Math

Integer arithmetic, shifts and rotates inside an 8, 16, 32 or 64 bit word, with the carry, overflow, zero and sign flags and every result in four bases.

Multiplies whole numbers of up to fifty digits and shows the working: a partial product for every digit, the column they add up in, and every carry.

Exact hypergeometric p value for a 2x2 contingency table, one tailed and two tailed, with the odds ratio and the whole distribution the p value is read from.

Expand a logarithm into a sum of simple terms with the product, quotient and power rules shown step by step, and condense a sum of logarithms back into one.

Surface area of a triangular prism from the three sides and the length, with the area of every face, the volume and a scale drawing of the unrolled net.

Writes a line as y = mx + b from a slope and a point, two points or standard form, and builds the parallel and perpendicular lines through any point.

Graph a parabola and get its vertex, axis of symmetry, intercepts, completed square, focus and directrix as exact values rather than read off the picture.

Multiplies two polynomials term by term, collects the like terms and returns the expanded product with its degree and leading coefficient.

Multiplies out a(b + c) with every individual product written down, handles any number of letters, and factors the common term back out of an expression.

Draws a box and whisker plot from your data, with the five number summary, the IQR, the Tukey fences and every outlier named.

Averages percentages the right way. Enter each percentage with the group size behind it and see the weighted answer next to the plain mean of the percentages.

One-way analysis of variance for up to six groups. Returns the sums of squares, degrees of freedom, mean squares, the F statistic and an exact p value.

Solves ax + b = c, x/a + b = c and equations with x on both sides, writing out every step with both sides shown and the answer substituted back as a check.

Evaluate a triple integral over a rectangular box, a cylindrical wedge or a spherical shell, with the inner integrals shown and a numerical check alongside.

Converts between real sizes and scale sizes for models and maps, finds the ratio behind two measurements, and re-scales a size from one ratio to another.

Solve an equation with x in the denominator, clearing the fractions and then throwing out the extraneous roots that a plain equation solver would keep.

Plot a polar curve on a polar grid with a table of theta, r, x and y, plus the petal count, the maximum radius, the symmetry tests and the area swept.

Draw the K-map for 2, 3 or 4 variables from your minterms and don't cares, group it, and return the minimal sum of products and product of sums.

Converts an inequality to interval notation and back, handles and, or and unions, and works out the union, intersection or difference of two intervals.

Solves any triangle from three measurements, SSS, SAS, ASA, AAS or SSA, returning every side, every angle, the area, the heights and both radii.

Approximates a definite integral with the trapezoidal rule, over a polynomial, a standard integrand or a table of measured points, with the error bound.

Gives the tangent line to a curve at a point, the normal line through the same point, and the linear approximation with the error it makes nearby.

Finds the rule behind a list of numbers, arithmetic, geometric, quadratic or Fibonacci style, then gives the nth term, the sum and the terms that come next.

Works out the pointwise mutual information of two events from their joint and marginal probabilities, or from raw counts and a corpus size, with PPMI and normalised PMI alongside.

Differentiates a polynomial in x, y and z with respect to any one of them, and returns the gradient, the second partials and the value of each partial at a point.

Writes a 2x2 or 3x3 matrix as P D P inverse, with the eigenvalues, the eigenvectors that form P, the inverse and the check that the product returns A.

Factorises a 2x2, 3x3 or 4x4 matrix into L and U by Doolittle with partial pivoting, returning P, the permutation sign and the determinant.

Sums geometric, p-series, telescoping and arithmetico-geometric series, names the convergence test that settles each one, and shows a partial sum beside it.

Evaluates a^(bx+c)+d at a point, solves it for x, turns a growth rate into a doubling time and half life, and fits a curve through two readings.

Builds f(g(x)) and g(f(x)) from two standard forms with your own coefficients, shows the substitution and evaluates both at any x you pick.

Finds the inverse sine of a value in degrees, radians and gradians, states the principal value range, and refuses anything outside -1 to 1 with a reason.

Multiplies decimals and shows the working: the whole-number multiplication in a column, how many decimal places the factors carry, and where the point goes.

Adds, subtracts, multiplies and divides hexadecimal numbers, and runs AND, OR, XOR, NOT and the shifts, with every answer given in hex, decimal and binary.

Finds the length of a circular arc from the radius and central angle, with the chord, the sector area and the segment area alongside it.

Adds a column of figures and prints a tape with the running total on every line, plus the added and subtracted subtotals and an optional percentage.

Works RSA through on small primes: the key pair, the encryption and decryption of a number, and the extended Euclid step that produces the private exponent.

Compares two values against their mean, which makes the answer the same whichever way round you enter them, and also gives percent error against a known value.

A fixed table of twelve standard Laplace transforms with your own constants in them, plus polynomials in t by linearity. Symbolic algebra is refused.

Finds the geometric mean of a list of positive numbers, plain or weighted, and shows it beside the arithmetic and harmonic means for comparison.

Expands (a x + b) raised to a whole power using the binomial theorem, term by term, with the Pascal row and the working behind each coefficient shown.

Adds, subtracts, multiplies and divides two binary numbers directly in binary, showing the carries, borrows or partial products, plus AND, OR, XOR, NOT and both bit shifts.

Solves absolute value equations in one variable, splits each one into its two cases and checks every candidate, so an extraneous root is named rather than handed back as an answer.

Finds where a line or parabola crosses each axis, from standard form, slope-intercept form, two points or a quadratic, with exact fractions.

Computes the z test statistic for a mean with a known sigma, for one proportion against a claimed value, and for two proportions compared.

Simplifies one polynomial over another, cancels the common factor, and lists the values the variable may not take, including the ones the cancelling hides.

Solves a : b = c : d for a missing term in any of the four slots, checks whether two ratios really are in proportion, and works out inverse proportions.

Poisson probabilities from a mean or from a rate and an interval: exactly k events, at most k, at least k, or anywhere in a range of counts.

Works a missing side or angle through the sine rule line by line, and prints both triangles when the ambiguous case leaves two of them standing.