Grade 9 Math Skills Checklist | What Your 9th Grader Should Know

Linear Functions & Equations

Solve multi-step linear equations

Solve equations with variables on both sides, parentheses, and multiple steps.

Examples: 3(x - 2) + 5 = 2x + 7, 4x - 3 = 2(x + 1) + 5

Solve and graph linear inequalities

Solve inequalities and represent solutions on number lines.

Examples: -2x + 5 > 11 → x < -3, 3x - 7 ≤ 8

Calculate and interpret slope

Find slope from two points, graphs, and equations; understand rate of change.

Examples: Slope between (2, 3) and (5, 9) = 2, Interpret slope as speed or cost per item

Graph linear equations

Graph lines using slope-intercept form, point-slope form, and standard form.

Examples: y = 2x + 3, y - 5 = -3(x - 2)

Write equations of lines

Write linear equations given slope and point, two points, or parallel/perpendicular lines.

Examples: Line through (1, 4) with slope 2, Parallel to y = 3x - 1 through (2, 5)

Use function notation

Understand f(x) notation and evaluate functions.

Examples: If f(x) = 2x + 1, find f(3), Evaluate g(-2) for g(x) = x² - 3x

Systems of Equations

Solve systems by graphing

Graph two lines and identify the intersection point.

Examples: y = 2x + 1 and y = -x + 7 intersect at (2, 5)

Solve systems by substitution

Substitute one equation into another to solve.

Examples: If y = 3x, substitute into x + y = 8

Solve systems by elimination

Add or subtract equations to eliminate a variable.

Examples: 2x + 3y = 12 and 2x - y = 4 → subtract to get 4y = 8

Identify special cases

Recognize systems with no solution (parallel) or infinite solutions (same line).

Examples: y = 2x + 1 and y = 2x + 5 are parallel (no solution)

Model with systems

Write and solve systems from real-world problems.

Examples: Tickets cost $5 adult and $3 child. 100 tickets sold for $400.

Quadratic Functions

Multiply polynomials

Use FOIL and distribution to multiply binomials and polynomials.

Examples: (x + 3)(x + 5) = x² + 8x + 15, (2x - 1)(x + 4)

Factor quadratic trinomials

Factor expressions of the form x² + bx + c.

Examples: x² + 7x + 12 = (x + 3)(x + 4), x² - 5x + 6 = (x - 2)(x - 3)

Factor special patterns

Recognize and factor difference of squares and perfect square trinomials.

Examples: x² - 9 = (x + 3)(x - 3), x² + 6x + 9 = (x + 3)²

Solve quadratics by factoring

Use zero product property after factoring.

Examples: x² + 5x + 6 = 0 → (x + 2)(x + 3) = 0 → x = -2 or x = -3

Graph parabolas

Identify vertex, axis of symmetry, and intercepts.

Examples: y = x² - 4x + 3: vertex at (2, -1), Opens up when a > 0

Exponents & Radicals

Apply exponent rules

Use product, quotient, and power rules for exponents.

Examples: x³ · x⁴ = x⁷, (x²)³ = x⁶, x⁵/x² = x³

Simplify with negative exponents

Convert negative exponents to fractions.

Examples: x⁻³ = 1/x³, 2⁻⁴ = 1/16

Use scientific notation

Perform operations with numbers in scientific notation.

Examples: (3 × 10⁴)(2 × 10³) = 6 × 10⁷

Simplify radicals

Factor out perfect squares from square roots.

Examples: √72 = √36 · √2 = 6√2, √50 = 5√2

Add and multiply radicals

Combine like radicals and multiply radical expressions.

Examples: 3√2 + 5√2 = 8√2, √3 · √12 = √36 = 6

Data & Statistics

Interpret data displays

Analyze histograms, box plots, and scatter plots.

Examples: Identify outliers, Compare distributions

Calculate statistics

Find mean, median, mode, range, and standard deviation.

Examples: Mean of 3, 5, 7, 9, 11 is 7

Understand correlation

Describe strength and direction of linear relationships.

Examples: Strong positive correlation, r ≈ 0.9

Where grade 9 students often struggle

FOIL errors: forgetting middle terms (x + 3)(x + 2) ≠ x² + 6
Sign errors when factoring: x² - 5x + 6 = (x - 2)(x - 3), not (x + 2)(x + 3)
Mixing up when to add vs multiply exponents
Forgetting to set each factor equal to zero when solving
Confusing slope with y-intercept in y = mx + b
Thinking √(a + b) = √a + √b (this is FALSE)
Not checking solutions in original equations

Signs your child is on track

Factors quadratics quickly without guess-and-check
Graphs lines rapidly from any form of equation
Solves systems using the most efficient method for each problem
Simplifies radical expressions without hesitation
Writes equations from word problems systematically
Checks all solutions and identifies extraneous solutions

Coming in grade 10

Mastering these grade 9 skills prepares your child for:

Quadratic formula and completing the square

Polynomial operations and factoring

Rational expressions and equations

Radical equations

Exponential and logarithmic functions introduction

Formal geometry proofs and constructions

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