Algebra Quiz

Try out this Algebra quiz to test your knowledge. Algebra Trivia trivia explores the language of patterns, equations, and unknowns that has been central to mathematics for centuries.

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15 questions

~3 min to finish

Easy to hard difficulty

480 pts max score

Question 1 · Hard · 40 pts
A vector space is defined over what kind of algebraic object?
Question 2 · Hard · 40 pts
Which theory links field extensions to groups of automorphisms, forming the classic bridge between polynomial equations and symmetry?
Question 3 · Hard · 40 pts
What is the name for a group whose operation commutes?
Question 4 · Hard · 40 pts
Fill in the missing structure: a commutative ring in which every nonzero element has a multiplicative inverse is a ______.?
Question 5 · Hard · 40 pts
What is the term for a linearly independent spanning set of a vector space?
Question 6 · Hard · 40 pts
If someone asks for the number of vectors in a basis of a vector space, what invariant are they asking for?
Question 7 · Hard · 40 pts
For the 2×2 matrix [[a,b],[c,d]], what expression gives its determinant?
Question 8 · Hard · 40 pts
A square matrix has a nonzero determinant. What does that tell you exactly about the matrix?
Question 9 · Hard · 40 pts
Which scalar λ is being described by the relation Av = λv for some nonzero vector v?
Question 10 · Hard · 40 pts
What matrix statistic is obtained by adding up all diagonal entries of a square matrix?
Question 11 · Hard · 40 pts
Rank is defined here as the dimension of which associated space of a matrix?
Question 12 · Easy · 10 pts
What do you call an algebraic expression with exactly one term?
Question 13 · Easy · 10 pts
A polynomial with exactly two terms is called what?
Question 14 · Easy · 10 pts
If a polynomial has three terms, what is it called?
Question 15 · Easy · 10 pts
What degree does a quadratic equation have?

A vector space is defined over what kind of algebraic object?

Which theory links field extensions to groups of automorphisms, forming the classic bridge between polynomial equations and symmetry?

What is the name for a group whose operation commutes?

Fill in the missing structure: a commutative ring in which every nonzero element has a multiplicative inverse is a ______.?

What is the term for a linearly independent spanning set of a vector space?

If someone asks for the number of vectors in a basis of a vector space, what invariant are they asking for?

For the 2×2 matrix [[a,b],[c,d]], what expression gives its determinant?

A square matrix has a nonzero determinant. What does that tell you exactly about the matrix?

Which scalar λ is being described by the relation Av = λv for some nonzero vector v?

What matrix statistic is obtained by adding up all diagonal entries of a square matrix?

Rank is defined here as the dimension of which associated space of a matrix?

What do you call an algebraic expression with exactly one term?

A polynomial with exactly two terms is called what?

If a polynomial has three terms, what is it called?

What degree does a quadratic equation have?