1019 past contests
Topic 10 · Riddle: independent events
Topic 42 · Related-angle equalities for $(2\pi-x)$ (true/false)
Topic 9 · Verifying congruences such as $15\equiv-13\pmod{14}$ (true/false)
Topic 19 · Constants in $10-12x-2x^2=a-b(x+c)^2$
Topic 8 · Finding all real roots of $4^{x^3}=256^x$
Topic 27 · Point of inflection of $y=x^3+6x^2-6x-8$
Topic 18 · Solving $\sqrt{2x^2-9}=x$, $\sqrt{5x^2-36}=2x$ and $\sqrt{\dfrac{3x^2}{2}-2}=x$
Topic 10 · Committee of three chosen from five girls and three boys
Topic 13 · Riddle: pascal's triangle
Topic 43 · Conditions for $ax^2+by^2+2fx+2gy+c=0$ to be a circle (true/false)
Topic 31 · Arc of $30^\circ$ at the centre of a circle of radius $2$ cm (true/false)
Topic 1 · Magnitude of $3\mathbf{a}+2\mathbf{b}$ for $\mathbf{a}=3\mathbf{i}-2\mathbf{j}$, $\mathbf{b}=2\mathbf{i}+3\mathbf{j}$
Topic 9 · Expressing $43$ as a difference of two squares
Topic 26 · Factorising $x^3-3x^2+4$ completely
Topic 27 · Points on a cubic curve with a given gradient (e.g. $y=x^3+6x^2+3x+3$, gradient $-6$)
Topic 8 · Solving $\log_a x - k\log_x a = c$ using the reciprocal relationship between mutual-base logs
Topic 9 · Riddle: an odd square between $100$ and $200$ whose square root is prime
Topic 40 · Greatest value of a linear combination of sine and cosine (true/false)
Topic 8 · Verifying $4\log x+2=\log(100x^4)$ and similar identities (true/false), second contest
Topic 11 · Image of $a(2,-4)$ under a reflection in the point $p(3,-2)$