AMC 8 Math Concepts Overview

1000

720

24

<p>True (A)</p> Signup and view all the answers

<p>60</p> Signup and view all the answers

<p>210</p> Signup and view all the answers

<p>4536</p> Signup and view all the answers

<p>300</p> Signup and view all the answers

<p>24</p> Signup and view all the answers

<p>12</p> Signup and view all the answers

<p>120, 42</p> Signup and view all the answers

<p>125</p> Signup and view all the answers

<p>320</p> Signup and view all the answers

<p>6</p> Signup and view all the answers

A permutation is a possible arrangement of objects in a set where the order of objects matter.

A factorial is the product of all positive integers less than or equal to a given positive integer. For example, 5! = 5 x 4 x 3 x 2 x 1.

The number of ways to order k objects out of n total objects is n!/(n-k)!

A combination is a collection of items where the order of the items does not matter.

The number of ways to choose k objects out of a total of n objects is n!/(k!*(n-k)!)

The binomial identity states that nC0 + nC1 + nC2 + ... + nCn = 2n. It provides a way to calculate combinations of all sizes.

Probability is the likelihood of something happening. It's calculated as (number of successful outcomes) / (total number of possible outcomes).

In probability, two events are independent if the outcome of one event does not affect the outcome of the other.

In probability, two events are dependent if the outcome of one event affects the outcome of the other.

Casework in probability involves breaking a problem into smaller cases to find the number of successful outcomes for each case, then adding them up.

A word rearrangement is a way of arranging the letters of a word. It considers the frequency of each letter.

The number of ways to order a word is n!/(d1! × d2! × d3! × ...), where n is the number of letters and d1, d2, d3, ... are the number of times each of the duplicate letters appears in the word.

Stars and Bars is a technique used in combinatorics to find the number of ways to distribute identical objects into distinct containers.

Geometric Counting involves counting the number of specific geometric shapes or arrangements within a larger geometric figure.

Recursion is a problem-solving technique where a solution is defined in terms of smaller instances of the same problem.

A ratio is a comparison of two quantities by division.

Percentage is a way of expressing a part of a whole as a fraction of 100.

Rate and work problems involve calculating the amount of work done by someone or something over a certain period of time.

A system of equations is a set of two or more equations with the same variables.

Speed, distance, and time problems explore the relationship between these three variables. Speed is calculated as distance divided by time.

A sequence is a list of numbers that follow a pattern.

A series is the sum of the terms in a sequence.

An arithmetic sequence is a sequence where the difference between consecutive terms is constant.

A geometric sequence is a sequence where the ratio between consecutive terms is constant.

The mean is the average of a set of numbers.

The median is the middle value in a sorted set of numbers.

The mode is the value that appears most frequently in a set of numbers.

A prime number is a whole number greater than 1 that has only two divisors: 1 and itself.

Divisibility rules are shortcuts to determine if a number is divisible by another number.

Prime factorization is the process of expressing a number as a product of its prime factors.

The Greatest Common Divisor (GCD) of two or more integers is the largest positive integer that divides all of them.

The Least Common Multiple (LCM) of two or more integers is the smallest positive integer that is a multiple of all of them.

Modular arithmetic is a system of arithmetic for integers where numbers ”wrap around” upon reaching a certain value called the modulus.

A Diophantine equation is a polynomial equation where the solutions are restricted to integers.

Angle chasing is a technique in geometry where we use known angles to find unknown angles.

An inscribed angle is an angle formed by two chords of a circle that share an endpoint on the circle.

A triangle is a polygon with three sides and three angles.

A quadrilateral is a polygon with four sides and four angles.

A circle is a set of points that are equidistant from a central point.

Similar triangles are triangles that have the same shape but different sizes. Their corresponding angles are equal, and their corresponding sides are proportional.

Congruent triangles are triangles that have the same shape and size. Their corresponding angles and sides are equal.