Algebra 1 Semester Exam

Front

What is the slope of a line through two points?

Back

The slope (m) of a line through two points (x1, y1) and (x2, y2) is calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

How do you solve for x in the equation -4x + 1 = 21?

Back

To solve for x, first subtract 1 from both sides: -4x = 20. Then divide by -4: x = -5.

Front

What is the result of adding the polynomials (3x^3 + 3x^2 - 4x + 5) and (x^3 - 2x^2 + x - 4)?

Back

The result is 4x^3 + 1x^2 - 3x + 1.

Front

How do you simplify the expression xy^-7?

Back

The expression simplifies to x/y^7.

Front

What is the product of b^2 and b^4?

Back

The product is b^6, using the property of exponents that states a^m * a^n = a^(m+n).

Front

What is the definition of a polynomial?

Back

A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

Front

What is the degree of the polynomial 4x^3 + 2x^2 - x + 7?

Back

The degree of the polynomial is 3, which is the highest exponent of the variable x.

Front

How do you find the x-intercept of a linear equation?

Back

To find the x-intercept, set y = 0 in the equation and solve for x.

Front

What is the formula for the area of a rectangle?

Back

The area (A) of a rectangle is calculated using the formula: A = length × width.

Front

What is the distributive property in algebra?

Back

The distributive property states that a(b + c) = ab + ac, meaning you multiply a by each term inside the parentheses.