Standard antiderivatives
Working back to antiderivatives up to a constant: reference functions, powers, polynomials and simple compositions.
Click a card to see its answer. Series no. 319474 — this page’s address gives these exact cards again.
Other series
Areas and perimeters
Working out the area or the perimeter of the usual shapes — square, rectangle, triangle, disc — without opening the formula sheet.
Arithmetic with signed numbers
Adding, subtracting and multiplying signed numbers, where the signs trip up the reflexes.
Complex numbers
Powers of i, modulus and conjugate: the reflexes that save time on any complex-number calculation.
Decimal form of simple fractions
Going from a simple fraction to its decimal form and back to the fraction, in your head, without long division.
Discriminant and roots
Discriminant, sum and product of the roots of a quadratic, read straight off the coefficients.
Fractions in lowest terms
Reducing a fraction to its lowest terms by spotting the common divisor at a single glance.