Number\( \mathbb{Q} \)

Teacher Edition

Generate random math problems for your students. NumberQ allows teachers to create unique problems in a wide array of subjects.

Addition & Subtraction

(arithmetic)

\(4-6+8-5\)

Multiplication & Division

(arithmetic)

\(4\cdot\frac{1}{6}\cdot3\cdot\frac{1}{2}\)

Linear Equations

(algebra)

\(3x+2=14-9x\)

Quadratics & Factoring

(algebra)

\(8x^{2}+10x+3\)

Systems of Equations

(algebra)

\(3x-2y=5\)
\(x+5=4y\)

Simplify Radicals

(algebra)

\(\sqrt{27}+\sqrt{75}\)

Trig Values

(pre-calculus)

\(\cos\left(\frac{4\pi}{3}\right)\)

Rational Expressions

(pre-calculus)

\(\frac{x+2}{x-3}+\frac{3x+1}{5x}\)

Polynomial Division

(pre-calculus)

\(\frac{x^{3}+6x^{2}+11x+6}{x+2}\)

Complex Division

(pre-calculus)

\(\frac{6+8i}{2-4i}\)

More Coming Soon

\(\frac{d}{dx}\left[5x^{2}\sin\left(x\right)\right]\) \(\sqrt[3]{\frac{3x^{5}y^{4}}{24y}}\) \(\log_{5}(x^{3}y)-\log_{5}(y^{4})\)

Info about the Generators

How are the answers verified?
How many problems are possible?
How will settings work?
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Q

A

Settings

[Coming Soon]

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Info & FAQ

How are the answers to the problems verified?

For many of the problem types, the answer to the question is actually determined first and is used to build the rest of the problem. In linear equations for instance, the x value that solves the equation is 'built-in' to the coefficients; so we can have random values for the coefficients and still always have a particular solution. Despite this, all of the generators have been tested extensively using a computer algebra system (CAS) by matching the answer supplied by the generator to the one calculated by the CAS. Each generator has been tested over 100,000 times.

How many different problems are possible in each generator?

The number of possible problems varies widely by the type of generator. As an example, up to 100,000 different combinations of numbers are possible with the linear equation generator, but only around 500 are possible with the polynomial division generator. It's hard to get the exact number of possible configurations for some of the generators (since they can take on so many different forms), but a conservative estimate can be obtained by multiplying the number of possible coefficients by the number of possible forms and ensuring cases like 2+3 and 3+2 are only counted as one problem. Generally speaking, the numerical generators have several hundred possible problems and the expression/equation generators have anywhere from a few thousand to a hundred thousand possible problems. One notable exception is the trig expression generator, which only has 68 possibilities (to ensure the values always have an exact form).

How will settings work?

The goal with settings will be to make the generators completely customizable. In quadratics and factoring for instance, the settings will allow you to specify a range for the numbers and pick the form (perfect square, no constant term, etc). In polynomial division, settings will allow you to pick the degree of the polynomial, which factors it has, and whether or not it will divide evenly. In other words, everything that is random now will be controllable by settings soon.