Algebra, Geometry, and Calculus Basics Quiz

Basics:
- Variables, constants, coefficients.
- Expressions, equations, and inequalities.
Operations:
- Addition, subtraction, multiplication, division of algebraic expressions.
Factoring:
- Techniques include factoring out common terms, using the quadratic formula.
Functions:
- Definition, domain, range, types (linear, quadratic, polynomial).
Systems of Equations:
- Solving methods: substitution, elimination, graphical.

Shapes:
- Basic: triangles, squares, rectangles, circles.
- Properties: area, perimeter, volume for 3D shapes.
Angles:
- Types: acute, right, obtuse, straight.
- Angle relationships: complementary, supplementary.
Theorems:
- Pythagorean theorem for right triangles.
- Congruence and similarity criteria for triangles.
Coordinate Geometry:
- Graphing points, lines, and shapes on a Cartesian plane.

Limits:
- Concept of approaching a value, continuity.
Derivatives:
- Definition: rate of change; rules (power, product, quotient, chain rule).
- Applications: slope of tangent lines, optimization problems.
Integrals:
- Definite vs. indefinite integrals.
- Fundamental theorem of calculus.
Applications:
- Area under curves, motion problems.

Descriptive Statistics:
- Measures of central tendency: mean, median, mode.
- Measures of dispersion: range, variance, standard deviation.
Probability:
- Basic concepts: events, sample space, independent vs. dependent events.
Inferential Statistics:
- Hypothesis testing, confidence intervals, p-values.
Distributions:
- Normal distribution, binomial distribution, Poisson distribution.

Basic Functions:
- Sine, cosine, tangent and their reciprocals (cosecant, secant, cotangent).
Unit Circle:
- Understanding angles in radians and degrees, coordinates of key angles.
Trigonometric Identities:
- Fundamental identities (Pythagorean, angle sum/difference).
- Double angle and half angle formulas.
Applications:
- Solving triangles (Law of Sines, Law of Cosines).
- Real-world applications: waves, oscillations, and circular motion.

Variables are symbols used to represent unknown values; constants are fixed values.
Coefficients are numbers that multiply variables in expressions.
Expressions are mathematical phrases without equality, while equations include equal signs; inequalities show relative sizes.
Operations on algebraic expressions involve addition, subtraction, multiplication, and division, applying specific rules for each.
Factoring is the process of breaking down expressions into simpler components, commonly using techniques such as finding common factors or applying the quadratic formula.
Functions are relationships involving inputs and outputs, characterized by domain (possible input values) and range (possible output values), with types including linear, quadratic, and polynomial.
Systems of equations can be solved using various methods, including substitution, elimination, and graphical representation.

Basic shapes include triangles, squares, rectangles, and circles, each with distinct properties.
Area and perimeter are critical for 2D shapes; volume measures for 3D shapes provide insights into their capacity.
Angles are categorized into acute (less than 90°), right (90°), obtuse (more than 90°), and straight (180°).
Angle relationships consist of complementary (angles that add to 90°) and supplementary (angles that add to 180°).
The Pythagorean theorem applies specifically to right triangles, establishing a relationship between side lengths.
Congruence criteria (sides and angles equal) and similarity criteria (same shape but different sizes) are essential for triangle comparisons.
Coordinate geometry involves plotting points, lines, and shapes on a Cartesian plane, facilitating visual representation.

Limits denote the behavior of a function as it approaches a particular point, highlighting continuity.
Derivatives represent the rate of change of a function, with basic rules including power, product, quotient, and chain rule applications.
Derivatives have applications such as determining the slope of tangent lines and solving optimization problems.
Integrals, which calculate the area under a curve, are classified as definite (specific interval) or indefinite (general antiderivative).
The fundamental theorem of calculus links differentiation and integration, providing a framework for calculus applications.
Real-world applications of calculus include solving motion problems and finding areas under curves.

Descriptive statistics encompass measures of central tendency: mean (average), median (middle value), and mode (most frequent value).
Measures of dispersion, including range (difference between highest and lowest values), variance, and standard deviation, indicate data spread.
Probability fundamentals involve events (outcomes), sample spaces (all possible outcomes), and differentiating independent (unrelated) and dependent (related) events.
Inferential statistics apply to hypothesis testing, confidence intervals (range of values estimating a population parameter), and p-values (evidence against a null hypothesis).
Distribution types are important in statistics, with the normal distribution reflecting a bell curve, while binomial and Poisson distributions model specific types of outcomes.

Basic trigonometric functions include sine, cosine, and tangent, alongside their reciprocals: cosecant, secant, and cotangent.
The unit circle provides a visual model for understanding angles measured in both radians and degrees, containing coordinates for key angles.
Trigonometric identities, such as the Pythagorean identity, angle sum and difference identities, facilitate simplification and solving of equations.
Double angle and half angle formulas assist in calculations involving angle transformations.
Applications of trigonometry include solving triangles using the Law of Sines and Law of Cosines, as well as modeling real-world phenomena such as waves, oscillations, and circular motion.