Algebra and Geometry Quiz

Definition: Algebraic expressions with variables raised to whole number powers.
Types: Monomials, binomials, trinomials.
Operations: Addition, subtraction, multiplication, and division of polynomials.
Factorization: Finding factors of polynomials using methods like grouping and synthetic division.

Basic Shapes: Properties of triangles, quadrilaterals, circles, and polygons.
Theorems: Pythagorean theorem, properties of angles and lines.
Area and Perimeter: Formulas for calculating area and perimeter for various shapes.

Linear Equations in Two Variables: Understanding and solving.
Quadratic Equations: Standard form ax² + bx + c = 0, methods of solving (factoring, completing the square, quadratic formula).

Basic Ratios: Sine, cosine, tangent and their reciprocals.
Key Angles: Special angles and their trigonometric values (0°, 30°, 45°, 60°, 90°).

Real numbers comprise both rational (fractions, integers) and irrational numbers (non-repeating, non-terminating decimals).
Decimal representation includes terminating decimals (e.g., 0.5) and non-terminating decimals (e.g., π).
Laws of exponents establish rules for multiplying (a^m × a^n = a^(m+n)) and dividing (a^m ÷ a^n = a^(m-n)) powers.

Defined as algebraic expressions consisting of variables raised to non-negative whole number powers.
Types of polynomials include monomials (one term), binomials (two terms), and trinomials (three terms).
Polynomial operations encompass addition, subtraction, multiplication, and division, using like terms and varying methods.
Factorization techniques include grouping (rearranging terms) and synthetic division (an efficient method to divide polynomials).

The Cartesian plane is formed by the intersection of the X-axis and Y-axis, where points are plotted as (x, y).
The distance formula calculates the distance between two points: d = √((x2 - x1)² + (y2 - y1)²).
The midpoint formula computes the midpoint between two points: M = ((x1 + x2)/2, (y1 + y2)/2).

Standard form of a linear equation is given by Ax + By + C = 0, where A, B, and C are constants.
Graphing a linear equation involves plotting the line that represents the equation on a two-dimensional graph.
Solutions to linear equations are coordinates (x, y) that satisfy the equation, often found by substitution or graphing.

Data can be represented visually through bar graphs, histograms, and pie charts, facilitating easier interpretation.
Measures of central tendency include the mean (average), median (middle value), and mode (most frequent value).
The range of a data set is determined by subtracting the smallest value from the largest value.

Basic concepts in probability include experiments (actions), outcomes (results), events (sets of outcomes), and sample spaces (all possible outcomes).
The probability of an event is calculated using the formula P(E) = Number of favorable outcomes / Total outcomes.
Types of probability events include independent (outcomes do not influence each other), dependent (outcomes are influenced), and mutually exclusive (cannot occur simultaneously).

Basic geometric shapes include triangles (three sides), quadrilaterals (four sides), circles, and polygons (multi-sided).
Important theorems include the Pythagorean theorem (relationship in right triangles) and properties relating to angles and lines.
Area and perimeter formulas vary by shape: e.g., Area of a rectangle = length × width; Perimeter of a rectangle = 2(length + width).

Surface area and volume formulas are crucial for three-dimensional shapes like cubes, cuboids (length × width × height), cylinders (πr²h), and spheres (4/3πr³).
Application problems illustrate how mensuration is used in real-world contexts, such as calculating paint needed for walls.

Linear equations in two variables refer to finding solutions for equations with two unknowns, represented graphically as lines.
Quadratic equations take standard form ax² + bx + c = 0, solved through factoring, completing the square, or using the quadratic formula.

Basic trigonometric ratios include sine (opposite/hypotenuse), cosine (adjacent/hypotenuse), and tangent (opposite/adjacent).
Key angles include special angles 0°, 30°, 45°, 60°, and 90°, each with specific sine, cosine, and tangent values for calculations.

Construction of angles and triangles using a compass and ruler is fundamental for creating accurate geometric figures.
Important constructions involve techniques like bisecting angles (dividing an angle into two equal parts) and drawing perpendicular lines (lines that intersect at 90 degrees).