Grade 8 math

The three core exponent rules and why each one comes down to counting factors: add the exponents to multiply, subtract to divide, multiply for a power of a power.

Why any number to the power of zero equals 1, what a negative exponent means, and how to convert between negative powers and fractions without guessing.

What makes a number irrational, why every rational number has a terminating or repeating decimal, and how to place an irrational number on a number line.

How to write a number in scientific notation, convert back to standard form, decide the sign of the exponent, and multiply or divide numbers written this way.

What a square root is, why √25 means 5 and not ±5, how to recognize perfect squares, and how to estimate a root like √50 to one decimal place without a calculator.

What domain and range mean, how to find them from a graph, a table or an equation, and why some inputs have to be excluded.

Understand f(x) as a name and an input rather than multiplication, how to evaluate it, and how to read statements like f(3) = 7 in context.

Graph a line three ways — from slope-intercept form, from intercepts, or from a table — and understand why every point on the line is a solution.

Four reliable tests for deciding whether a relationship is linear — from its equation, its table, its graph, or its rate of change.

Rearrange a formula to solve for any variable using the same inverse operations you use on numbers, with worked examples from geometry, physics, and finance.

Solve multi-step equations by distributing, combining like terms, then undoing operations in reverse order, with worked examples and practice problems.

Solve multi-step inequalities by distributing, combining like terms, and undoing operations in reverse order, including when to flip the inequality sign.

Learn point-slope form, why it is the slope formula rearranged, and how to use it to write a line's equation from a single point and a slope.

Learn the quadratic formula, where it comes from, and how to use it to solve any quadratic equation, with worked examples and practice problems.

What average rate of change means, how it relates to slope, how to compute it from a table or a function, and how to read its units and sign.

Learn what slope measures, how to find it with rise over run and the slope formula, and why similar triangles guarantee it is the same everywhere on a line.

Understand y = mx + b, what m and b each control, how to graph a line from it in two moves, and how to rewrite any linear equation into this form.

What standard form is, when it beats slope-intercept form, how to convert between the two, and how to find the slope without rearranging.

Solve a system by graphing, substitution or elimination, why the solution is the intersection point, and how to spot systems with none or infinitely many.

Solve two-step equations by undoing addition first and multiplication second, with worked examples, common mistakes, and practice problems with full solutions.

Solve equations with variables on both sides by collecting variable terms on one side, plus how to recognize no solution and infinitely many solutions.

Find a line's equation from any two points: compute the slope, substitute into point-slope form, then simplify — with worked examples and full solutions.

Find the x- and y-intercepts of any equation by setting the other variable to zero, why that works, and what intercepts mean in a real situation.

How to compare two functions given in different forms, build a linear function from a table or a description, and read the rate of change from each one.

How to read a graph qualitatively — where it increases, decreases or stays flat, what steepness means, and how to sketch a graph from a story without any numbers.

Read a scatter plot, describe its association, draw and use a line of best fit, and understand why correlation does not prove causation.

How to build and read a two-way frequency table, how relative frequencies reveal an association between two categories, and why raw counts can mislead.

Why the angles of a triangle add to 180 degrees, what the exterior angle theorem says, and how parallel lines cut by a transversal produce equal angles.

What makes two figures congruent or similar, how a dilation resizes a figure about a center, what scale factor does to lengths and angles, and how to find a missing side.

How to find the distance between two points using the Pythagorean theorem, where the distance formula comes from, and how to measure a polygon drawn on a grid.

How to use a² + b² = c² to find a missing side of a right triangle, why c must be the hypotenuse, and how to find a leg rather than the hypotenuse.

How to translate, reflect and rotate a figure on the coordinate plane, the coordinate rule for each, and why all three leave lengths and angles unchanged.

The volume formulas for a cylinder, cone and sphere, why a cone is exactly a third of its cylinder, and how to work backwards from a volume to a radius.