Do basic arithmetic. Work with fractions, percentages and similar fundamentals.

Solve place value and word problems. Find roots of and expand, factor or simplify mathematical expressions—everything from polynomials to fields and groups. Compute integrals, derivatives and limits as well as analyze sums, products and series. Solve an ordinary differential equation:.

Compute the properties of geometric objects of various kinds in 2, 3 or higher dimensions. Explore and apply ideas from many subfields of geometry. Compute properties of a geometric figure:. Plot a conic section and identify its type:. Solve differential equations of any order. Examine solutions and plots of the solution families.

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Specify initial conditions to find exact solutions. Solve a linear ordinary differential equation:. Visualize functions, equations and inequalities. Do so in 1, 2 or 3 dimensions. Make polar and parametric plots. Plot a region satisfying multiple inequalities:.

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Work with various kinds of numbers. Check for membership in larger sets, such as the rationals or the transcendental numbers. Convert between bases. Compute a decimal approximation to a specified number of digits:. Convert a decimal number to another base:. Perform trigonometric calculations and explore properties of trigonometric functions and identities. Compute values of trigonometric functions:.

Determine whether a set of vectors is linearly independent:. Analyze integers; subsets of the integers, including the prime numbers; and related ideas.

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Explore sequences and recurrences, solve common problems in combinatorics and compute properties of graphs and lattices. Compute a possible formula and continuation for a sequence:. Schoolgirl with glasses solving math problem on blackboard. Little girl solved a problem in maths.

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