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Browse all Trig/Calculus Problems of the Week
Participation in the Trig/Calculus Problems of the
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NCTM
Problem Solving Standard for Grades 912, 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
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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?
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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.
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Around the Corner
 Louis Holmes

Trig/Calc, difficulty level 4. A girder must be carried along a corridor that has a 90degree turn at the end. How wide must the corridor be in order for the girder to fit around the corner?
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Basketball Angles
 Richard Tchen

Trig/Calc, difficulty level 4. Find the minimum angle at which a basketball will pass through a basketball hoop.
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Be My Valentine
 Leigh Nataro

Trig/Calc, difficulty level 4. Find the areas of two heartshaped valentines.
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Building a Sandbox
 Leigh Nataro

Trig/Calc, difficulty level 3. Find the maximum area for a triangularshaped sandbox.
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Building Boxes
 Leigh Nataro

Trig/Calc, difficulty level 2. Find the maximum volume of a rectangular prism constructed from an 8.5inch by 11inch piece of paper.
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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.
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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.
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Center Coordinates
 Leigh Nataro

Trig/Calc, difficulty level 2. Find the coordinates of the center of a circle circumscribed around a triangle.
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Cooling Colas
 Leigh Nataro

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

Trig/Calc, difficulty level 1. Find the angle of intersection of two roads based on given information.
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Costly Cable
 Leigh Nataro

Trig/Calc, difficulty level 3. Find where to lay a fiber optic cable in order to minimize the cost.
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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.
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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.
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Cup Capacity
 Leigh Nataro

Trig/Calc, difficulty level 3. Find the volume of a cup based on its dimensions.
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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 ?
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A Deviation from the Average
 Leigh Nataro

Trig/Calc, difficulty level 2. Create some data sets with a specific mean and standard deviation.
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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.
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Doughnut Dilemma
 Leigh Nataro

Trig/Calc, difficulty level 2. Which doughnut shop makes a doughnut with a greater volume?
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An Eggstra Special Problem
 Leigh Nataro

Trig/Calc, difficulty level 2. Find the area of a crosssection of an egg given some dimensions of the crosssection.
... more>>

Ellipse Areas
 Leigh Nataro

Trig/Calc, difficulty level 3. Use calculus to show that the area of an ellipse is pi*a*b.
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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.
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Find the Function
 Leigh Nataro

Trig/Calc, difficulty level 3. Find a cubic polynomial that has a given maximum, minimum, and point of inflection.
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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.
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Five Golden Rings
 Leigh Nataro

Trig/Calc, difficulty level 5. Based on the given information, find the volume of five golden rings.
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Football Volume
 Leigh Nataro

Trig/Calc, difficulty level 3. Given the dimensions of a football, find its volume.
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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.
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George's Gutters
 Leigh Nataro

Trig/Calc, difficulty level 2. Find the maximum volume of a gutter.
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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.
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The Growing Snowflake
 Leigh Nataro

Trig/Calc, difficulty level 4. Find the limit for the area of the Koch snowflake.
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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?
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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.
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How Are These Equal?
 Leigh Nataro

Trig/Calc, difficulty level 2. Solve a trig identity: cot^{2}x  cos^{2}x equals the product of cot^{2}x and cos^{2}x.
... 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' quadrilateralshaped 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.
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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.
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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 CanCan 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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