加拿大滑铁卢数学竞赛真题分享及答案!

加拿大数学教赛体系在中国较为知名的,是滑铁卢大学University of Waterloo举办的一系列以数学家为名的数学竞赛,从7年级到12年级各有对应的比赛。所以我们今天准备一些考试真题,快来做做看!

1.The digits from 1 to 9 are written in order so that the digit n is written n times. This forms the block of digits 1223334444 · · · 999999999. The block is written 100 times. What is the 1953rd digit written? (2018 Gauss 7)

2.In the diagram, two larger circles with radius 1 have centres P and Q. Also, the smaller circle has diameter PQ. The region inside the two larger circles and outside the smaller circle is shaded. The area of the shaded region is closest to (2018 Pascal 9)

3.The number of ways that 135 can be expressed as the sum of at leastt two consecutive positive integers is?

4.In a magic triangle, each of the six whole numbers 10-15 is placed in one of the circles so that the sum, S, of the three numbers on each side of the triangle is the same. The largest possible value for S is

5.Two different prime numbers between $4$ and $18$ are chosen. When their sum is subtracted from their product, which of the following numbers could be obtained?

A)  22

B) 60

C)119

D) 94

E)231


答案:

1. 6

2.约等于0.443

3. 7

4. 39

5.C

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