1019 past contests
Topic 9 · Riddles identifying prime numbers from their divisibility property
Topic 27 · Functions with no finite stationary point: $x$, $\dfrac{1}{x}$, $(x-2)^2$ (true/false)
Topic 43 · Identifying the centre of a circle from its general equation (true/false)
Topic 40 · Maximum values of trig functions within restricted intervals (true/false)
Topic 4 · Riddle: standard deviation as a measure of dispersion
Topic 20 · Riddles identifying pascal's triangle from its properties
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 $1$ cm (true/false)
Topic 9 · Riddle: an odd square between $100$ and $200$ with a prime base
Topic 19 · Is $\alpha^2+\beta^2=b^2+4c$ for the roots of $x^2+bx+c=0$? (true/false)
Topic 8 · Verifying $4\log x+2=\log(100x^4)$ and similar identities (true/false)
Topic 40 · Greatest value of $6\cos\theta+8\sin\theta$ is $10$ (true/false)
Topic 31 · Riddles identifying the segment, sector, chord, diameter, arc and circumference
Topic 26 · Sum and difference of two cubes, such as $x^3-y^3=(x-y)(x^2-xy-y^2)$ (true/false)
Topic 46 · Locus of points defined by distance and coordinate-sum conditions such as $x=3$, $x+y=15$ (true/false)
Topic 8 · Expressing $\log\sqrt{\dfrac{a^2b^4}{c^6}}$ in terms of $\log a$, $\log b$ and $\log c$
Topic 42 · Parametric identity $(x+1)^2+(y-3)^2=4$ (true/false)
Topic 13 · Inserting three numbers between $-17$ and $7$ to form a linear sequence
Topic 26 · Cubic $x^3+px^2+qx+6$ divisible by $x-2$ and $x-1$: find $p$ and $q$
Topic 26 · Factorising $x^3-3x^2+2x-6$ by grouping