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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.

Additional Signals - Lisa Lavelle
Trig/Calc, difficulty level 2. Help locate Joey's and Erin's new friend. ... more>>

Add It Up - Leigh Nataro
Trig/Calc, difficulty level 2. Find the sum for an infinite series. ... more>>

Adventure Airlines - Leigh Nataro
Trig/Calc, difficulty level 1. How far from the airport does the plane need to begin its descent? ... more>>

Another Problematic Pizza - Leigh Nataro
Trig/Calc, difficulty level 3. Find the area of a triangular piece of pizza. ... more>>

Another Product Max - Leigh Nataro
Trig/Calc, difficulty level 5. Use calculus to find the maximum product for xyz if x + y + z = B, where B is a real number. ... more>>

Around the Corner - Louis Holmes
Trig/Calc, difficulty level 4. A girder must be carried along a corridor that has a 90-degree turn at the end. How wide must the corridor be in order for the girder to fit around the corner? ... more>>

Basketball Angles - Richard Tchen
Trig/Calc, difficulty level 4. Find the minimum angle at which a basketball will pass through a basketball hoop. ... more>>

Be My Valentine - Leigh Nataro
Trig/Calc, difficulty level 4. Find the areas of two heart-shaped valentines. ... more>>

Building a Sandbox - Leigh Nataro
Trig/Calc, difficulty level 3. Find the maximum area for a triangular-shaped sandbox. ... more>>

Building Boxes - Leigh Nataro
Trig/Calc, difficulty level 2. Find the maximum volume of a rectangular prism constructed from an 8.5-inch by 11-inch piece of paper. ... more>>

Building Bridges - Leigh Nataro
Trig/Calc, difficulty level 3. Given some dimensions, find the length of a cable that lies along the diagonal of a bridge. ... more>>

Can You Prove It? - Leigh Nataro
Trig/Calc, difficulty level 3. Prove that the square root of 2 is irrational, and explain how to use a straightedge and compass to construct a segment that is the square root of 2 in length. ... more>>

Center Coordinates - Leigh Nataro
Trig/Calc, difficulty level 2. Find the coordinates of the center of a circle circumscribed around a triangle. ... more>>

Cooling Colas - Leigh Nataro
Trig/Calc, difficulty level 3. Use Newton's Law of cooling to determine when the colas will freeze. ... more>>

Coordinateville - Leigh Nataro
Trig/Calc, difficulty level 1. Find the angle of intersection of two roads based on given information. ... more>>

Costly Cable - Leigh Nataro
Trig/Calc, difficulty level 3. Find where to lay a fiber optic cable in order to minimize the cost. ... more>>

Count to Ten? - Leigh Nataro
Trig/Calc, difficulty level 3. Use the given clues to determine the base system for counting used by people of the planet Torus. ... more>>

Count Your Seinneps - Leigh Nataro
Trig/Calc, difficulty level 2. Find a system of coins that uses the fewest number of coins possible without repeating coins. ... more>>

Cup Capacity - Leigh Nataro
Trig/Calc, difficulty level 3. Find the volume of a cup based on its dimensions. ... more>>

Cutting the Cookie - Leigh Nataro
Trig/Calc, difficulty level 2. Where should you cut a circular cookie so its area is in a ratio of 1:2 ? ... more>>

A Deviation from the Average - Leigh Nataro
Trig/Calc, difficulty level 2. Create some data sets with a specific mean and standard deviation. ... more>>

Don't Be Late for Dinner - Leigh Nataro
Trig/Calc, difficulty level 2. Based on given distances, determine whether Susy will be late getting home for dinner. ... more>>

Doughnut Dilemma - Leigh Nataro
Trig/Calc, difficulty level 2. Which doughnut shop makes a doughnut with a greater volume? ... more>>

An Eggstra Special Problem - Leigh Nataro
Trig/Calc, difficulty level 2. Find the area of a cross-section of an egg given some dimensions of the cross-section. ... more>>

Ellipse Areas - Leigh Nataro
Trig/Calc, difficulty level 3. Use calculus to show that the area of an ellipse is pi*a*b. ... more>>

Environmentally Friendly - Leigh Nataro
Trig/Calc, difficulty level 2. What dimensions for a given page will use the least amount of paper? ... more>>

Extending the Signals - Lisa Lavelle
Trig/Calc, difficulty level 1. Determine how far Erin needs to "rotate" to signal Joey at his cousin's house. ... more>>

Ferris Wheel Function - Leigh Nataro
Trig/Calc, difficulty level 3. Based on given information, determine a function to describe the height above the ground of a person on a Ferris wheel as a function of time. ... more>>

Find the Function - Leigh Nataro
Trig/Calc, difficulty level 3. Find a cubic polynomial that has a given maximum, minimum, and point of inflection. ... more>>

Fishing on the Bay - Leigh Nataro
Trig/Calc, difficulty level 3. Will the depth of the water on the bay be at the right level for fishing? Write a trig function to find out. ... more>>

Five Golden Rings - Leigh Nataro
Trig/Calc, difficulty level 5. Based on the given information, find the volume of five golden rings. ... more>>

Football Volume - Leigh Nataro
Trig/Calc, difficulty level 3. Given the dimensions of a football, find its volume. ... more>>

The General Box Company - Leigh Nataro
Trig/Calc, difficulty level 3. A rectangular piece of cardboard is folded up to make a box. Find a general formula for the maximum volume of the box. ... more>>

George's Gutters - Leigh Nataro
Trig/Calc, difficulty level 2. Find the maximum volume of a gutter. ... more>>

Googol the Giant's Gargantuan Goblet - Leigh Nataro
Trig/Calc, difficulty level 2. Find the volume of Googol the Giant's elliptical paraboloid goblet. ... more>>

Goose Bay Mountain - Johnson, Patnode, Desautels, Brault, Mahoney
Trig/Calc, difficulty level 2. Using trigonometry, find the angle of takeoff needed for a plane to clear a mountain. ... more>>

Green Pastures - Carol Dormuth
Trig/Calc, difficulty level 1. Find the area of the cow's grazing pasture. ... more>>

The Growing Snowflake - Leigh Nataro
Trig/Calc, difficulty level 4. Find the limit for the area of the Koch snowflake. ... more>>

Happy Birthday to You, & You, & You... - Leigh Nataro
Trig/Calc, difficulty level 3. What is the probability that in a room of 30 people, at least two people will share the same birthday? ... more>>

A Holiday Card - Leigh Nataro
Trig/Calc, difficulty level 3. Find the ratio of the red area to the green area as the number of squares approaches infinity. ... more>>

How Are These Equal? - Leigh Nataro
Trig/Calc, difficulty level 2. Solve a trig identity: cot2x - cos2x equals the product of cot2x and cos2x. ... more>>

How Do You Measure a Mountain? - Leigh Nataro
Trig/Calc, difficulty level 2. Find the height of a mountain based on two angles and the height of a nearby hill. ... more>>

How Large Is The Yard? - Leigh Nataro
Trig/Calc, difficulty level 2. Given three sides and two included angles, find the area of my parents' quadrilateral-shaped backyard. ... more>>

The Indoor Driving Range - Leigh Nataro
Trig/Calc, difficulty level 3. Determine the minimum amount of netting needed to make an indoor driving range golf cage. ... more>>

Irregular Acreage - Leigh Nataro
Trig/Calc, difficulty level 2. Based on the given information, find the missing length of a lot in the shape of a quadrilateral. ... more>>

Is It a Midpoint? - Leigh Nataro, Andrea Medini
Trig/Calc, difficulty level 3. Prove that the point of inflection of a cubic function is the midpoint of the segment that connects the function minimum and the function maximum. ... more>>

Job Interview at the Can-Can Company - Leigh Nataro
Trig/Calc, difficulty level 3. Find the smallest amount of tin needed to make a can that can hold 12 cubic inches. ... more>>

Kite Construction - Leigh Nataro
Trig/Calc, difficulty level 2. Given some information about the dimensions of a kite, find its area. ... more>>

Let Me Guess Your Number - Leigh Nataro
Trig/Calc, difficulty level 3. Discover the patterns behind a number puzzle. ... more>>

Let's Measure the Earth - Leigh Nataro
Trig/Calc, difficulty level 3. Use Eratosthenes' measurements to calculate the radius of the earth. ... more>>

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