- Add It Up - Leigh Nataro
Trig/Calc, difficulty level 2. Find the sum for an infinite series.
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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 90-degree turn at the end. How wide must the corridor be in order for the girder to fit around the corner?
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- Be My Valentine - Leigh Nataro
Trig/Calc, difficulty level 4. Find the areas of two heart-shaped valentines.
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- Building a Sandbox - Leigh Nataro
Trig/Calc, difficulty level 3. Find the maximum area for a triangular-shaped 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 8.5-inch by 11-inch piece of paper.
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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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- 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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- 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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- 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 cross-section of an egg given some dimensions of the cross-section.
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- 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?
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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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- 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.
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- 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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- 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.
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- 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.
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- 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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- 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 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.
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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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- 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 6-ft by 100-ft 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 non-overlapping regions of two circles.
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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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- Rolle's Theorem Rediscovered - John Feminella
Trig/Calc, difficulty level 3. Prove the Mean Value theorem.
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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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- 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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- 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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- 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?
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- The Suspension Bridge - Leigh Nataro
Trig/Calc, difficulty level 4. Determine the length of a parabola-shaped cable on a suspension bridge.
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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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- 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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- 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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- 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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- Your Interview Question Is... - Leigh Nataro
Trig/Calc, difficulty level 3. If you want to minimize the surface area of a can with a fixed volume, what should be the ratio of the height to the radius?
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- Your Speeding Ticket - Leigh & Chip Nataro
Trig/Calc, difficulty level 2. Work with powers of ten and the metric system to determine your fine.
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