Maths Squared: 100 Concepts You Should Know Pdf

FREE MATHS SQUARED: 100 CONCEPTS YOU SHOULD KNOW PDF

In mathematicsa square number or perfect square is an Maths Squared: 100 Concepts You Should Know that is the square of an integer; [1] in other words, it is the product of some integer with itself. The name square number Maths Squared: 100 Concepts You Should Know from the name of the shape. Hence, a square with side length n has area n 2. In other words, if a square number is represented by n points, the points can be arranged in rows as a square each side of which has the same number of points as the square root of n ; thus, square numbers are a type of figurate numbers other examples being cube numbers and triangular numbers. Square numbers are non-negative. Another way of saying that a non-negative integer is a square number is that its square root is again an integer. A positive integer that has no perfect square divisors except 1 is called square-free. The concept of square can be extended to some other number systems. If rational numbers are included, then a square is the ratio of two square integers, and, conversely, the ratio of two square integers is a square, e. The number m is a square number if and only if one can arrange m points in a square:. The expression for the n th square number is n 2. This is also equal to the sum of the first n odd numbers as can be seen in the above pictures, where a square results from the previous one by adding an odd number of points shown in magenta. The formula follows:. There are several recursive methods for computing square numbers. For example. Thus, 3 is the only prime number one less than a square. A square number is also the sum of two consecutive triangular numbers. The sum of two consecutive square numbers is a centered square number. Every odd square is also a centered octagonal number. Another property of a square number is that except 0 it has an odd number of positive divisors, while other natural numbers have an even number of positive divisors. An integer root is the only divisor that pairs up with itself to yield the square number, while other divisors come in pairs. Lagrange's four-square theorem states that any positive integer can be written as the sum of four or fewer perfect squares. This is generalized by Waring's problem. In base 12 Maths Squared: 100 Concepts You Should Know, a square number can end only with square digits like in base 12, a prime number can end only with prime digits or 1i. Similar rules can be given for other bases, or for earlier digits the tens instead of the units digit, for example. Repeating the divisions of the previous sentence, one concludes that every prime must divide a given perfect square an even number of times including possibly 0 times. Thus, the number m is a square number if and only if, in its canonical representationall exponents are even. Squarity testing can be used as alternative way in factorization of large numbers. This is an application of the factorization of a difference of two squares. A square number cannot be a perfect number. The sum of the n first cubes is the square of the sum of the n first positive integers; this is Nicomachus's theorem. It follows that square roots of even square numbers are even, and square roots of odd square numbers are odd. Every odd perfect square is a centered octagonal number. The difference between any two odd perfect squares is a multiple of 8. The difference between 1 and any higher odd perfect square always is eight times a triangular number, while the difference between 9 and any higher odd perfect square is eight times a triangular number minus eight. From Wikipedia, the free encyclopedia. Product of an integer with itself. This article includes a list of general referencesbut it remains largely unverified because it lacks sufficient corresponding inline citations. Maths Squared: 100 Concepts You Should Know help to improve this article by introducing more precise citations. February Learn how and when to remove this template message. OEIS Foundation. Figurate numbers. Centered triangular numbers Maths Squared: 100 Concepts You Should Know square numbers Centered pentagonal numbers Centered hexagonal numbers Centered heptagonal numbers Centered octagonal numbers Centered nonagonal numbers Centered decagonal numbers Star numbers. Triangular numbers Square numbers Pentagonal numbers Hexagonal numbers Heptagonal numbers Octagonal numbers Nonagonal numbers Decagonal numbers Dodecagonal numbers. Centered tetrahedral numbers Centered cube numbers Centered octahedral numbers Centered dodecahedral numbers Centered icosahedral numbers. Tetrahedral numbers Cube numbers Octahedral numbers Dodecahedral numbers Icosahedral numbers Stella octangula numbers. Square pyramidal numbers Pentagonal pyramidal numbers Hexagonal Maths Squared: 100 Concepts You Should Know numbers Heptagonal pyramidal numbers. Pentatope numbers Squared triangular numbers Tesseractic numbers. Classes of natural numbers. Powers and related numbers. Recursively defined numbers. Possessing a specific set of other numbers. Expressible via specific sums. Centered triangular Centered square Centered pentagonal Centered hexagonal Centered heptagonal Centered octagonal Centered nonagonal Centered decagonal Star. Centered tetrahedral Centered cube Centered octahedral Centered dodecahedral Centered icosahedral. Square pyramidal Pentagonal pyramidal Hexagonal pyramidal Heptagonal pyramidal. Pentatope Squared triangular Tesseractic. Arithmetic functions and dynamics. Almost prime Semiprime. Amicable Perfect Sociable Untouchable. Euclid Fortunate. Other prime factor or divisor related numbers. Numeral system -dependent numbers. Persistence Additive Multiplicative. Digit sum Digital root Self Sum-product. Multiplicative digital root Sum-product. Automorphic Trimorphic. Cyclic Digit-reassembly Parasitic Primeval Transposable. Binary numbers. Evil Odious Pernicious. Generated via a sieve. Lucky Prime. Sorting related. Pancake number Sorting number. Natural language related. Aronson's sequence Ban. Graphemics related. Mathematics portal. Hidden categories: Articles with short description Short description is different from Wikidata Articles lacking in-text citations from February All articles lacking in-text citations All articles with unsourced statements Articles with unsourced statements from March Namespaces Article Talk. Views Read Edit View history. Help Learn to edit Community portal Recent changes Upload file. Download as PDF Printable version. Wikimedia Commons. 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SAT Math. The SAT math test is unlike any math test you've taken before. It's designed to take concepts you're used to and make you apply them in new and often strange ways. It's tricky, but with attention to detail and knowledge of the basic formulas and concepts covered by the test, you can improve your score. So what formulas do you need to have memorized for the SAT math section before the day of the test? In this complete guide, I'll cover every critical formula you MUST know before you sit down for the test. I'll also explain them in case you need to jog your memory about how a formula works. If you understand every formula in this list, you'll save yourself valuable time on the test and probably get a few extra questions correct. This is exactly what you'll see at the beginning of both math sections the calculator and no calculator section. It can be easy to look right past it, so familiarize yourself with the formulas now to avoid wasting time on test day. You are given 12 formulas on the test itself and three geometry laws. It can be helpful and save you time and effort to memorize the given formulas, but it is Maths Squared: 100 Concepts You Should Know unnecessary, as they are given on every SAT math section. You are only given geometry formulas, so prioritize memorizing your algebra and trigonometry formulas before test day we'll cover these in the next section. Nonetheless, you do need to know what the given geometry formulas mean. The explanations of those formulas are as follows:. Gear up that brain because here come the formulas you have to memorize. For most of the formulas on this list, you'll simply need to buckle down and memorize them sorry. Some of them, however, can be useful to Maths Squared: 100 Concepts You Should Know but are ultimately unnecessary to memorize, as their results can be calculated via other means. It's still useful to know these, though, so treat them seriously. We've broken the list into "Need to Know" and "Good to Know," depending on if you are a formula-loving test taker or a fewer-formulas-the- better kind of test taker. You don't need this formulaas you can simply graph your points and then create a right triangle from them. The distance will be the hypotenuse, which you can find via the Pythagorean Theorem. Some of the polynomials you'll come across on the SAT are easy to factor e. In these cases, the quadratic equation is your friend. Note: If you know how to complete the squarethen you don't need to memorize the quadratic equation. However, if you're not completely comfortable with completing the square, Maths Squared: 100 Concepts You Should Know it's relatively easy to memorize the Maths Squared: 100 Concepts You Should Know formula and have it ready. Trigonometry is a new addition to the new SAT math section. S ine equals O pposite over H ypotenuse. C osine equals A djacent over H ypotenuse. T angent equals O pposite over A djacent. Though these are all the formulas you'll need the ones you're given as well as the ones you need to memorizethis list doesn't cover every aspect of SAT Math. You'll also need to understand how to factor equations, how to manipulate and solve for absolute values, and how to manipulate and use exponents, and much more. These topics are all covered here. Maths Squared: 100 Concepts You Should Know important thing to remember is that while memorizing the formulas in this article that aren't given to you on the test is important, knowing this list of formulas doesn't mean you're all set for SAT Math. You also need to practice applying these formulas to answer questions, so that you know when it makes sense to use them. For instance, if you're asked to calculate how likely it is that a white marble would be drawn from a jar that contains three white marbles and four black marbles, it's easy enough to realize you need to take this probability formula:. On the SAT math section, however, you will also run into more complex probability questions like this one:. The data in the table above were produced by a sleep researcher studying the number of dreams people recall when asked to record their dreams for one week. Group X consisted of people who observed early bedtimes, and Maths Squared: 100 Concepts You Should Know Y consisted of people who observed later bedtimes. If a person is chosen at random from those who recalled at least 1 dream, what is the probability that the person belonged to Group Y? There's a lot of information to synthesize in that question: a table of data, a two-sentence long explanation of the table, and then, finally, what you need to solve for. If you haven't practiced these kinds of problems, you won't necessarily realize that you'll need that probability formula you memorized, and it might take you a few minutes of fumbling through the table and racking your brain to figure out how to get the answer— minutes that you now can't use on other problems in the section or to check your work. If you have practiced these kinds of Maths Squared: 100 Concepts You Should Know, however, you'll be able to quickly and effectively deploy that memorized probability formula and solve the problem:. OK, so the number of desired outcomes is anyone in Group Y who remembered at least one dream. That's these bolded cells:. And then the total number of possible outcomes is all people who recalled at least one dream. To get that, I have to subtract the number of people who didn't recall at least one dream 36 from the total number of people Now I'll plug it all back into the equation:. The takeaway from this example: once you've memorized these SAT math formulas, you need to learn when and how to use them by drilling yourself on practice questions. Now that you know the critical formulas for the SAT, it might be time to check out the complete list of SAT math knowledge and know-how you'll need before test day. Currently scoring in the mid-range on math? Look no further than our article on how to improve your score if you're currently scoring below the range. Check out our best-in-class online SAT prep classes. We guarantee your money back if you don't improve your SAT score by points or more. Our classes are entirely online, and they're taught by SAT experts. If you liked this article, you'll love our classes. Along with expert-led classes, you'll get personalized homework with thousands of practice problems organized by individual skills so you learn most effectively. We'll also give you a step-by-step, custom program to follow so you'll never be confused about what to study next. Courtney scored in the 99th percentile on the SAT in high school and went on to graduate from Stanford University Maths Squared: 100 Concepts You Should Know a degree in Cultural and Social Anthropology. She is passionate about bringing education and the tools to succeed to students from all backgrounds and walks of life, as she believes open education is one of the great societal equalizers. She has years of tutoring experience and writes creative works in her free time. How to Get a Perfectby a Perfect Scorer. Score on SAT Math. Score on SAT Reading. Score on SAT Writing. What ACT target score should you be aiming for? How to Get a Perfect 4. How to Write an Amazing College Essay. A Comprehensive Guide. Choose Your Test. Formulas Given on the SAT, Explained This is exactly what you'll see at the beginning of both math sections the calculator and no calculator section. It is a line that bisects the circle through the midpoint and touches two ends of the circle on opposite sides. It is twice the radius. For non-right triangles, the height Maths Squared: 100 Concepts You Should Know drop down through the interior of the triangle, as shown above unless otherwise given. Their sum is the equal to the square of the hypotenuse c, longest side of the triangle. Properties of Special Right Triangle: Isosceles Triangle An isosceles triangle has two sides that are equal in length and two equal angles opposite those sides. An isosceles right triangle always has a degree angle and two 45 degree angles. Properties of Special Right Maths Squared: 100 Concepts You Should Know 30, 60, 90 Degree Triangle A 30, 60, 90 triangle describes the degree measures of the triangle's three angles. Formulas Not Given on the Test For most of the formulas on this list, you'll simply need to buckle down and memorize them sorry. It is very common for the SAT to give you an equation in a different form and then ask you about whether the slope and intercept are positive or negative. You know the formulas for the area and circumference of a circle because they are in your given equation box on the test. You know how many degrees are in a circle because it is in your given equation box on the text. The concept is exactly the same as the formula, but it may help you to think of it this way instead of as a "formula" to memorize. A probability of 0 will never happen. Percentages Need to Know Find x percent of a given number n. Need Maths Squared: 100 Concepts You Should Know Know Find the sine of an angle given the measures of the sides of the triangle. Find the cosine of an angle given the measures of the sides of the triangle. Find the tangent of an angle given the measures of the sides of the triangle. Want to improve your SAT score by points? Try it risk-free today:. Courtney Montgomery. About the Author. 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R-squared R 2 is a statistical measure that represents the proportion of the variance for a dependent variable that's explained by an independent variable or variables in a regression model. Whereas correlation explains the strength of the relationship between an independent and dependent variable, R-squared explains to what extent the variance of one variable explains the variance of the second variable. For example, an R-squared for a fixed-income security versus a bond index identifies the security's proportion of price movement that is predictable based on a price movement of the index. It may also be known as the coefficient of determination. The actual calculation of R-squared requires several steps. This includes taking the data points observations of dependent and independent variables and finding the line of best fitoften from a regression model. From there you would calculate predicted values, subtract actual values and square the results. Maths Squared: 100 Concepts You Should Know yields a list of errors squared, which is then summed and equals the unexplained variance. To calculate the total variance, you would subtract the average actual value from each of the actual values, square the results and sum them. From there, divide the first sum of errors explained variance by the second sum total variancesubtract the result from one, and you have the R-squared. R-Squared only works as intended in a simple linear regression model with one explanatory variable. With a multiple regression made up of several independent variables, the R-Squared must be adjusted. The adjusted R-squared compares the descriptive power of regression models that include diverse numbers of predictors. Every predictor added to a model increases R-squared and never decreases it. This is not the case with the adjusted R-squared. Beta and R-squared are two related, but Maths Squared: 100 Concepts You Should Know, measures of correlation but beta is a measure of relative riskiness. R-squared measures how closely each change in the price of an asset is correlated to a benchmark. Used together, R-squared and beta give investors a thorough picture of the performance of asset managers. A beta of exactly 1. It doesn't tell you whether your chosen model is good or bad, nor will it tell you whether the data and predictions are biased. Advanced Technical Analysis Concepts. Risk Management. Tools for Fundamental Analysis. Mutual Fund Essentials. Financial Ratios. Your Privacy Rights. To change or withdraw your consent choices for Investopedia. I Accept. Your Money. Personal Finance. Your Practice. Popular Courses. Financial Analysis How to Value a Company. What Is R-Squared? Key Takeaways R- Squared is a statistical measure of fit that indicates how much variation of a dependent Maths Squared: 100 Concepts You Should Know is explained by the independent variable s in a regression model. Compare Accounts. The offers that appear in this table are from partnerships from which Investopedia receives compensation. Related Terms How Multiple Linear Regression Works Multiple linear regression MLR is a statistical technique that uses several explanatory variables to predict the outcome of a response variable. How the Coefficient of Determination Works The coefficient of determination is a measure used in statistical analysis to assess how well a model explains and predicts future outcomes. Heteroskedasticity In statistics, heteroskedasticity happens when the standard deviations of a variable, monitored over a specific amount of time, are nonconstant. Beta Beta is a measure of the volatility, or systematic risk, of a security or portfolio in comparison to the market as a whole. It is used in the capital asset pricing model. Defining Index Hugger An index hugger is a managed Maths Squared: 100 Concepts You Should Know fund that tends to perform much like a benchmark index. Error Term An error term is a variable in a statistical model when the model doesn't represent the actual relationship between the independent and dependent variables. Partner Links. Related Articles. Mutual Fund Essentials 5 ways to measure mutual fund risk. Risk Management How does Beta reflect Maths Squared: 100 Concepts You Should Know risk? Investopedia is part of the Dotdash publishing family.