Math

Turn a decimal into a percentage or a percentage back into a decimal, with the working shown and the decimal point moved exactly rather than multiplied.

Average rate of change of a function over an interval, with f(a), f(b), the working, the secant line and the mean value theorem point for a polynomial.

Reduce a product or quotient of powers to a single term, applying the product, quotient, power of a power, negative and zero exponent laws with the arithmetic shown.

Runs a paired-samples t-test on the raw before and after columns, returning the differences, t, both p-values, a confidence interval and the effect size.

Solve a linear program two ways: two variables with the feasible region drawn and the optimum at a vertex, or the simplex tableau with every pivot shown.

Find the root mean square of a list of numbers, or convert between the RMS, peak, peak-to-peak and average values of a sine, square, triangle or rectified waveform.

Left, right, midpoint and trapezoidal sums for one integrand at once, with the strips drawn, the exact value from the antiderivative and each rule's error.

Decide whether a number is rational or irrational, with the exact fraction when it is one and the named theorem when it is not.

Find the sample size a study needs, or the power it already has, for comparing two means or two proportions, using the noncentral t distribution rather than a shortcut.

Find the outliers in a list by the IQR fence rule, the z-score, the modified z-score on the MAD and Grubbs' test, and see where the four disagree.

Odds ratio from a 2 x 2 table with the log-scale confidence interval, the Haldane correction for an empty cell, and the relative risk printed beside it.

Differentiates log_b(u(x)) by the chain rule, and does logarithmic differentiation of a product, a quotient or a variable exponent.

Orders a mixed list of integers, decimals, fractions, mixed numbers, percentages, square roots and multiples of pi, showing each one converted.

Finds k in y = k/x from a table of pairs, fills the gaps, and says whether the numbers really are an inverse variation at all.

Arcsec, arccsc and arccot of a value in degrees, radians, gradians and DMS, with the principal range and both arccot conventions.

Expected value, variance and standard deviation from a list of outcomes and probabilities, with the working shown outcome by outcome and the probabilities checked against one.

Decides whether two algebraic expressions are the same by expanding both to an exact canonical form, with the difference and a counterexample.

Dilates a point or a figure about any centre, giving the image coordinates, the coordinate rule and the length, perimeter and area factors.

Simplify (f(x+h) - f(x))/h for a polynomial, exactly, and see the limit as h approaches zero. Also evaluates the quotient at a chosen x and step size.

Turns two quantities into a unit rate and its reciprocal, and ranks up to four pack sizes at once to show which one is cheapest per unit.

Clears a square root out of a denominator, either a single surd or a sum handled with its conjugate, with every step shown and the surviving root simplified.

Fills in the missing cells of a ratio table, shows the scale factor behind each column, and checks that the columns you already had agree with each other.

Finds the orthocenter of a triangle from three vertices as an exact fraction, with the altitude equations, the circumcenter, the centroid and the Euler line.

Raises a number or a fraction to a fractional exponent and returns the radical form, the exact simplified surd where one exists, and the decimal.

Exact sine, cosine and tangent anywhere on the unit circle, with the quadrant, the reference angle, the coterminal angle and the point written in radicals.

Writes any number as a x 10^n, expands a standard form pair back into an ordinary number, and multiplies, divides, adds or subtracts two of them.

Applies the ratio, root, integral, limit comparison and alternating series tests to a general term, with the limit, the verdict and the reason for each.

Finds the scale factor between two similar figures from matching sides, areas or volumes, and gives the area factor squared and the volume factor cubed.

Inverse tangent in degrees, radians and gradians, with the principal value, the full family of angles, and the two-argument atan2 form.

Solve a trapezoid completely: height, area, perimeter, median, both diagonals and all four angles, from the four sides or from a base angle.

Sideways parabolas and the conic form: x = ay2 + by + c, or a focus and directrix, or a vertex and focus, with the curve drawn.

Transposes a matrix of any shape up to 8 by 8 by swapping its rows and columns, flags symmetry, and can also return the products A^T A and A A^T.

Area of any irregular polygon from a traverse of bearings and distances, or from side lengths with interior angles, with the closure error and a scale drawing.

Integrates a polynomial times e^(kx), sin(kx), cos(kx) or ln(kx) by parts, showing the choice of u and dv and every row of the table, indefinite or between limits.

Solves two or three linear equations by elimination and writes out every row operation, in exact fractions, with the answer checked in the original equations.

Finds where a polynomial's derivative is zero, classifies each point as a maximum, a minimum or neither, and gives the absolute extremes on an interval.

Solves a 2x2 or 3x3 linear system by Cramer's rule, showing the coefficient determinant, each replaced-column determinant and the division that gives every unknown.

Surface area of a cube, box, sphere, cylinder, cone or square pyramid, split into the lateral area and the bases, in square metres, feet and inches.

Solves a two-variable linear system by substitution and writes out every step: the variable isolated, the expression substituted, the collecting, and the check.

Runs the Mann-Whitney U test on two samples, with the exact null distribution for small samples and a tie-corrected normal approximation for large ones.

Differentiates a polynomial equation in x and y implicitly, giving dy/dx as an exact quotient, the second derivative, and the tangent line at a point.

Turn a fraction or a mixed number into a percentage, with the exact value when the division repeats, the lowest terms and the decimal alongside.

Dot product of two vectors in 2D or 3D, with both magnitudes, the angle between them, the projection of one onto the other and an orthogonality check.

Critical values for the z, t, chi-square and F distributions at any alpha, one tailed or two, with the rejection rule and the confidence level spelled out.

Reduces an augmented matrix to reduced row echelon form and reports both ranks, whether the system is consistent, and the full solution set.

Finds the vertical, horizontal and slant asymptotes of a rational function, separates holes from asymptotes, and sketches the curve with the lines drawn on it.

Volume of a pyramid with a triangular base, from the base and height of that triangle, its three sides, an equilateral side or a regular tetrahedron edge.

Tests whether a gap between two conversion rates is real. Gives the z score, the p value, a confidence interval on the difference, and the sample size a test needs.