You may also like

problem icon

Modular Fractions

We only need 7 numbers for modulus (or clock) arithmetic mod 7 including working with fractions. Explore how to divide numbers and write fractions in modulus arithemtic.

problem icon

Power Quady

Find all real solutions of the equation (x^2-7x+11)^(x^2-11x+30) = 1.

problem icon

Areas and Ratios

Do you have enough information to work out the area of the shaded quadrilateral?

Mind Your Ps and Qs

Age 16 to 18 Short Challenge Level:

Here are 16 propositions involving a real number $x$:


$x\int^x_0 ydy < 0$ $x> 1$ $0< x< 1 $ $x^2+4x+4 =0$
$x=0 $ $\cos(x/2)> \sin(x/2)$ $x> 2$ $x=1$
$2\int^{x^2}_0ydy> x^2 $ $x< 0 $ $x^2+x-2=0$ $x=-2 $
$x^3> 1$ $|x|> 1$ $x> 4$ $\int^x_0 \cos y dy =0$

[Note: the trig functions are measured in radians]

By choosing $p$ and $q$ from this list, how many correct mathematical statements of the form $p\Rightarrow q$ or $p\Leftrightarrow q$ can you make?

It is possible to rearrange the statements into four statements $p\Rightarrow q$ and four statements $p\Leftrightarrow q$. Can you work out how to do this?


Logical thinking is at the heart of higher mathematics: In order to construct clear, correct arguments in ever more complicated situations mathematicians rely on clarity of language and logic. Logic is also at the heart of computer programming and circuitry.