Zero Product Property

Definition If   a × b = 0   then   a = 0   or   b = 0   or  a = b = 0 A product of factors is zero if and only if one or more of the factors is zero. Standard Form of an Equation The Standard Form of an equation is: “some expression” = 0 Learn More Partial Sum General Form of … Continue reading "Zero Product Property"

Partial Sum

A series is the sum of the terms in a sequence (not the list of terms, like a sequence). The series with a finite number of terms is a easy to find the sum of the series just by adding the terms. However, for the series with an infinite number of terms, the summation is more difficult and complicated. … Continue reading "Partial Sum"

General Form of Equation of a Line

Definition General Form of the equation of a straight line is: Ax + By + C = 0 Note: A or B can’t be zero at the same time. (if A = 0 then B ≠ 0, vice versa) The General Form is not always the most useful form, and you may prefer to use: Slope-Intercept Form … Continue reading "General Form of Equation of a Line"

Subtracting Fractions

Definition A fraction like 2/3 says we have 2 out of the 3 parts the whole is divided into. The top number is called numerator The bottom number is called denominator There are 3 simple steps to subtract fractions Make sure the bottom numbers (the denominators) are the same Subtract the top numbers (the numerators). … Continue reading "Subtracting Fractions"

Infinite Series

Definition of Infinite Series Infinite series are the sum of infinitely many numbers listed in a given order & related in a given way. For an infinite series a1 + a2 + a3 + … , a quantity sn = a1 + a2 + … + an, which involves adding only the first n terms, is called a partial sum. For Sn approaches a fixed number … Continue reading "Infinite Series"

Dividing Fractions

There are 3 Simple Steps to Divide Fractions: Turn the second fraction (the one you want to divide by) upside down (this is now a reciprocal). Multiply the first fraction by that reciprocal of second fraction Simplify the fraction (if needed) Fractions and Whole Numbers What about division with fractions and whole numbers? Make the … Continue reading "Dividing Fractions"

Geometric Sequences and Sums

Sequence A Sequence is a set of things (usually numbers) that are in order. 2, 4, 6, 8, … Geometric Sequences In a Geometric Sequence, each term is found by multiplying the previous term by a constant. This sequence has a factor of 3 between each number. Each term (except the first term) is found … Continue reading "Geometric Sequences and Sums"

Parallel and Perpendicular Lines

Definition of Parallel Lines If 2 lines are parallel, their slopes are same. Slope is the value m in the equation of a line. y = mx + b If two lines are parallel lines, they will never intersect. They have exactly the same steepness which means their slopes are identical. Since: Slope is a … Continue reading "Parallel and Perpendicular Lines"

Trigonometric Identities

Right Triangle The Trigonometric Identities are equations that are true for Right Angled Triangles. Each side of a right triangle has a name: Adjacent is always next to the angle Opposite is opposite the angle Sine, Cosine and Tangent 3 main functions in trigonometry are Sine, Cosine and Tangent. They are just the length of one … Continue reading "Trigonometric Identities"

Arithmetic Sequences and Series Sums

Sequence A Sequence is a set of things (usually numbers) that are in order. 1, 3, 5, 7, … Each number in the sequence is called a term (or sometimes “element” or “member”). Arithmetic Sequence In an Arithmetic Sequence, the difference between one term and the next is called a constant. In other words, we … Continue reading "Arithmetic Sequences and Series Sums"