Grade 9 math

Solve absolute value equations by splitting into two cases, why two answers appear, when there is no solution, and how absolute value inequalities differ.

Learn completing the square: why the method works geometrically, how to handle a leading coefficient, and how it produces vertex form and the quadratic formula.

Solve compound inequalities joined by AND or OR, graph the solution on a number line, and tell which combinations give no solution or every number.

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.

Parallel lines have equal slopes and perpendicular lines have negative reciprocal slopes — why both rules are true, and how to write equations using them.

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.

Solve quadratics by factoring using the zero product property, why the equation must equal zero first, and how to factor the common trinomial patterns.

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 equations with variables on both sides by collecting variable terms on one side, plus how to recognise 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.