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Practice Problems

This page contains question sheets which are sent out to new students by many colleges before they arrive to start their undergraduate degree. These questions make suitable bridging material for students with single A-level Mathematics as they begin university - the material is partly revision, partly new material. All 11 sheets cover material relevant to the Mathematics, Mathematics & Statistics and Maths and Philosophy courses; sheets 8, 9 and 10 are not relevant to the Mathematics and Computer Science degree.

For each sheet the subject matter is briefly described, and there is some recommended reading material; the chapter numbers refer to the fourth edition of D.W.Jordan and P.Smith's book Mathematical Techniques, published by Oxford University Press in 2008.

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University of Northern Colorado

Math Challenge Problem

The Math Challenge Problem is taking a little break to invent some exciting new challenges.  Please enjoy previous problems from the last few years below.

If you have suggestions for future problems, please email them to [email protected] .

Previous Problems

September Challenge  | October Challenge | November Challenge

September Challenge  | October Challenge  | November Challenge  | January Challenge  | February Challenge  | March Challenge | April Challenge

September Challenge 1 | September Challenge 2 | October Challenge 1 | October Challenge 2  | November Challenge 1 | November Challenge 2 | January Challenge | February Challenge 1 | February Challenge 2 | March Challenge 1 | March Challenge 2  | April Challenge

September Challenge 1 | September Challenge 2 | October Challenge 1 | January Challenge | February Challenge 1 | February Challenge 2 | March Challenge 1 | March Challenge 2 | April Challenge 1 | April Challenge 2

September Challenge 1 | September Challenge 2 | October Challenge 1 | October Challenge 2 | November Challenge 1 | November Challenge 2 | January Challenge | February Challenge 1 | February Challenge 2 | March Challenge 1 | March Challenge 2 | April Challenge 1 | April Challenge 2

2012 - 2013

September Challenge  | October Challenge |  November Challenge | January Challenge | February Challenge  | March Challenge  | April Challenge

2011 - 2012

September Challenge  | October Challenge  | November Challenge | January Challenge  | February Challenge 1  | February Challenge 2 | March Challenge | April Challenge

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Problem of the Week BUGCAT Zassenhaus Conference Hilton Memorial Lecture BingAWM Math Club

Problem of the Week

Problem 3 (due Monday, March 6)

Let $\displaystyle s(n)=\sum_{j=1}^n {n\choose j} \frac{1}{j}$ and $\displaystyle f(n)=\frac{2^{n+1}}{n}$. Prove that \[\lim_{n\to\infty} n\left (\frac{s(n)}{f(n)}-1\right)\] exists and find its value.

Every other Monday (starting 01/23/23), we will post a problem to engage our mathematical community in the problem solving activity and to enjoy mathematics outside of the classroom. Students (both undergraduate and graduate) are particularly encouraged to participate as there is no better way to practice math than working on challenging problems. If you have a solution and want to be a part of it, e-mail your solution to Marcin Mazur ( [email protected] ) by the due date. We will post our solutions as well as novel solutions from the participants and record the names of those who've got the most number of solutions throughout each semester.

When you submit your solutions, please provide a detailed reasoning rather than just an answer. Also, please include some short info about yourself for our records.

Previous Problems and Solutions

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math problems university

Link to the University of Waterloo home page

Problem of the Week

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The Problem of the Week is designed to provide students with an ongoing opportunity to solve mathematical problems. Each week, problems from various areas of mathematics will be posted here and e-mailed to teachers for use with their students from grades 3 and up.

Current Problems

Problems for the 2021-2022 year will begin September 16.

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Information for teachers.

Problems are organized into themes . A problem may have more than one theme.

These problems may be used in a variety of different ways including:

We know that teachers will use these problems in many creative ways!

Solutions to the problems will be sent out to teachers one week after the problems are e-mailed.

Problems & Solutions from 2022-2023

Problem and solution archive.

The following table has links to booklets containing all the problems and solutions from particular years. The problems are organized into themes , grouping problems into various areas of the curriculum. A problem often appears in multiple themes.

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College of Arts and Sciences » Academic Units » Mathematical Sciences » Mathematics Placement Assessment » Sample Questions

Sample Questions

Entry-level mathematics courses at UC are divided into three groups (see the table at the bottom of this page). The sample questions have been divided into three corresponding groups. The "Print Questions" and "Print Answers" links (below) allow to download the printable PDFs.

Do not use a calculator! These questions represent mathematical tasks that you are expected to do in the various courses without the aid of electronic devices.

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Spring 2023 Edition

Spring 2021 Edition

Fall 2021 Edition

Spring 2022 Edition

Fall 2022 Edition

The department of Mathematical Sciences is running the competition “Math Problem of the Week”. This competition will run for the remaining of the Spring 2023 semester. Each week a new problem will be announced and we welcome solutions for everyone and the undergraduate participant from NMSU main campus with the most correct solutions at the end of the semester will receive an award of $500. If there are more than one winners, this amount will be divided among all of them. The problems from the competition do not assume much background and everyone is encouraged to participate. At the end of the semester, the participants that submit correct solutions to at least half of the problems, regardless of their status (student, faculty, staff, etc.), will receive a Honorable Mention and their names will be listed on this webpage. 

Solutions can be submitted to  [email protected]

Below is the list of the problems per week:

Problem of the Week 1 ( link ) due Monday, February 27, 10am.

Problem of the Week 2 ( link ) due Monday, March 6, 10am.

Solutions to the problems of the week:

Solution to the Problem of the Week 1: ( link )

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Problems and solutions to the U of I Undergraduate Math Contest

Purdue University

The Purdue Problem of the Week retired effective January 2019. The archives are still available with many problems to entertain and to illustrate a wide range of mathematical techniques.

About the Problem of the Week...

The Purdue Problem of the Week will has returned in a new, interactive format.

Problem of the Week is now a discussion board that functions similarly to StackExchange . Each Friday of the semester the problem will be posted on the webpage and will also appear in The Exponent. We will lock the associated discussion board for the first 24 hours to allow people time to read and ponder the problem.

After that time we will invite solutions to be posted on the discussion page and we strongly encourage people to post alternative solutions even when a good, existing solution has already been posted. The problems will remain of the same general type though we will occasionally have more advanced problems than what we have given in the past.

The discussion board for each problem will be moderated. Any user can post a solution.  Users will be able to use MathJax to present their solutions and will also be able to vote up/down any solution and comment on any solution just like on StackExchange . We provide the problems, and you provide the solutions.

As Problem of the Week is strictly for entertainment purposes, we ask kindly that users work the problems themselves. Finding good problems is difficult and often problems (and solutions) can be found elsewhere on-line. We prefer problem of the week not test your ability to search the Internet.

About the founder of Problem of the Week

Michael Golomb, who passed away on April 9, 2008 at the age of 98, began the Problem of the Week program and ran it for many years. Several years prior to his passing, health problems forced him to stop administering the program, but he continued to provide the problems. And even now many of the problems appearing in Problem of the Week were provided by Michael Golomb. He created many of the problems himself, and collected (and often modified) the others from various sources.

Spring 2018

Spring 2017

Spring 2016

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COMMENTS

  1. Practice Problems

    These questions make suitable bridging material for students with single A-level Mathematics as they begin university - the material is

  2. Math Challenge Problem

    Each month, a new math problem to challenge students in mathematical sciences and beyond.

  3. Problem of the Week

    Every other Monday (starting 01/23/23), we will post a problem to engage our mathematical community in the problem solving activity and to enjoy mathematics

  4. Problem of the Week

    Each week, problems from various areas of mathematics will be posted here and e-mailed to teachers for use with their students from grades 3 and up. Problem A (

  5. Sample Questions

    Entry-level mathematics courses at UC are divided into three groups (see the ... These questions represent mathematical tasks that you are expected to do in

  6. Math Problem of the Week

    The department of Mathematical Sciences is running the competition “Math Problem of the Week”. This competition will run for the remaining of the Spring

  7. College-Level Mathematics Test

    There are six content areas measured on this test: (a) Algebraic Operations, (b). Solutions of Equations and Inequalities, (c) Coordinate.

  8. Problems and solutions to the U of I Undergraduate Math Contest

    For general information about math contest activities at the U of I go to the U of I Math Contests Webpage. 2014 Undergrad Math Contest. Problems · Solutions.

  9. Problem of the Week

    The Purdue Problem of the Week archives are still available with many problems to entertain and to illustrate a wide range of mathematical techniques.

  10. Teaching Problem-solving in Undergraduate Mathematics

    leave university. It is problematic to allow students to graduate with first class degrees who cannot handle unfamiliar problems. The report concludes with 14