Negative Numbers - January 2008, Stage 4&5

Problems

First Connect Three

Stage: 2, 3 and 4 Challenge Level:

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

Negatively Triangular

Stage: 4 Challenge Level:

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

Minus One Two Three

Stage: 4 Challenge Level:

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 ?

Negative Power

Stage: 4 Challenge Level:

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

' Tis Whole

Stage: 4 and 5 Challenge Level:

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?

Root Hunter

Stage: 5 Challenge Level:

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

Differential Equation Matcher

Stage: 5 Challenge Level:

Match the descriptions of physical processes to these differential equations.

It's Only a Minus Sign

Stage: 5 Challenge Level:

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