Math Prompts

Solve a separable differential equation by isolating x and y terms, integrating both sides, and verifying it, or generate practice problems with an answer key.

Evaluate a logarithm in exponential form, solve a log equation with solutions checked against the domain, expand or condense expressions, and generate practice problems.

Generate a solved triangle area using base and height or Heron's formula from three side lengths, whichever method fits, with every step shown and verified.

Solve any math expression step by step using the order of operations, PEMDAS or BODMAS, showing the full expression before and after each operation.

Solve for the area of a parallelogram from its base and height, keeping perpendicular height separate from a slanted side, with the result verified.

Classify a conic equation as a circle, ellipse, parabola, or hyperbola using the coefficient test, convert to standard form, or build one from a description.

Convert numbers to and from scientific notation or solve arithmetic on them with exponent and coefficient steps shown, plus practice problems with an answer key.

Convert numbers to and from Roman numerals with each symbol step shown and verified, or generate fresh conversion practice problems with an answer key.

Factor a trinomial, difference of squares, or GCF-style polynomial with the result verified by expansion, or generate a mixed batch of factoring practice problems.

Generate unit circle practice problems for sine, cosine, and tangent at standard angles, with full worked solutions using reference angles and quadrant sign rules.

Explain whether a sequence is arithmetic, geometric, or quadratic using differences and ratios, derive its formula, or generate mixed-pattern practice sequences with an answer key.

Generate integral practice problems with an answer key, or find the antiderivative of a function or evaluate a definite integral using the power rule.

Find the slope between two points and build the slope-intercept or point-slope equation with every step verified, or generate practice problems with an answer key.

Solve a quadratic equation for x using factoring, the quadratic formula, or completing the square, with step-by-step work and an answer verified against the equation.

Generate practice problems on complementary, supplementary, vertical, and linear pair angles, with full worked solutions showing which relationship applies, or solve a specific angle problem.

Evaluate a limit through direct substitution, factoring, rationalizing, or L'Hopital's rule with the exact indeterminate form identified, plus generate fresh limit practice problems.

Write a circle's equation from its center and radius, or complete the square to extract center and radius from a general-form equation, verifying every step.

Solve for a sphere's surface area from its radius, or the radius from a known area, with the squaring step and four-times factor shown separately.

Solve for a missing triangle side, check whether a triangle is right, or work a word problem using the Pythagorean theorem, with every step shown.

Generate practice problems for Pythagorean and double-angle trig identities, with full worked solutions showing every substitution, or verify an identity or expression step by step.

Solve a triangle using the law of sines from two angles and a side, or two sides and a non-included angle, checking valid SSA triangles.

Multiply two matrices with every row-by-column dot product shown step by step, or generate fresh matrix pairs at a chosen size with an answer key.

Generate practice problems on the triangle inequality theorem and side-angle relationship, checking valid triangles and ordering sides or angles by size.

Solve for the volume or total surface area of a cylinder from its radius and height, with every calculation step shown and the result verified.