Directly Proportional Directly proportional: when one amount increases, another amount increases at the same rate. The symbol for “directly proportional” is ∝ Inversely Proportional Inversely Proportional: when one value increases, at the same rate that the other decreases. Examples Directly Proportional Inversely Proportional Have more workers You pay more Work time is shorter How
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
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.
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
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).
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
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
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
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
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