Eighth Grade Math

What are repeating decimals?

Decimals with repeating digits or patterns.

What are square and cube roots?

Values multiplied 2 or 3 times to get original number.

What are irrational numbers?

Non-repeating, non-terminating decimals.

How do you approximate irrational numbers?

Find decimal values or locate on a number line.

How do exponents affect negative bases?

Even: positive, odd: negative result.

What are exponent properties?

Rules for multiplying, dividing, and raising powers.

What do negative exponents indicate?

Reciprocal of base to positive exponent.

What are integer exponent properties?

Rules for positive, negative, and zero exponents.

What are powers of 10?

Numbers like 10, 100, 1000, etc. (10^n).

What is scientific notation?

Writing large or small numbers using powers of 10.

How to do arithmetic in scientific notation?

Multiply/divide coefficients, add/subtract exponents.

How to solve scientific notation word problems?

Use scientific notation for real-world scenarios.

How to solve equations with variables on both sides?

Simplify and isolate the variable.

How to solve equations with parentheses?

Distribute, then combine like terms.

How many solutions can equations have?

One, none, or infinitely many.

How to solve equation word problems?

Translate to equation, solve for variable.

How to graph proportional relationships?

Straight line through origin.

What are solutions to linear equations?

Points where line intersects coordinate plane.

What are x and y-intercepts?

Points where line crosses x or y-axis.

What is slope?

Steepness, change in y / change in x.

What is slope-intercept form?

y = mx + b, m = slope, b = y-intercept.

How to graph slope-intercept form?

Plot y-intercept, use slope to find other points.

How to write slope-intercept equations?

Find slope and y-intercept.

What is a function?

Each input has one output.

What are linear models?

Equations with constant rate of change.

How to compare linear functions?

Compare slopes and y-intercepts.

How to construct linear models for real-world relationships?

Find slope and y-intercept from data.

How to recognize functions?

Check if each input has one output.

What are linear and nonlinear functions?

Linear: straight lines, nonlinear: curves.

What are systems of equations?

Two or more equations with same variables.

How to solve systems with graphing?

Plot equations, find intersection point.

How to solve systems with substitution?

Solve one equation, substitute into the other.

How many solutions can systems have?

One, none, or infinitely many.

How to solve systems of equations word problems?

Translate to equations, solve for unknowns.

What are angles between intersecting lines?

Opposite angles equal, adjacent angles supplementary.

What are triangle angles?

Sum to 180 degrees.

What is the Pythagorean theorem?

a² + b² = c² in right triangles.

How to apply Pythagorean theorem?

Solve real-world problems with right triangles.

What is the distance formula?

d = √((x₂ - x₁)² + (y₂ - y₁)²)

What are Pythagorean theorem proofs?

Algebraic and geometric proofs.

How to calculate volume?

Use formulas for 3D shapes.

What are transformations?

Changes in position, size, or orientation of a figure.

What are translations?

Moving a figure without changing size or shape.

What are rotations?

Turning a figure around a fixed point.

What are reflections?

Flipping a figure over a line.

What are properties of transformations?

How points, distances, shapes are preserved or altered.

What are dilations?

Resizing a figure, preserving shape.

What are congruence and similarity?

Congruent: same size and shape, similar: same shape.

What are scatter plots?

Graphs showing relationship between two variables.

How to interpret scatter plots?

Analyze correlation (positive, negative, none).

What are lines of best fit?

Lines representing overall pattern in scatter plots.

What are two-way tables?

Tables organizing data with two categorical variables.