanna's test scores to date are \(90,80,70,60,\) and 85. Her goal is to raise her test average at least 3 points with her next test. What is the minimum test score she would need to accomplish […]
Question 1 Each third-grade classroom at Pearl Creek Elementary has 18 students and 2 pet rabbits. How many more students than rabbits are there in all 4 of the third-grade classrooms? (a) 48 (b) 56 (c) 64 (d) 72 (e) 80 Question 2 A circle of radius 5 is inscribed in a rectangle as shown. […]
Question 1 What is \[ \frac{2+4+6}{1+3+5}-\frac{1+3+5}{2+4+6}? \] (a) \(-1\) (b) \(\frac{5}{36}\) (c) \(\frac{7}{12}\) (d) \(\frac{49}{20}\) (e) \(\frac{43}{3}\) Question 2 Mr.\ Green measures his rectangular garden by walking two of the sides and finds that it is 15 steps by 20 steps. Each of Mr.\ Green's steps is 2 feet long. Mr.\ Green expects half a […]
Question 1 Leah has 13 coins, all of which are pennies and nickels. If she had one more nickel than she has now, then she would have the same number of pennies and nickels. In cents, how much are Leah's coins worth? (a) 33 (b) 35 (c) 37 (d) 39 (e) 41 Question 2 What […]
Question 1 What is the value of $$ \frac{2 a^{-1}+\frac{a^{-1}}{2}}{a} $$ when $a=\frac{1}{2}$ ? (a) 1 (b) 2 (c) $\frac{5}{2}$ (d) 10 (e) 20 Question 2 If $n \circlearrowleft m=n^{3} m^{2}$, what is $\frac{294}{49^{2}}$ ? (a) $\frac{1}{4}$ (b) $\frac{1}{2}$ (c) 1 (d) 2 (e) 4 Question 3 Let $x=-2016$. What is the value of $|||x|-x|-|x||-x$ […]
Question 1 What is the value of \(2-(-2)^{-2}\)? (a) \(-2\) (b) \(\frac{1}{16}\) (c) \(\frac{7}{4}\) (d) \(\frac{9}{4}\) (e) \(6\) Question 2 Marie does three equally time-consuming tasks in a row without taking breaks. She begins the first task at 1:00 PM and finishes the second task at 2:40 PM. When does she finish the third task? […]
Question 1 Mary thought of a positive two-digit number. She multiplied it by 3 and added 11. Then she switched the digits of the result, obtaining a number between 71 and 75, inclusive. What was Mary's number? (a) 11 (b) 12 (c) 13 (d) 14 (e) 15 Question 2 Sofia ran 5 laps around the […]
Question 1 Kate bakes 20 -inch by 18 -inch pan of cornbread. The cornbread is cut into pieces that measure 2 inches by 2 inches. How many pieces of cornbread does the pan contain? (a) 90 (b) 100 (c) 180 (d) 200 (e) 360 Question 2 Sam drove 96 miles in 90 minutes. His average […]
Question 1 What is the value of $$ 1-(-2)-3-(-4)-5-(-6) ? $$ (a) -20 (b) -3 (c) 3 (d) 5 (e) 21 Question 2 Carl has 5 cubes each having side length 1 , and Kate has 5 cubes each having side length 2 . What is the total volume of these 10 cubes? (a) 24 […]
Cheenta is hosting the National Mathematics Talent Contest (NMTC) 2026 Preliminary Round on 30th August 2026 at Mitra Institution (Main), Kolkata. In the weeks leading up to it, Cheenta ran an offline workshop at its Lake Place Road center, from 8th to 29th August to get students ready for the kind of thinking NMTC actually […]
Week 18 of the Hundred Miles Project brought together composition and financial planning in this stage's assessment paper, alongside a hands-on session that returned to the French knot and buttonhole stitch. In the Literacy module, participants read a letter left by a grandmother for her grandchildren, urging them to keep reading, questioning, and learning no […]
Week 17 of the Hundred Miles Project moved learners into more composition-focused territory as they worked through this stage's assessment paper, alongside a hands-on session dedicated to the buttonhole stitch. In the Literacy module, participants read about a woman who kept an evening notebook, recording what she learned, what she found difficult, and one goal […]
Cheenta’s after-school programme for thinkers and doers is presently open to children between the ages of 6 and 11. It is frugal by design and driven by mathematical sciences and creativity.
Question 1 The value of \(\frac{999 \times 999 \times 999}{(999+999) \times 111 \times 111}\), when simplified, is (a) \(\frac{999}{2}\) (b) \(\frac{111}{3}\) (c) \(\frac{81}{2}\) (d) 1000 Question 2 When \(4 \frac{1}{2}\) is divided by \(3 \frac{1}{4}\), the result is x. When \(3 \frac{3}{4}\) is divided by \(2 \frac{1}{8}\), the result is y. Then the numerical value […]
Week 16 of the Hundred Miles Project moved learners further into real-world digital and numerical reasoning as they worked through this stage's assessment paper, alongside a hands-on session focused on the bullion stitch and French knot. In the Literacy module, participants read a passage on how smartphones now let people receive orders, send messages, and […]
Cheenta recently hosted the Australian Mathematics Competition (AMC) 2026 on 4th, 5th, and 6th August, starting at 2:30 PM, at its Kolkata center, and simultaneously at Innovation Story in Mumbai. Students from both cities sat for one of the world's most respected school-level mathematics contests, marking another year of Cheenta's continued involvement in bringing international […]
Every so often, a student's journey with Cheenta comes full circle — not in a competition hall, but in a classroom hundreds of kilometers away, teaching the very ideas that once shaped their own love of mathematics and science. This summer, that student was Samaira Kedia. A Strong Foundation in Competition Mathematics Samaira's own track […]
Cheenta recently hosted the final round of the Sharygin Geometrical Olympiad 2026 at its Kolkata center, spread across two days — 31st July and 1st August, from 12 PM to 4 PM each day. Students sat across the table from a panel of jurors and defended their geometric proofs the old-fashioned way: pen, paper, and […]
Week 15 of the Hundred Miles Project saw learners continue steadily through this stage's assessment paper, even as the week's embroidery class had to be cancelled after the instructor was unable to arrive due to inclement weather. In the Literacy module, participants read a short passage about a community that came together after a flood, […]