Algebra quiz

More questions about Algebra

These visible examples show the question style. LearnClash turns the full topic into ranked duels and spaced repetition.

1. 1 Easy

   What is the name for the symbol √x?

   Answer: radical

   Why: Christoff Rudolff printed the sign in 1525, probably a stylised r for the Latin radix; Descartes added the overbar in 1637.

2. 2 Medium

   What shape does every quadratic equation form when graphed?

   Answer: parabola

   Why: Every ray arriving parallel to its axis bounces to a single focus, which is why satellite dishes and headlight mirrors use this curve.

3. 3 Hard

   What expression is the discriminant of a quadratic equation?

   Answer: $b^2 - 4ac$

   Why: James Joseph Sylvester coined the name discriminant in 1851; its sign alone says whether a parabola meets the x-axis twice, once or never.

4. 4 Easy

   When multiplying powers with the same base, how do the exponents combine?

   Answer: They are added

   Why: For example, $x^2 \cdot x^3 = x^{2+3} = x^5$ because combining factors of $x$ sums their total occurrences.

5. 5 Medium

   General formulas cannot solve polynomial equations starting at what degree?

   Answer: Fifth degree

   Why: Cubics and quartics do have formulas; a proof of just six pages, published in 1824, showed that beyond them none can exist.

6. 6 Hard

   Which mathematician developed the algebraic system for binary logic?

   Answer: George Boole

   Why: Boole set it out in his 1854 book Laws of Thought; in 1937 Claude Shannon showed the same rules describe electrical switches.