Category Archives: Algebra

MATHCOUNTS Exercises – 14

Posted on January 19, 2020 by kevin

Lisa wants to use her calculator to square a two-digit positive integer, but she accidentally enters the tens digit incorrectly. When she squares the number entered, the result is 2340 greater than the result she would have gotten had she … Continue reading →

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MATHCOUNTS Exercises – 13

Posted on January 16, 2020 by kevin

In regular pentagon $ABCDE$, point $M$ is the midpoint of side $AE$, and segments $AC$ and $BM$ intersect at point $Z$. If $ZA = 3$, what is the value of $AB$? Express your answer in simplest radical form. Source: MATHCOUNTS … Continue reading →

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MATHCOUNTS Exercises – 11

Posted on January 11, 2020 by kevin

As shown in the following figure, a quarter circle is drawn in a unit square, and 3 smaller squares are inscribed inside the quarter circle. Find the total area of the 3 smaller squares. Click here for the hint. Hint … Continue reading →

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Problem of the Day – November 28, 2019

Posted on November 28, 2019 by kevin

There is a staircase with 13 steps, and you can climb either 1 step or 2 steps at a time. Can you find out the number of unique ways you can climb to the top of the staircase? The order … Continue reading →

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Problem of the Day – November 22, 2019

Posted on November 22, 2019 by kevin

Line $A$ is defined by $y = 4x + 3$ and line $B$ is defined by $y = 4$, and they intersect at a point, $D$. Line $C$, which has the equation $y = mx + 1$, intersects line $A$ and $B$ … Continue reading →