FINAL

Front

What is the determinant of a 2x2 matrix?

Back

For a 2x2 matrix \( \begin{pmatrix} a & b \\ c & d \end{pmatrix} \), the determinant is calculated as \( ad - bc \).

Front

How do you multiply two matrices?

Back

To multiply two matrices, the number of columns in the first matrix must equal the number of rows in the second matrix. The element at position (i,j) in the resulting matrix is the dot product of the i-th row of the first matrix and the j-th column of the second matrix.

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the solutions of a quadratic equation \( ax^2 + bx + c = 0 \). It is given by \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \).

Front

What is the sum of two numbers?

Back

The sum of two numbers is the result of adding them together. For example, the sum of 3 and 5 is 8.

Front

What is the product of two numbers?

Back

The product of two numbers is the result of multiplying them together. For example, the product of 4 and 5 is 20.

Front

How do you solve a quadratic equation using factoring?

Back

To solve a quadratic equation by factoring, express it in the form \( (x - p)(x - q) = 0 \) and then set each factor to zero: \( x - p = 0 \) or \( x - q = 0 \).

Front

What is the difference between a scalar and a vector?

Back

A scalar is a quantity that has only magnitude (e.g., temperature), while a vector has both magnitude and direction (e.g., velocity).

Front

What is the formula for the area of a triangle?

Back

The area of a triangle is given by the formula \( A = \frac{1}{2} \times base \times height \).

Front

What is the Pythagorean theorem?

Back

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): \( c^2 = a^2 + b^2 \).

Front

What is a linear equation?

Back

A linear equation is an equation of the first degree, meaning it has no exponents greater than one. It can be written in the form \( ax + b = 0 \).