9th Grade Math, Unit 1

What is Quantitative reasoning?

Ability to analyze, understand, and apply math and numerical data to solve real life problems. Uses graphs, tables, and mathematical concepts. Quantitative reasoning also compares changes in between different quantities.

How do you convert rates?

By using a method for conversion. In this example we convert 10l into ml.

10L * 1000ml/1L sets up the equation. The L variables cancel out and we are left with 10000ml/1 which is 10000ml. Set up the equation so that the unit your converting from cancels out, leaving only the unit you want to convert to. We use 1000ml because that is how much 1 litre is in ml.

What are the properties of equality?

A mathematical statement that says adding, dividing, or any action done on both sides equally in a equation does not change the solution set.

What is the identify property of addition?

States that the sum of a number is the number + 0

What is the Identity Property of Multiplication?

States That The Product Of a number is the number times 1

What are inverse operations?

Operations that when are done, cancel each other out. Like multiplying and dividing.

What is absolute value?

A numbers distance from 0 in a number line. The absolute value of 3 is 3 and the absolute value of -3 is 3. A absolute value can never be negative. Example: Absolute value of 3 being -3 is not possible.

What is absolute value notation?

|x|

What is a inequality?

A type of equation that states one side is greater, or smaller then the other side.

What are the properties of inequality?

Adding or subtracting by the same value in both sides of a inequality does not change the solution set. Multiplying and dividing by the same value does not change the solution set of a inequality as long as its positive. But when multiplying or dividing on both sides of a inequality with negative numbers. You MUST change the inequality sign backwards to keep the solution set the same.

What do Closed and open circles mean in number lines?

Closed circles mean the number the closed circle is on top is included in the solution set. Open circles means that the number the circle is on is not included in the solution set.

What is interval notation?

Is a method of notation used to describe the solution set of a inequality. () and [] are used in this. [] mean the number is included in the solution set. () means the number is NOT included in the solution set. For example, if the solution set is x <= 3. The solution set is [3 -infinity)

What is a restricted set?

A restricted set is a set of numbers that could be the value of x in a inequality. But only a few values in the restricted set can be possible values of x while satisfying the inequality. The values that satisfy the inequality are a part of the solution set.

When can a 2 variable equation not be solved?

If both variables values are unknown. At least one variable value must be known.

What are continuous graphs?

Graphs with no gaps in the line that they make when graphed.

What is a discrete graph?

A graph with a finite line when graphed, and gaps between the line graphed. And a graph that has finite number of data points.