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Started by Alex Killilea in Challenge of the Week: The graph $f(x)=ax^{2}+bx+c$ cuts the $y$-axis at the point $(0,2)$ and the $x$ -axis at the points $(1,0)$ and $(2,0)$. Find the value of...

Started by Alex Killilea in Challenge of the Week: What is the second most irrational number?

Started by Alex Killilea in Challenge of the Week: If $ax^{2}+bx+c=0$, prove that $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$ for all values of $x$.

Started by Alex Killilea in Challenge of the Week: Find $ y$ when $4y-2=2$ .

Started by Alex Killilea in Challenge of the Week: What are the odds of picking a picture card or an ace out of a standard deck of playing cards?

Started by Alex Killilea in Challenge of the Week: Find $p$ when $3(4p-7)=7p+9$.

Started by Alex Killilea in Challenge of the Week: The perimeter of a rectangle is 18cm. If it has a width $2x$ 2x cm and a length $(x+3)$ (x+3) cm, find the value of $x$ x .

Started by Alex Killilea in Challenge of the Week: What palindrome represented by the arrangement $abba$ satisfies the equation $3(b-a)=\frac{3b}{2(b-a)}$.

Started by Alex Killilea in Challenge of the Week: If a passcode has to be ten digits long, only numbers, and no number can only be repeated twice, how many possible passcodes could there be?

Started by Alex Killilea in Challenge of the Week: Evaluate $\lim_{x\to2}\frac{8-x^{3}}{4-x^{2}}$.

Started by Alex Killilea in Challenge of the Week: Solve for $x=\sqrt{19-2x}+2$.

Started by Alex Killilea in Challenge of the Week: Solve for $x-11+\frac{24}{x}=0$

Started by Alex Killilea in Challenge of the Week: Solve for $x$ when $\frac{1}{27}\cdot3^{59}\cdot\frac{1}{243}\cdot27^{x}=\frac{1}{3}\cdot3^{x}$

Started by Alex Killilea in Challenge of the Week: How many numbers less than 1,000,000 have digits that total 3 (e.g, 12, 300, 2001)

Started by Alex Killilea in Challenge of the Week: At a certain school, the ratio of first-year students to third-year students is 4 to 7. The ratio of transition year students to first-year students...

Started by Alex Killilea in Challenge of the Week: Solve for $3x-5=16$.

Started by Alex Killilea in Challenge of the Week: What do 8 and -9 have in common?

Started by Alex Killilea in Challenge of the Week: Which mathematician's name contains "bob" and arm"?

Started by Alex Killilea in Challenge of the Week: Divide $ x^{2}+5x+6$ by $x-3$.

Started by Alex Killilea in Challenge of the Week: The sum of a number and half of the number is 12. Find the number.

Started by Alex Killilea in Challenge of the Week: Express $\frac{3}{5}-\frac{2x-1}{10}+\frac{3x-2}{4}$ a s a single fraction.

Started by Alex Killilea in Challenge of the Week: A contractor estimated that he could do a certain job in 1 year with 280 men. If he were asked to do the work in 10 months, how many more men would...

Started by Alex Killilea in Challenge of the Week: Why is 1 not a prime number?

Started by Alex Killilea in Challenge of the Week: Solve the inequality: $4-3x -5, x \in \mathbb{Z}$.

Started by Alex Killilea in Challenge of the Week: How many three-litre bottles of water can you fill with seven two and a half beakers of six-hundred litres, each a quarter filled?

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