1019 past contests
Topic 8 · Solving $9^{2x-2}=3^{3x+4}$, $8^{x+4}=4^{2x-3}$ and $25^x=5^{3x-5}$
Topic 7 · Riddle: intersection of sets
Topic 26 · Factor theorem: $x^2-25$ is a factor of $x^3-125$ (true/false)
Topic 38 · Evaluating inverse trig functions outside the principal range (true/false)
Topic 30 · Curve $y=x(8-x)$: intersections with $y=12$, area under the curve and a tangent
Topic 44 · Tangent of the angle between two lines from their gradients
Topic 8 · Solving $3^{\log x}=\dfrac{1}{27}$
Topic 13 · First term and common difference given $u_2=5$ and $u_7=-5$
Topic 44 · Equation of a line through two given points
Topic 25 · Constants $a$ and $b$ in $a(x-2)+b(x+1)=3x-3$
Topic 25 · Inconsistent system $3y+4=5x$ and $10x-12=6y$ with no solution
Topic 14 · Composite function $f(g(x))$ for $f(x)=x^2+5$ and $g(x)=2x-3$
Topic 38 · Inverse of $y=\sin\left(\dfrac{x}{2}\right)$ for $-\pi\lt x\lt\pi$
Topic 1 · Magnitudes of $2a-b$, $3a+3b$, $a+2b$ for $a=2i+j$, $b=i-3j$
Topic 30 · Evaluating $\int_{-1}^{1}(4x^3-3x^2+2x)\,dx$
Topic 31 · Riddle: the tangent, a secant meeting a circle at one point
Topic 26 · Difference of two squares factorisations such as $x^2-3=(x-\sqrt{3})(x+\sqrt{3})$ (true/false)
Topic 42 · Signs of trig ratios for an obtuse angle (true/false)
Topic 11 · Finding $t$, its matrix and its inverse from $t(1,0)=(2,1)$ and $t(0,1)=(5,3)$
Topic 44 · Slope and y-intercept of a line in intercept form