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Browse all Trig/Calculus Problems of the Week

Participation in the Trig/Calculus Problems of the Week allows teachers and students to address the NCTM Problem Solving Standard for Grades 9-12, enabling students to build new mathematical knowledge through problem solving; solve problems that arise in mathematics and in other contexts; apply and adapt a variety of appropriate strategies to solve problems; and monitor and reflect on the process of mathematical problem solving.

For background information elsewhere on our site, explore the High School Trigonometry and Calculus areas of the Ask Dr. Math archives. To find relevant sites on the Web, browse and search Trigonometry and Calculus (Single Variable) in our Internet Mathematics Library.


Access to these problems requires a Membership.

Let the Sunshine In - Leigh Nataro
Trig/Calc, difficulty level 2. Find the dimensions of a window designed to let in the maximum amount of sunshine. ... more>>

Making Money at the Movies - Leigh Nataro
Trig/Calc, difficulty level 3. How much should the manager of a theater raise his prices in order to maximize his profit? ... more>>

Managing a Mall - Leigh Nataro
Trig/Calc, difficulty level 2. Find how many square feet there are in a quadrilateral-shaped store. ... more>>

My Hot Chocolate is Too Hot! - Leigh Nataro
Trig/Calc, difficulty level 3. Use Newton's Law of Cooling to determine how long it will take for your hot chocolate to cool. ... more>>

My Snow-Shoveling Business - Leigh Nataro
Trig/Calc, difficulty level 2. Determine the number of customers needed to maximize the revenue for a snow-shoveling business. ... more>>

Needles and Lines - Leigh Nataro
Trig/Calc, difficulty level 5. Use trigonometry and calculus to find the probability of a needle touching a line. ... more>>

Nice Shot, Robin Hood! - Sara Aucoin, Marcie Sawyer, Pattie Draper
Trig/Calc, difficulty level 2. Answer some questions about the flight of Robin Hood's arrow. ... more>>

The Ninja Mission - Steve Earth
Trig/Calc, difficulty level 4. Find the measurement of a spike's angle, given the star's perimeter. ... more>>

One Area - Many Solutions - Leigh Nataro
Trig/Calc, difficulty level 2. Find the area of a triangle given the coordinates of its vertices. ... more>>

The Oval Braided Rug - Leigh Nataro
Trig/Calc, difficulty level 2. Find the area of a shaded portion of an ellipse. ... more>>

Painting the Sine Curve - Leigh Nataro
Trig/Calc, difficulty level 4. Find the length of the sine curve that would fill a 6-ft by 100-ft rectangle. ... more>>

A Parabola Proof - Leigh Nataro
Trig/Calc, difficulty level 3. Prove that the area of a parabola is 2/3 the product of its width and height. ... more>>

Pete's Predictions - Leigh Nataro
Trig/Calc, difficulty level 2. Verify the formula for finding the maximum height of a ball thrown upward. ... more>>

A Picture Is Worth A Thousand Words - Leigh Nataro
Trig/Calc, difficulty level 4. Find the ratio of the area of the overlapping region to the area of non-overlapping regions of two circles. ... more>>

Pie Puzzler - Paul Robinson
Trig/Calc, difficulty level 2. Where should a pie wedge be cut to divide it into two pieces having the same area? ... more>>

Preparing for the Test - Leigh Nataro
Trig/Calc, difficulty level 2. Find the original three numbers in an arithmetic sequence. ... more>>

A Problematic Pizza - Leigh Nataro
Trig/Calc, difficulty level 2. Find the area of a specific region of a circle based on given information. ... more>>

Product Max - Leigh Nataro
Trig/Calc, difficulty level 2. Find the maximum value for two numbers whose sum is a. ... more>>

Rationals and Irrationals - Asher Walkover
Trig/Calc, difficulty level 2. Can you sum two irrationals and get a rational? Can you take an irrational number to an irrational power and get a rational? ... more>>

A Rhyming Riddle - John Allard, Carlton Shedrick, Donnie Sartwell
Trig/Calc, difficulty level 3. Find the solutions for x and y in an exponential equation. ... more>>

Rolle's Theorem Rediscovered - John Feminella
Trig/Calc, difficulty level 3. Prove the Mean Value theorem. ... more>>

The Seal of Dalvek - Steve Earth
Trig/Calc, difficulty level 3. Discover the area of a circular segment based upon its circumference. ... more>>

A Sequence of Logs - Leigh Nataro
Trig/Calc, difficulty level 2. If you have a geometric sequence and take its log, what type of sequence is formed? ... more>>

Sharing the Car - Leigh Nataro
Trig/Calc, difficulty level 2. Use matrices to figure out how much each person contributes to the cost of a car. ... more>>

Shipping Packages - Leigh Nataro
Trig/Calc, difficulty level 2. Find the maximum volume of a box based on the given information. ... more>>

Simple Signals - Lisa Lavelle
Trig/Calc, difficulty level 1. Determine the distance between Erin and Joey as well as how far Joey has travelled in "Perpendicular City." ... more>>

Skiing in Vermont - Leigh Nataro
Trig/Calc, difficulty level 2. How far must you ski and what does your heading need to be for you to return to your starting point? ... more>>

A Sprinkling of Dust - Leigh Nataro
Trig/Calc, difficulty level 2. Find the length of the Cantor Set after n iterations. ... more>>

The Square and the Line - Leigh Nataro
Trig/Calc, difficulty level 1. Find the equation of the line that will split a unit square into two pieces that have equal areas. ... more>>

Squares Inside Squares - Leigh Nataro
Trig/Calc, difficulty level 3. Find the sum of the perimeters of three nesting squares. Imagine that the process of nesting squares continues forever. The sum of the perimeters approaches a finite number. What is that number? ... more>>

Stonybrooke River Bridge - Leigh Nataro
Trig/Calc, difficulty level 2. Based on given information, find the distance across a river. ... more>>

The Supermarket Shelf - Leigh Nataro
Trig/Calc, difficulty level 3. What is the optimal shelf height in the supermarket? ... more>>

The Super-Ultra-Mega-Big Cup - Alvirne High School Calculus Class
Trig/Calc, difficulty level 3. What is the minimum cost to make a cup based on given information? ... more>>

The Super Yard XT - Leigh Nataro
Trig/Calc, difficulty level 1. Based on information about the area of a regular polygon-shaped play yard, find the length of one of the walls of the yard. ... more>>

The Suspension Bridge - Leigh Nataro
Trig/Calc, difficulty level 4. Determine the length of a parabola-shaped cable on a suspension bridge. ... more>>

Swimming Sea Turtles - Leigh Nataro
Trig/Calc, difficulty level 4. Using latitude and longitude data collected from three sea turtles, determine how far each turtle is from its starting position. ... more>>

Tangents and Slopes - Leigh Nataro
Trig/Calc, difficulty level 3. Use the tangent ratio to show that the product of the slopes of two perpendicular lines is -1. ... more>>

That's A Lot of Rock! - Leigh Nataro
Trig/Calc, difficulty level 3. Find the volume of a tunnel through a mountain. ... more>>

Time to Make the Doughnuts - David Turner
Trig/Calc, difficulty level 4. Find the radius of a doughnut with center at (0, 10) and a volume of 3158 cubic centimeters. ... more>>

The Triangle Inside an Angle - Ramani Jv
Trig/Calc, difficulty level 5. Based on the given information, find the area of the smallest triangle contained within an angle. ... more>>

Triangles, Sines, and Areas - Leigh Nataro
Trig/Calc, difficulty level 3. Show that the area of any triangle is .5*b*c*sin(A). ... more>>

The Unit Circle Triangle - Leigh Nataro
Trig/Calc, difficulty level 2. Find the area of the largest right triangle in the first quadrant of the unit circle. ... more>>

Up, Up, and Away (Part II) - Leigh Nataro
Trig/Calc, difficulty level 3. Find the compass setting required to send a balloon on the shortest route from Honolulu, Hawaii, to Essex Junction, Vermont. ... more>>

Up, Up, and Away (Part I) - Leigh Nataro
Trig/Calc, difficulty level 4. Can you determine the shortest distance a balloon could travel from Essex Junction, Vermont, to Honolulu, Hawaii? ... more>>

Vehicle Value - Leigh Nataro
Trig/Calc, difficulty level 2. Find the future value of a car based on its current price and initial selling price. ... more>>

Vinnie Valentine's Mix-Up - Leigh Nataro
Trig/Calc, difficulty level 4. What is the probability of getting exactly 10 out of 20 valentines to the correct person? ... more>>

What Is My Dimension? - Leigh Nataro
Trig/Calc, difficulty level 4. Find the fractal dimension of the Koch curve. ... more>>

Where Did It Come From? - Leigh Nataro
Trig/Calc, difficulty level 3. Find the three fractions that produce a given sum. What is a unit fraction? ... more>>

Where in the World is Essex Junction? - Leigh Nataro
Trig/Calc, difficulty level 3. How far is Essex Junction, Vermont, from the equator? ... more>>

Where Is Whitehall? - Leigh Nataro
Trig/Calc, difficulty level 3. Find the distance from Whitehall, Pennsylvania, to the equator. ... more>>

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