Mathematics Midterm Reviewer

CHAPTER 1 Existential Statement says that there is at least one thing for which the property is true, even Mathematics is the study of numbers, forms, and though a given property may or may...

CHAPTER 1 Existential Statement says that there is at least one thing for which the property is true, even Mathematics is the study of numbers, forms, and though a given property may or may not be true. their relationships. Universal Conditional Statement (for all; if) is a Pattern is a repeated arrangement of numbers, statement that is both universal and conditional. shapes, colors, objects, and events. Universal Existential Statement (for all; there is) Symmetry indicates that you can draw an is a statement that is universal because its first part imaginary line across an object and the resulting says that a certain property is true for all objects for parts are mirror images of each other. a given type, and it is existential because the Leonardo Davinci’s Virtuvian Man shows the second part asserts the existence of something. proportion or symmetry of the human body. Existential Universal Statement (there is; for all) Rotational Symmetry explains that when an object is a statement that is existential because its first is rotated on its own axis, the shape of the object part asserts that a certain object exists and is looks the same. universal because its second part says that the Bilateral Symmetry is a condition in which the object satisfies a certain property for all things of a right and left sides of an item are mirror images of certain kind. one another. Notation consists of using symbols for Radial symmetry is a type of balance where parts representing operations, unspecified numbers, of an object are arranged around a central point. relations, and any other mathematical objects and Angle of rotation is a geometric transformation assembling them into expressions and that rotates every point of a figure in a plane by a formulas. given angle and direction around a fixed point. Roster Notation where every element that is more Order of Rotation is the number of times it can be than one is separated by a comma symbol. rotated around a full circle and still look the same. Set-Builder Notation used to ''build'' sets by Packing problems are a class of optimium method classifying numbers according to their properties. that involve attempting to pack objects together into Subset of a set is a part of the set or the whole set containers. itself. Exponential growth is a pattern of data that shows Cartesian Product is the collection of all ordered greater increases with passing time, creating the pairs obtained by the product of two non-empty curve of an exponential function. sets. Sequence is defined as an ordered list of terms Ordered pairs means that two elements are taken that may have repeated values. from each set. it is represented by an INPUT or Series is defined as the sum of the elements of a OUTPUT. sequence. Symbols: Fibonacci Sequence follows the rule that each Z = “Zahlen”; Integers number is equal to the sum of the preceding two Z¯= Negative Integers, numbers. Z+ = Positive Integers The Golden Ratio is the sum of two numbers that N = Natural Numbers are next to each other in the Fibonacci sequence. R = Real Numbers Q = “Quotient”; Rational Numbers CHAPTER 2 ∈ = Elements ⊂ = Proper Subset Variable is a symbol for a number where the value ⊆ = Subset is not known. Relation shows the relationship between INPUT Universal Statement says that a certain property and OUTPUT. is true for all elements on a set. Arrow Diagram of a Relation tells us how the Conditional Statement says that if one thing is relation assigns elements of each set. If two true then some other thing also has to be true. elements are connected by an arrow, then they are related. For a relation to represent a function, every Graph displays data in a visual format. input must be assigned to exactly one output. Function is a relation which derives one OUTPUT CHAPTER 4 for each given INPUT. Properties of a Function: Statistics is the science of collecting, analyzing, 1. For every element X in A, there is an element Y and interpreting data to make decisions or in B. predictions. It helps in understanding patterns and 2. No two distinct ordered pairs have the same first trends from the data. element. Measures of Central Tendency describe the center or typical value of a dataset. The three main CHAPTER 3 measures are the mean, median, and mode. Mean is the average of all values in a dataset, Inductive Reasoning is the process of reaching a calculated by adding all the values and dividing by general conclusion by examining specific the number of values. examples. Summation notation (Σ) is used to indicate the Conjecture is a conclusion formed by using sum of values. inductive reasoning. Population refers to the entire group that is being Counterexamples is a specific case for which the studied or about which conclusions will be drawn. conjecture is false. Sample is a subset of the population used to Deductive Reasoning is the process of reaching a represent the entire group. conclusion by applying general assumptions, Median is the middle value of a dataset when procedures, or principles. arranged in order. Arithmetic Sequence (common difference) is a Mode is the value that occurs most frequently in a sequence of numbers where the differences dataset. between every two consecutive terms is the same. Weighted Mean is the mean where each value is Geometric Sequence (common ratio) is a series multiplied by a specific weight before of numbers, where each number is the previous summing, to give more importance to certain number multiplied by a certain constant. values. Triangular Number is a number that can be Raw Data refers to unprocessed or original data as represented by a pattern of dots arranged in an collected from a source. equilateral triangle with the same number of dots Frequency Distribution shows how often each on each side. value in a dataset occurs. Square Number is when you multiply a number by Frequency Distribution Table is a table that lists itself, you get a square number. data values and their corresponding frequencies. Pentagonal Number is the number of distinct dots Measures of Dispersion describe the spread of in a pattern of dots consisting of the outlines of the data. regular pentagons with sides up to n dots, when the Range is the difference between the highest and pentagons are overlaid so that they share one lowest values in a dataset. vertex. Standard Deviation measures the average Polya's Problem-Solving Strategy was developed distance of each data point from the mean. by a mathematician, and the “Father of Modern Symbol of Standard Deviation: Problem-Solving”, George Polya, provides a 𝞼 = population standard deviation structured approach to problem-solving. s = sample standard deviation. Four Steps of Problem-Solving Strategy Variance is the average of the squared differences (UnDeCaL): from the mean. 1. Understand the Problem Symbol for Variance: 2. Devise a Plan 𝞼² = population variance 3. Carry out the Plan s² = sample variance. 4. Look Back or Review the Solution Measures of Relative Position are conversions of values, usually standardized test scores, to show where a given value stands in relation to other values of the same grouping. Z-scores represent how many standard deviations a data point is from the mean. Percentiles indicate the value below which a given percentage of data falls. Quartiles divide data into four equal parts.