### Maths Sample Paper Class 10 2023 Standard

Contents

### Which exam has toughest maths?

Can you solve any of these questions from the William Lowell Putnam Mathematical Competition ? Source Question 1. Determine all possible values of the expression A³ + B³ + C³ — 3ABC where A, B, and C are nonnegative integers. Question 2. In triangle ∆ABC, let G be the centroid, and let I be the center of the inscribed circle. Let α and β be the angles at the vertices A and B, respectively.

- Suppose that the segment IG is parallel to AB and that β = 2 tan^-1 (1/3). Find α.
- Question 3.
- Let f be a continuous real-valued function on R³.
- Suppose that for every sphere S of radius 1, the integral of f(x, y, z) over the surface of S equals 0.
- Must f(x, y, z) be identically 0? Question 1.
- All nonnegative integers not congruent to 3 or 6 (mod 9).

Explanation: To show this, we start by expressing X in terms of other variables, namely A, b, and c. By doing so, we can manipulate X to take on different values. We first show that X can take on all non-negative integers that are not divisible by 3 by choosing different values for b and c.

By letting b and c equal to 0 and 1 respectively, or by letting b and c equal to 1 and 1 respectively, we can obtain X equal to 3A + 1 or 3A + 2, respectively. By varying A, we can achieve every non-negative integer not divisible by 3. By letting b and c equal to 1 and 2 respectively, we obtain X equal to 9A + 9, and by varying A, we can achieve every positive integer divisible by 9.

Finally, by letting b and c both equal 0, we obtain X equal to 0. To show that X is always non-negative, we can apply the arithmetic mean-geometric mean inequality or express b²−bc+c² as (b−c/2)²+3c²/4, which is always non-negative. To prove that if X is a multiple of 3, then it is a multiple of 9, we use modular arithmetic.

## What is the hardest math in school?

What is the Hardest Math Class in High School? – In most cases, you’ll find that AP Calculus BC or IB Math HL is the most difficult math course your school offers. Note that AP Calculus BC covers the material in AP Calculus AB but also continues the curriculum, addressing more challenging and advanced concepts.

#### Which math exam is the hardest?

The William Lowell Putnam Mathematical Competition – Mathematical Association of America (MAA). Image source: https://www.cmu.edu/news/stories/archives/2016/april/putnam-2015.html M athematics is one of my favorite subjects. I love it because it is beautiful, it is logical and we can use it to explain any physical phenomena of the universe.

- It is the language we use to understand the world around us.
- It is the language we use to buy and sell things, to measure things, to count things, to compute, and innovate things.
- But it can be hard sometimes, especially for those of us who do not really understand it, find it tough.
- When it comes to examinations, it is particularly the subject most of us fear, as it incorporates loads of axioms, theorems, principles, formulae, and geometry.

In this article, I shall be talking about the toughest math exam in the world, The William Lowell Putnam Mathematical Competition. It is an annual mathematics competition that takes place in the United States and Canada on the first Saturday of December every year.

Even though it takes place in the States, the competition is open for students of all nationalities. It is administered by the Mathematical Association of America, The competition is primarily for undergraduate students, and definitely not for the students who hate math. The Putnam as competition has been going on since 1938.

It was established by Elizabeth Lowell Putnam in the love of her husband William Lowell Putnam, an American lawyer who was also an advocate and preacher of inter-college and university of academic competitions. Photo by Yustinus Tjiuwanda on Unsplash It consists of a six-hour-long test. The participants sit for two three-hour sittings separated by a short break to solve a total of 12 mathematical problems each of which are graded from zero to ten point scales making a total of 120 scores.

#### Which is the toughest subject in 10th?

Indeed, mathematics and science are among the most difficult subjects to master in board examinations. Nevertheless, if adequately studied, these two courses might lay the groundwork for your success in the CBSE 2022 Term 2 Class 10 board examinations.