1019 past contests
Topic 27 · $y=x^3-3x^2+8$ at $x=2$: increasing, stationary or a maximum? (true/false)
Topic 19 · Factorised equation with $x$-intercepts $-3$, $5$ and $y$-intercept $30$ (speed race)
Topic 46 · Locus of points defined by abscissa and ordinate conditions (true/false)
Topic 35 · Area of a rhombus with side $13$ cm and diagonal $10$ cm
Topic 8 · Solving $\log(x+6)+\log(x-2)=\log(2x+3)$ for a positive value of $x$
Topic 40 · Riddle: identifying a trig function from period, amplitude and zeros
Topic 39 · Solving $2\sin^2x-\sin x=0$ for $0\lt x\lt\pi$
Topic 16 · Significant figures: counting them and rounding, e.g. $0.00340$ and $45.678$ to $3$ s.f.
Topic 11 · Matrix algebra: is $ab=ba$? distributive law and symmetric matrices (true/false)
Topic 11 · Zero determinant: transformations such as $t(x,y)\to(x-y,\ -x+y)$ with no inverse
Topic 44 · Triangle vertices from three intersecting lines
Topic 9 · Riddle: identifying a three-digit number from digit clues
Topic 15 · Selecting committees of men and women using combinations, e.g. $\binom{m}{k}\binom{w}{l}$
Topic 21 · Solving $|ax+b|=x$ (second contest)
Topic 10 · Probability that two fair dice give a total of $6$ with both scores odd (speed race)
Topic 19 · Quadratic equation with integer coefficients having the root $3+\sqrt{7}$
Topic 8 · Solving $(2x-3)^{x+2}=1$
Topic 35 · If the diagonals bisect the vertex angles, is the quadrilateral a parallelogram, square or rectangle? (true/false)
Topic 23 · Is $\dfrac{\sqrt{x-2}}{\sqrt{x+2}}$ a rational expression? (true/false)
Topic 23 · Solving $\dfrac{2x-3}{x-1}\lt1$