Integrated Math III H Semester 1 Final Review

Front

Calculate the volume of a cube with side length 4 cm.

Back

The volume of a cube is calculated using the formula V = s^3, where s is the side length. For a cube with side length 4 cm, V = 4^3 = 64 cm³.

Front

Simplify (-4r^5)(2r^8).

Back

To simplify, multiply the coefficients and add the exponents: (-4 * 2)r^(5+8) = -8r^13.

Front

Add the polynomials: (3x^3 + 3x^2 - 4x + 5) + (x^3 - 2x^2 + x - 4).

Back

Combine like terms: (3x^3 + x^3) + (3x^2 - 2x^2) + (-4x + x) + (5 - 4) = 4x^3 + 1x^2 - 3x + 1.

Front

What is the range of the function?

Back

The range of a function is the set of possible output values. For this function, the range is [-1, ∞).

Front

What is the standard form of a quadratic expression?

Back

The standard form of a quadratic expression is ax^2 + bx + c, where a, b, and c are constants.

Front

What is the formula for the area of a triangle?

Back

The area of a triangle is given by the formula A = 1/2 * base * height.

Front

Define a polynomial function.

Back

A polynomial function is a function that can be expressed in the form f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n, a_(n-1), ..., a_0 are constants and n is a non-negative integer.

Front

What is the difference between a linear function and a quadratic function?

Back

A linear function has the form f(x) = mx + b, where m and b are constants, and its graph is a straight line. A quadratic function has the form f(x) = ax^2 + bx + c, where a ≠ 0, and its graph is a parabola.

Front

How do you find the x-intercepts of a quadratic function?

Back

To find the x-intercepts of a quadratic function, set the function equal to zero and solve for x using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a).

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards. For a quadratic function in standard form, the vertex can be found using the formula (-b/(2a), f(-b/(2a))).