CRCT Overview Math 8 Introduction to Algebra and GeometryReminder:

Properties

A - The Number System

Rational Numbers

A rational number is a number that can be written as a ratio. That means it can be written as a fraction, in which both the numerator (the

number on top) and the denominator (the number on the bottom) are whole numbers.

The number 8 is a rational number because it can be written as the fraction 8/1.

Likewise, 3/4 is a rational number because it can be written as a fraction.

Even a big, clunky fraction like 7,324,908/56,003,492 is rational, simply because it can be written as a

fraction.

Every whole number is a rational number, because any whole number can be written as a fraction. For example, 4 can be written as 4/1, 65 can

be written as 65/1, and 3,867 can be written as 3,867/1.

Irrational Numbers

All numbers that are not rational are considered irrational. An irrational number can be written as a decimal, but not as a fraction.

An irrational number has endless non-repeating digits to the right of the decimal point. Here are some irrational numbers:

π = 3.141592… = 1.414213…

Although irrational numbers are not often used in daily life, they do exist on the number line. In fact, between 0 and 1 on the number line, there

are an infinite number of irrational numbers!

Locating square roots on Number line.

B - Expressions and Equations

Exponents & Square Roots

Scientific Notation

Ratio and Proportional RelationshipsProportion: relationship between two ratios written as an equation

34 =

912

Ratio: comparison of two or more amounts

3 out of 4 3:4 3 to 434

Unit rate: comparison of two measurements written as a fraction with the denominator equaling one (as in miles per hour or cost per item)

$2.00 for 4 pencils Unit rate = $0.50 2.00

4= x

1

Data can be placed in table and create ordered pairs for the coordinate plane.Cost Unit Rate5.00 for 10 .5012.00 for 10 1.20 3.00 for 10 .30

Percent: out of 100; to find percent set up a proportion 34= x

100 Cross multiply and then solve equation 20% of 60 means .20 times 60 = 12

2 4 6 8 10 12 140

0.20.40.60.8

11.21.4

Slope Intercept

Standard Form to slope intercept

EquationsEquations are complete mathematical sentences. The equal sign can be represented by the word IS in a word problem. OF means multiply usually. THAN tells you to switch the order of the numbers in the word problem.Inverses- operations that undo or reverse another operation. Addition/Subtraction Multiplication/Division

Two step equations: undo Add/Sub first then Mult/Div

Systems Elimination Method (multiplication): Substitution Method:

C – Functions

Rule—the math operation(s) you have to do to the inputInput or independent variable—number you start with (x)Output or dependent variable – value you get after using the rule (y)

Use substitution and order of operation to complete a function table. 14 = x + 9 x=5 Y = 2 + 9 y=11

Radical Expressions

D – GeometryReflection: Translation Rotation

Angle Relationships

Pythagorean Theorem

Volume

E - Statistics and Probability

Scatter plots:

Inequalities

Inequalities compare two or more values that are not equal. Numbers to left on the number line are always smaller than those on the right. If you graph numbers on the number line, you can compare their values from least to greatest going left to right.

Use the same rules for solving equations.

NOTE: multiplying or dividing by a negative number reverses the inequality symbol.

- Statistics and Probability

Independent Events

Dependent Events

Measures of Central Tendency