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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 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
High School Trigonometry
and Calculus
areas of the Ask Dr. Math archives. To find relevant
sites on the Web, browse and search
Trigonometry and
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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.
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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?
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Managing a Mall
 Leigh Nataro

Trig/Calc, difficulty level 2. Find how many square feet there are in a quadrilateralshaped store.
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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.
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My SnowShoveling Business
 Leigh Nataro

Trig/Calc, difficulty level 2. Determine the number of customers needed to maximize the revenue for a snowshoveling business.
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Needles and Lines
 Leigh Nataro

Trig/Calc, difficulty level 5. Use trigonometry and calculus to find the probability of a needle touching a line.
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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.
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The Ninja Mission
 Steve Earth

Trig/Calc, difficulty level 4. Find the measurement of a spike's angle, given the star's perimeter.
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One Area  Many Solutions
 Leigh Nataro

Trig/Calc, difficulty level 2. Find the area of a triangle given the coordinates of its vertices.
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The Oval Braided Rug
 Leigh Nataro

Trig/Calc, difficulty level 2. Find the area of a shaded portion of an ellipse.
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Painting the Sine Curve
 Leigh Nataro

Trig/Calc, difficulty level 4. Find the length of the sine curve that would fill a 6ft by 100ft rectangle.
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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.
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Pete's Predictions
 Leigh Nataro

Trig/Calc, difficulty level 2. Verify the formula for finding the maximum height of a ball thrown upward.
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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 nonoverlapping regions of two circles.
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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?
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Preparing for the Test
 Leigh Nataro

Trig/Calc, difficulty level 2. Find the original three numbers in an arithmetic sequence.
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A Problematic Pizza
 Leigh Nataro

Trig/Calc, difficulty level 2. Find the area of a specific region of a circle based on given information.
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Product Max
 Leigh Nataro

Trig/Calc, difficulty level 2. Find the maximum value for two numbers whose sum is a.
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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?
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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.
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Rolle's Theorem Rediscovered
 John Feminella

Trig/Calc, difficulty level 3. Prove the Mean Value theorem.
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The Seal of Dalvek
 Steve Earth

Trig/Calc, difficulty level 3. Discover the area of a circular segment based upon its circumference.
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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?
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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.
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Shipping Packages
 Leigh Nataro

Trig/Calc, difficulty level 2. Find the maximum volume of a box based on the given information.
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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."
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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?
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A Sprinkling of Dust
 Leigh Nataro

Trig/Calc, difficulty level 2. Find the length of the Cantor Set after n iterations.
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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.
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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?
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Stonybrooke River Bridge
 Leigh Nataro

Trig/Calc, difficulty level 2. Based on given information, find the distance across a river.
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The Supermarket Shelf
 Leigh Nataro

Trig/Calc, difficulty level 3. What is the optimal shelf height in the supermarket?
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The SuperUltraMegaBig Cup
 Alvirne High School Calculus Class

Trig/Calc, difficulty level 3. What is the minimum cost to make a cup based on given information?
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The Super Yard XT
 Leigh Nataro

Trig/Calc, difficulty level 1. Based on information about the area of a regular polygonshaped play yard, find the length of one of the walls of the yard.
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The Suspension Bridge
 Leigh Nataro

Trig/Calc, difficulty level 4. Determine the length of a parabolashaped cable on a suspension bridge.
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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.
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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.
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That's A Lot of Rock!
 Leigh Nataro

Trig/Calc, difficulty level 3. Find the volume of a tunnel through a mountain.
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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.
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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.
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Triangles, Sines, and Areas
 Leigh Nataro

Trig/Calc, difficulty level 3. Show that the area of any triangle is .5*b*c*sin(A).
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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.
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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.
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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?
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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.
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Vinnie Valentine's MixUp
 Leigh Nataro

Trig/Calc, difficulty level 4. What is the probability of getting exactly 10 out of 20 valentines to the correct person?
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What Is My Dimension?
 Leigh Nataro

Trig/Calc, difficulty level 4. Find the fractal dimension of the Koch curve.
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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?
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Where in the World is Essex Junction?
 Leigh Nataro

Trig/Calc, difficulty level 3. How far is Essex Junction, Vermont, from the equator?
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Where Is Whitehall?
 Leigh Nataro

Trig/Calc, difficulty level 3. Find the distance from Whitehall, Pennsylvania, to the equator.
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