60Upper Secondary Big Buttonhttp://nrich.maths.org/secondary-upperen 2012 http://nrich.maths.org/public/terms.phpVanishing RootsIf $y=x^2-6x+c$, and we vary $c$, what happens to the roots when $c>9$?http://nrich.maths.org/13167Wed, 01 Dec 1999 00:00:01 +0000Imagine This!http://nrich.maths.org/13166Wed, 01 Dec 1999 00:00:01 +0000Strolling AlongWhat happens when we multiply a complex number by a real or an imaginary number?http://nrich.maths.org/13131Wed, 01 Dec 1999 00:00:01 +0000Opening the DoorWhat happens when we add together two complex numbers?http://nrich.maths.org/13129Wed, 01 Dec 1999 00:00:01 +0000Stretching an IntegralWhat happens to areas under the graph of $\frac{1}{x}$ when they are stretched? <a href="https://undergroundmathematics.org/calculus-trig-log/stretching-an-integral"></a>http://nrich.maths.org/12912Wed, 01 Dec 1999 00:00:01 +0000Trigsy IntegralsWhat different ways can you find to calculate these integrals? <a href="https://undergroundmathematics.org/calculus-trig-log/trigsy-integrals"></a>http://nrich.maths.org/12911Wed, 01 Dec 1999 00:00:01 +0000Sine StretchingCan you find the gradient function of $\sin 3x$. How did you convince yourself? <a href="https://undergroundmathematics.org/calculus-trig-log/sine-stretching"></a>http://nrich.maths.org/12910Wed, 01 Dec 1999 00:00:01 +0000Slippery AreasCan you find the definite integral of a transformed function? <a href="https://undergroundmathematics.org/chain-rule/slippery-areas"></a>http://nrich.maths.org/12909Wed, 01 Dec 1999 00:00:01 +0000Can You Find... Asymptote EditionCan you work out the equation of the function from its graph? <a href="https://undergroundmathematics.org/polynomials/can-you-find-asymptote-edition"></a>http://nrich.maths.org/12825Wed, 01 Dec 1999 00:00:01 +0000Rotating DerivativesBy considering a point on a unit circle, can you use geometry to find the derivatives of $\sin x$ and $\cos x$? <a href="https://undergroundmathematics.org/calculus-trig-log/rotating-derivatives"></a>http://nrich.maths.org/12824Wed, 01 Dec 1999 00:00:01 +0000Slices of PiHow are $\sin x$, $\cos x$ and $\tan x$ related to each other? Can you make sense of the the 'slices'? <a href="https://undergroundmathematics.org/trigonometry-triangles-to-functions/slices-of-pi"></a>http://nrich.maths.org/12823Wed, 01 Dec 1999 00:00:01 +0000ParabellaCan you prove an algebraic statement using geometric reasoning? <a href="https://undergroundmathematics.org/quadratics/parabella"></a>http://nrich.maths.org/12822Wed, 01 Dec 1999 00:00:01 +0000Worth 1000 WordsWhich of the sketches matches the function given? <a href="https://undergroundmathematics.org/thinking-about-functions/worth-1000-words"></a>http://nrich.maths.org/12476Wed, 01 Dec 1999 00:00:01 +0000Muddled TrigCan you match all the different trig functions to their graphs? <a href="https://undergroundmathematics.org/trigonometry-triangles-to-functions/muddled-trig"></a>http://nrich.maths.org/12475Wed, 01 Dec 1999 00:00:01 +0000Translating or Not?Can you sketch the graphs of these two reciprocal functions? What are the links between them? <a href="https://undergroundmathematics.org/combining-functions/translating-or-not"></a>http://nrich.maths.org/12474Wed, 01 Dec 1999 00:00:01 +0000Function Builder 1What happens when you combine functions? Can you sketch the results? <a href="https://undergroundmathematics.org/combining-functions/function-builder-i"></a>http://nrich.maths.org/12473Wed, 01 Dec 1999 00:00:01 +0000Underground Mathematics - Share Your SolutionsHere's how you can send in your solutions to these Underground Mathematics problems.http://nrich.maths.org/12349Wed, 01 Dec 1999 00:00:01 +0000Towering TrapeziumsCan you find the areas of the trapezia in this sequence?http://nrich.maths.org/11449Sun, 01 Mar 2015 00:00:01 +0000Difference of Two SquaresWhat is special about the difference between squares of numbers adjacent to multiples of three?http://nrich.maths.org/11120Mon, 01 Sep 2014 00:00:01 +0100Pythagoras PerimetersIf you know the perimeter of a right angled triangle, what can you say about the area?http://nrich.maths.org/11106Mon, 01 Sep 2014 00:00:01 +0100Mega Quadratic EquationsWhat do you get when you raise a quadratic to the power of a quadratic?http://nrich.maths.org/11009Wed, 01 Dec 1999 00:00:01 +0000Graphs of Changing AreasUse graphs to gain insights into an area and perimeter problem, or use your knowledge of area and perimeter to gain insights into the graphs...http://nrich.maths.org/7559Fri, 01 Jul 2011 00:00:01 +0100Inner EqualityCan you solve this inequalities challenge?http://nrich.maths.org/7105Tue, 01 Feb 2011 00:00:01 +0000Unit IntervalCan you prove our inequality holds for all values of x and y between 0 and 1?http://nrich.maths.org/7051Tue, 01 Feb 2011 00:00:01 +0000Classical MeansUse the diagram to investigate the classical Pythagorean means.http://nrich.maths.org/6593Tue, 01 Feb 2011 00:00:01 +0000Area LBy sketching a graph of a continuous increasing function, can you prove a useful result about integrals?http://nrich.maths.org/2375Tue, 01 Feb 2011 00:00:01 +0000In BetweenCan you find the solution to this algebraic inequality?http://nrich.maths.org/2056Tue, 01 Feb 2011 00:00:01 +0000Of All the AreasCan you find a general rule for finding the areas of equilateral triangles drawn on an isometric grid?http://nrich.maths.org/693Tue, 01 Feb 2011 00:00:01 +0000System SpeakFive equations... five unknowns... can you solve the system?http://nrich.maths.org/543Tue, 01 Feb 2011 00:00:01 +0000