Category Archives: Math Classes

AMC 10 Exercise – 2

Posted on October 20, 2024 by kevin

What is the tens digit of $2019^{2020}-2021$? All the numbers $2$,$3$,$4$,$5$ are assigned to the four faces of a tetrahedron. For each of the four vertices of the tetrahedron, a product of three numbers are computed, where the three numbers … Continue reading →

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AMC 10 Exercise – 1

Posted on September 20, 2024 by kevin

Two years ago Pete was three times as old as his cousin Claire. Two years before that, Pete was four times as old as Claire. In how many years will the ratio of their ages be $2:1$? Two right circular cylinders … Continue reading →

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AMC 10 Training – Number Theory – 1

Posted on February 25, 2024 by kevin

Let $a$, $b$, $c$ be real numbers with $|a-b|=3$, $|b-c|=4$, and $|c-d|=5$. What is the sum of all possible values of $|a-d|$? What is the greatest integer less than or equal to $$\dfrac{5^{200}+3^{200}}{5^{197}+3^{197}}$$ How many negative integers can be written … Continue reading →

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AMC 8/MathLeague Mock Test – 1

Posted on January 26, 2024 by kevin

If the hands on a circular clock start at midnight, what number will the hour hand point to 1000 hours later? $(A)\ 2 \ \ \ \ \ \ \ \ \ (B)\ 4 \ \ \ \ \ \ … Continue reading →

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Algebra Exercise – Simplify Square Root

Posted on October 6, 2023 by kevin

Simplify $$\sqrt{\sqrt{9}-\sqrt{8}}$$ Simplify $$\sqrt{\sqrt{4}-\sqrt{3}}$$ Simplify $$\sqrt{\sqrt{25}-\sqrt{24}}$$ Simplify $$\sqrt{\sqrt{49}-\sqrt{48}}$$ Simplify $$\sqrt{\sqrt{64}-\sqrt{63}}$$ Simplify $$\sqrt{\sqrt{225}+\sqrt{224}}$$ Simplify $$\sqrt{\sqrt{16}+\sqrt{15}}$$ Simplify $$\sqrt{\sqrt{5}+\sqrt{4}}$$ Simplify $$\sqrt{\sqrt{81}+\sqrt{80}}$$ Simplify $$\sqrt{\sqrt{121}+\sqrt{120}}$$

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