7th and 8th graders
February 2015
C.1009. The edges of a cube measured in centimeters are whole numbers. Its volume in cubic cm is a 6-digit number that is divisible by 336. How big is this cube?
C.1010. How many positive whole numbers not greater than 2015 have at least one prime digit?
C.1011. (1 + 1/2)(1 + 1/3)(1 + 1/4) ... (1 + 1/2015) = ?
C.1012. 2^2015 + 2^2014 + 2^2013 + 2^2012 + 2^2011 = k(2^2011)
Find k.
C.1013. Steve's rectangular shaped window is divided into 3x3 smaller sections.
Steve paints an identical sized digital number-digit in the middle of each of two of these sections so that the whole window looks just the same from the outside as from the inside. How many different ways can he do this?
The digital number-digits look like these:
C.1014. 1! + 2! + 3! + ... + 2015! = N
Find the last two digits of N. (As you probably know, n! means the product of the first n positive whole numbers.)
C.1015. Is there such a positive whole power of 5 in which all ten digits appear and exactly the same number of times?
C.1016. In triangle ABC (see the diagram) AB = AC. We know also that angle BAC is 20 degrees, angle QCB is 50 degrees, and angle PBC is 40 degrees. How big is angle PQC?
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providing instruction for over 700 students in Junior Kindergarten through Grade 12.
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