Math concepts

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Math concepts

Linear relations

Slope

The slope is the rise over the run or Δx (change in x) over Δy (change in y) Example of slope on a graph:

Linear and non linear

A relation is non linear if it's not a line on a graph. Example of non linear relation:

A relation is linear when it's a line on a graph. Example of a linear relation:

Algebra

Distributive property

The distributive property is when you multiply a number by each member in a package, instead of doing the part in the brackets first. An example is 8(4x + 2x). You could do 4x + 2x first, then multiply that by 8. Or, you could use the distributive property and do 8 • 4x + 8 • 2x = 48x

Polynomials

A trinomial is three unlike terms that are joined by addition or subtraction. 3x⁶ + x - 2⁹ is a trinomial.

A binomial is two unlike terms that are joined by addition or subtraction. 8x⁴ + 9x⁷ is a binomial.

A monomial is one term. 7x⁵ is a monomial.

Polynomials are any number of terms that are joined together by addition or subtraction.

Alike and unlike terms

Unlike terms are terms that don't have the same variables or exponents. 4x³ and 6x⁵ are unlike terms.

Alike terms are terms that have the same variables and exponents. 3x² and 9x² are alike terms.

You get a term when you multiply a number and a variable. The variable can also contain exponents.

Number sense

Exponents

There are some rules that you have to follow when using exponents. They're called the laws of exponents. Here they are:

Fractions, decimals and percent

To convert a fraction to a percent, divide the numerator by the denominator to get a decimal. Then, multiply the decimal by 100 to get a percent. An example is 6/8. 6 ÷ 8 = 0.75 0.75 • 100 = 75 The percent is 75%. I you want to convert a decimal to a fraction, do the opposite.

To convert a decimal to a percent, multiply the decimal by 100 to get a percent. An example is 0.7. 0.7 • 100 = 70 The percent is 70% I you want to convert a percent to a decimal, do the opposite.

To convert a fraction to a decimal, divide the numerator by the denominator. An example is 2/10. 2 ÷ 10 = 0.2 The decimal is 0.2. I you want to convert a decimal to a fraction, do the opposite.

Rational and irrational numbers

Irrational numbers are numbers that have ongoing non repeating decimals. π is an irrational number because it has ongoing non repeating decimals.

Rational numbers are numbers that have a terminating decimal or ongoing repeating decimals. 25.8573628 is a rational number because it has a terminating decimal.

Financial literacy

Terminology

Financial terminology: Interest (I): The amount earned or the increase in value. Principal (P): The amount at the beginning, the initial amount. Future amount (A): The amount after the interest has been added.

Simple and compound interest

Compound interest is interest that is always calculated on principal amount and the interest that gets added. The formula is A = P(1 + r/n)^(nt)

Simple interest is interest that is always calculated on the principal amount. The formula is: A = P(1 + rt)

Data management

Quartiles

A box plot is useful for displaying the quartiles on a number line. Example of a box plot:

Quartile 1, is the number between the minimum and the median. Quartile 2 is the median. Quartile 3, is the number between the median and the maximum.

Discrete and continuous data

Continuous data is data that falls on a continuum and has an infinite amount of points in between the values. This data includes things that can be measured very precisely like height or weight. An example of continuous data is the height of your friend.

Discrete data is data that has spaces between values that are distinguishable. Usually, this data is countable. An example of discrete data is the number of people in a family.

Geometry and measurement

Pythagorean theorum

The Pythagorean theorem is used to figure out the value of a side of a right triangle, usually the hypotenuse (the opposite side of the right angle). The formula is: a² + b² = c² Then, you have to unsquare c² to get the value of the hypotenuse.