Algebra II Final Exam

Front

What is Pascal's Triangle?

Back

Pascal's Triangle is a triangular array of the binomial coefficients. Each number is the sum of the two directly above it.

Front

How do you locate a point in the complex plane?

Back

A point in the complex plane is represented as a + bi, where 'a' is the real part and 'b' is the imaginary part.

Front

What is the formula for calculating the determinant of a 2x2 matrix?

Back

For a 2x2 matrix [[a, b], [c, d]], the determinant is calculated as det = ad - bc.

Front

How do you express a complex number?

Back

A complex number is expressed in the form a + bi, where 'a' is the real part and 'b' is the imaginary part.

Front

What is the element in the second row, third column of a matrix?

Back

To find the element in the second row, third column, count down to the second row and across to the third column.

Front

What is the binomial theorem?

Back

The binomial theorem describes the algebraic expansion of powers of a binomial, expressed as (a + b)^n = Σ (n choose k) * a^(n-k) * b^k.

Front

What is the definition of a matrix?

Back

A matrix is a rectangular array of numbers arranged in rows and columns.

Front

How do you add two complex numbers?

Back

To add two complex numbers, add their real parts and their imaginary parts separately: (a + bi) + (c + di) = (a+c) + (b+d)i.

Front

What is the conjugate of a complex number?

Back

The conjugate of a complex number a + bi is a - bi.

Front

What is the purpose of finding the determinant of a matrix?

Back

The determinant helps determine if a matrix is invertible and provides information about the matrix's properties.