Mathematics
Maths calculators
Percentages, descriptive statistics, fractions and equations: the calculations that come up most often at school, at university and in everyday work.
Which calculation you need
Percentages cover four different questions that only look alike: what a percentage of a total comes to, what percentage one figure is of another, what an amount becomes after a markup or a discount, and what the price was before a change that has already been applied — the reverse calculation, and the one most often got wrong. Descriptive statistics boil a set of data down to a handful of measures: mean and median say where the centre is, standard deviation and quartiles say how spread out the values are. Fractions matter when the exact form counts for more than the decimal, as in ratios and probabilities. Linear and quadratic equations are the next step: they find the value of the unknown, and for the quadratic case the vertex of the parabola and the factored form as well.
Percentages
Percentage of a total, markups and discounts, change between two values, and reverse percentage.
Derivatives
First, second and third derivative, with the rules each one took.
Integrals
Antiderivative and definite integral, with the method used for each.
Domain of a function
Where a function exists: denominators, roots, logarithms and arcsines checked for you.
Limits
Left and right limits, limits at ±∞ and the indeterminate form a limit starts from.
Asymptotes
Every asymptote of a function, vertical, horizontal or oblique, drawn on its graph.
Study of a function
The whole study from domain to graph, with the exact values of zeros, extrema and inflections.
Descriptive statistics
Mean, median, mode, variance and standard deviation, quartiles and distribution.
Fractions
The four operations on fractions, reduction to lowest terms and decimal-to-fraction conversion.
Linear and quadratic equations
Real or complex roots, discriminant, vertex and factored form.
Synthetic division
Division by (x − a) with the table step by step, rational roots and the factorisation.
Trigonometric formulas
Every identity evaluated on your own angles: half-angle, double-angle, addition, prosthaphaeresis and Werner.
GCD and LCM
Greatest common divisor and least common multiple with prime factorization and Euclid's algorithm.
Proportions
The missing term of a proportion, the fourth proportional, the geometric mean and the third proportional.
Combinatorics
Factorial, permutations, arrangements, combinations and the binomial coefficient.
Inequalities
Linear and quadratic inequalities solved by sign analysis.
Logarithms and exponentials
Logarithm in any base, exponential equations, antilogarithm and change of base.
Radicals
Simplifying roots and rationalising denominators.
Probability
Classical and conditional probability, Bayes' theorem and the binomial distribution.
Sequences
Arithmetic and geometric sequences, nth term and sums.
Grade average
Simple and weighted averages, and the mark needed to hit a target.
Complex numbers
Operations, rectangular, polar and exponential form, powers and n-th roots, with the Argand diagram.
Prime factorisation
Prime factors of a number up to 30 digits, with the division ladder, divisors and a primality test.
Factoring polynomials
Common factor, the factor theorem, special products and quadratics: factoring a polynomial step by step.
Repeating decimal to fraction
From a recurring decimal to a fraction and from a fraction to a decimal, with the repeating block and the rule explained.
Scientific notation
Scientific and engineering notation, significant figures and rounding of any number.
Differential equations
First and second-order linear differential equations with constant coefficients, with solution and graph.