2013 - 29 & 30

Another geometry question? This test seemed to have a bunch in a row.

Difficulty: Hard.

Difficulty: Medium. Series and complex numbers in the same question? What fun !

Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest 2013

answer 29, answer 30. Published 5/1.

2013 ... 25 & 26

Today, we have a nice addition to the questions about synthetic division and complex numbers.

Difficulty: Easy, but the "three solutions must be positive" is a nice twist on this.

Difficulty: Medium, because of the time pressure ... determining the patterns is straightforward.

Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest 2013

answer 25, answer 26. Published 4/29.

2002 #7 and 35

Complex numbers, binomial expansion, rationalizing the denominator, oh-my! Then combinations!

Difficulty: moderately difficult, time is the problem for some.

Difficulty: Combinations annoy me.

Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest

answer 07 and answer 35.