Negative Numbers - January 2008, Stage 4&5

Problems

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Negatively Triangular

Stage: 4 Challenge Level: Challenge Level:1

How many intersections do you expect from four straight lines ? Which three lines enclose a triangle with negative co-ordinates for every point ?

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Minus One Two Three

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Substitute -1, -2 or -3, into an algebraic expression and you'll get three results. Is it possible to tell in advance which of those three will be the largest ?

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Negative Power

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

What does this number mean ? Which order of 1, 2, 3 and 4 makes the highest value ? Which makes the lowest ?

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' Tis Whole

Stage: 4 and 5 Challenge Level: Challenge Level:2 Challenge Level:2

Take a few whole numbers away from a triangle number. If you know the mean of the remaining numbers can you find the triangle number and which numbers were removed?

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Root Hunter

Stage: 5 Challenge Level: Challenge Level:1

In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.

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Differential Equation Matcher

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Match the descriptions of physical processes to these differential equations.

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It's Only a Minus Sign

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Solve these differential equations to see how a minus sign can change the answer