Pre-Calculus Semester 1 Exam Review

A fraction with a numerator and a denominator, where both are polynomials.

A mathematical expression that represents a relationship between two quantities, often involving variables, numbers, and operations.

A set of values that can be substituted into a formula or equation.

The distance from the center of a circle to a point on its circumference.

The point where a line intersects the y-axis.

The measure of how steep a line is; the ratio of the vertical change (rise) to the horizontal change (run).

A mathematical equation that describes a relationship between two or more variables, often used to represent real-world situations.

The process of dividing a polynomial by another polynomial, similar to long division with numbers.

The amount of salt in a barrel at a given time, represented by the function Q(t) = 25(1 - e^(-0.08t)), where t is time in minutes and Q(t) is salt in pounds.

A mathematical concept that describes the growth of an investment over time, considering the principal, interest rate, and compounding frequency.

The process of rewriting a logarithmic equation into an exponential equation.

Rewriting an exponential equation into a logarithmic equation.

A function that describes the relationship between a variable and its logarithm.

A mathematical property that allows us to simplify expressions involving logarithms.

Finding the value of a variable that makes a logarithmic equation true.

The process of writing a logarithmic expression in a simpler form, without logarithms of products, quotients, or powers.

A curve defined by the equation y = ax^2 + bx + c. In a suspension bridge, the suspension cables form a parabolic shape.

A conic section defined by the equation (x^2/a^2) + (y^2/b^2) = 1. It is characterized by its two focal points.

The distance from the center of an ellipse to a point on the ellipse along the longer axis. It's the longest distance across the ellipse.

The distance from the center of an ellipse to a point on the ellipse along the shorter axis. It's the shortest distance across the ellipse.

A conic section defined by the equation (x^2/a^2) - (y^2/b^2) = 1 or (y^2/a^2) - (x^2/b^2) = 1. It is characterized by its two branches and asymptotes.

A line that a curve approaches as it goes to infinity. For a hyperbola, there are two asymptotes, intersecting at the center.

A fixed point inside a parabola. The distance from any point on the parabola to the focus is equal to the distance from that point to the directrix.

A line that is perpendicular to the axis of symmetry of a parabola. Any point on the parabola is equidistant to the focus and the directrix.

A mathematical expression that can be written in the form of a sum or difference of terms, where each term is a product of a constant and one or more variables raised to non-negative integer powers.

The value of a function f(x) when x is equal to a specific number.

The set of all possible input values (x) for which a function is defined.

To factor a polynomial is to rewrite it as a product of simpler polynomials.

A function that undoes the action of another function.

A special factoring formula used to factor expressions in the form a ³ + b ³ or a ³ - b ³

A function where each input value (x) corresponds to only one output value (y).

The set of all possible input values for which the expression is defined. It avoids creating undefined situations, like dividing by zero.

The process of multiplying fractions, where the numerators are multiplied together and the denominators are multiplied together.

A function that involves polynomials, specifically expressions with variables raised to non-negative integer powers.

The highest point on a curve (local maximum) or the lowest point on a curve (local minimum).

The process of dividing one rational expression by another, which is equivalent to multiplying the first expression by the reciprocal of the second expression.

A formula used to model the height of an object thrown upwards, where h is the height, t is time, v₀ is the initial velocity, and -16 represents the acceleration due to gravity.

Finding the values of x where a polynomial equals zero.

An equation where the highest power of the variable is 1. The graph is a straight line.

A function that involves a logarithm with a base of 8, where the input is the argument of the logarithm.

A mathematical formula that expresses the sum of a series of consecutive terms in a geometric sequence.

The process of rewriting a logarithmic expression as a sum or difference of simpler logarithmic expressions using the rules of logarithms.

Simplifying expressions involving logarithms by using the properties of logarithms, such as the change of base formula.

The point on a parabola where the curve changes direction from increasing to decreasing or vice versa.

A curve that represents the path of an object that is moving around another object, often used to describe the orbit of a satellite or planet.