SAT Math

Heart of Algebra

Focuses on linear equations, functions, and inequalities.

Problem Solving and Data Analysis

Involves interpreting data from tables and graphs, ratios, and percentages.

Passport to Advanced Mathematics

Covers polynomial equations, exponents, and structures in expressions.

Additional Topics in Math

Includes geometry, trigonometry, and complex numbers.

PEMDAS

Order of operations: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.

SADMEP

Reverse order of PEMDAS for solving equations: Subtraction/Addition, Division/Multiplication.

Slope-Intercept Form

Equation format of a line: y = mx + b, where m is the slope and b is the y-intercept.

Absolute Value

The distance of a number from zero on a number line, denoted by |x|.

Linear Equations

Equations of the form Ax + By = C, representing straight lines.

Systems of Equations

Two or more linear equations graphed together, finding intersections.

Function Notation

A way to express a function, typically in the form f(x).

Quadratic Formula

Formula used to find the roots of a quadratic equation: x = (-b ± √(b²-4ac)) / 2a.

Mean

The average of a set of numbers, calculated by summing the numbers and dividing by the count.

Median

The middle value when a set of numbers is ordered from least to greatest.

Mode

The value that appears most frequently in a data set.

Range

The difference between the highest and lowest values in a data set.

Ratios

A comparison of two quantities expressed as a fraction or with a colon.

Percentages

A way to express a number as a fraction of 100.

Unit Rate

A rate expressed in terms of one unit, such as miles per hour.

Proportions

An equation stating that two ratios are equivalent.

Data Collection

The process of gathering and measuring information.

Graphing Linear Equations

Visual representation of linear equations in an xy-plane.

Density

Mass per unit volume of a substance.

Exponential Growth

An increase where the growth rate is proportional to the current value.

Exponential Decay

A decrease where the rate of decline is proportional to the current value.

Scatterplot

A graph that shows the relationship between two variables.

Best-fit Line

A straight line that best represents the data points on a scatterplot.

Vertical Angles

Angles that are opposite each other when two lines intersect, always congruent.

Alternate Interior Angles

Angles located between parallel lines and on opposite sides of a transversal, always congruent.

Exterior Angle Theorem

An exterior angle of a triangle equals the sum of the two non-adjacent interior angles.

Triangle Inequality Theorem

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Polynomials

Algebraic expressions consisting of variables, coefficients, and non-negative integer exponents.

Zeros of a Polynomial

Values of x for which the polynomial equation equals zero.

Like Terms

Terms that have the same variables raised to the same power.

Radical Expressions

Expressions that include roots, such as square roots.

Rational Expressions

Fractions where the numerator and/or denominator is a polynomial.

Completing the Square

A method used to solve quadratic equations by rewriting them in a specific form.

Distance Formula

d = √((x2 - x1)² + (y2 - y1)²), used to find the distance between two points.

Trigonometry

The study of relationships between the angles and sides of triangles.

Circumference of a Circle

C = 2πr, where r is the radius of the circle.

Area of a Circle

A = πr², where r is the radius.

Volume of a Cylinder

V = πr²h, where r is the radius and h is the height.

Confidence Intervals

A range of values that is likely to contain a population parameter.

Standard Deviation

A measure of the amount of variation or dispersion of a set of values.

Complex Numbers

Numbers in the form a + bi, where a and b are real numbers and i is the imaginary unit.

Imaginary Unit (i)

Defined as √-1, used to extend the real number system.

Right Triangle

A triangle with one angle measuring 90 degrees.

Slope of a Line

The ratio of the vertical change to the horizontal change between two points.

Linear Growth

A type of growth where the increase is constant over time.

Quadratic Relations

Relationships represented by quadratic equations, often forming parabolas.

Function Transformation

Altering the position or size of the graph of a function.

Volume of a Sphere

V = (4/3)πr³, where r is the radius.

Center of a Circle

The point equidistant from all points on the circle's circumference.

Central Angle

An angle whose vertex is at the center of a circle and whose sides are radii.