Category Archives: Math Classes

MathCounts Training – Number Theory – 2

Posted on August 25, 2023 by kevin

________ In base $b$, $441_b$ is equal to $n^2$ in base 10, and $351_b$ is equal to $(n-2)^2$. What is the value of $b$, expressed in base 10? ________ The base-three representation of $0.\overline{12}$ is equivalent to what base-ten common … Continue reading →

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MathCounts Training – Number Theory – 1

Posted on August 18, 2023 by kevin

________ Some positive integers have exactly four positive factors. For example, 35 has only 1, 5, 7, and 35 as its factors. What is the sum of the smallest five positive integers that have exactly four factors. ________ What is … Continue reading →

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MathCounts Geometry Exercise – 4

Posted on December 2, 2022 by kevin

________ In parallogram $ABCD$, $EF\parallel AC$. The area of $\triangle{AED}=72\ cm^2$. Find the area the shaded region in $cm^2$. ________ In parallelogram $ABCD$, $CE$ intersects with $DA$ at $F$. The area of $\triangle{BEF}$ is $4\ cm^2$. Find the area the … Continue reading →

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MathCounts Geometry Exercise – 3

Posted on November 18, 2022 by kevin

________ In $\triangle{ABC}$, $D$ is the midpoint of $BC$. $E$ is on $AC$ so that $AE=2\ EC$. The area of $\triangle{ABC}$ is $60\ cm^2$. Find the area of $\triangle{ABF}$ in $cm^2$. ________ The area of rectangle $ABCD$ is $36$. $E$ … Continue reading →

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MathCounts Geometry Exercise – 2

Posted on November 4, 2022 by kevin

A B C D E P ________ The area of $\triangle{ABC}$ is $1$. $BD:DC=2:1$, and $E$ is the midpoint of $AC$. $AD$ intersects $BE$ at point $P$. Find the area of quadrilateral $PDCE$. ________ Rectangle $ABCD$ is divided into 4 … Continue reading →

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