North Carolina EOG Grade 8 Math Free Worksheets: Printable EOG-Ready Practice, Answers Included

There is a moment in eighth grade when a North Carolina student realizes the math has quietly changed shape. The problems used to end with a number. Now they end with a relationship — a slope that describes how fast something grows, a function that pairs every input with exactly one output, an equation that might have one answer, none at all, or infinitely many. Getting the right number is no longer the whole job. Understanding the structure behind it is.

The geometry shifts the same way. Eighth grade brings transformations on the coordinate plane, the idea of congruence as the result of slides, flips, and turns, and similarity through dilations. It introduces the Pythagorean theorem and the volume of cylinders, cones, and spheres — not as formulas to recite, but as relationships a student should be able to reason about out loud. Holding all of it together is a deeper sense of the real number system: irrational numbers, scientific notation, and the laws of exponents.

These worksheets were made for that stretch of the year. Whether your student is in Charlotte, Raleigh, Greensboro, or Durham, each PDF gives them one skill at a time, with enough practice to turn a shaky idea into a steady one.

What’s on this page

Seventy-two single-skill PDFs, each aligned to the North Carolina Standard Course of Study in Mathematics for Grade 8. Every file targets exactly one skill, which means a student working on functions is not also untangling scatter plots, and a student practicing volume is not knocked off course by inequalities. The narrow focus is the point — it makes progress visible.

Each PDF begins with a one-page Quick Review that lays out the skill in plain language and works through an example start to finish. Twenty practice problems follow, climbing from straightforward to genuinely challenging, and then four word problems set the skill in a real-world context. The final page is a student-facing answer key written for the student — short, friendly explanations they can read alone and use to fix their own mistakes.

Real Numbers

• Rational and Irrational Numbers — [NC.8.NS, NC.8.NS.1] tell a fraction-able number from one whose decimal never repeats
• Turning Repeating Decimals into Fractions — [NC.8.NS, NC.8.NS.1] the algebra trick that turns 0.272727… into a clean fraction
• Estimating Irrational Numbers — [NC.8.NS, NC.8.NS.2] pin a root like √20 between two whole numbers, then closer
• Estimating Expressions with Irrational Numbers — [NC.8.NS, NC.8.NS.1] approximate whole expressions that mix roots and π
• Personal Financial Literacy — [8.PFL.1] real-money math: budgets, balances, and simple percent work
• Prime Factorization with Exponents — [8.NS.1] break a number all the way down and write it with exponents
• Density of Real Numbers — [8.NS.1] there is always another number between any two — find it

Exponents, Roots & Scientific Notation

• Properties of Integer Exponents — [NC.8.EE, NC.8.EE.1] product, quotient, power, zero, and negative-exponent rules
• Square Roots and Cube Roots — [NC.8.EE, NC.8.EE.2] undo a square or a cube, including the ± on x² equations
• Understanding Scientific Notation — [NC.8.EE, NC.8.EE.3] move the decimal the right way for huge and tiny numbers
• Operations with Scientific Notation — [NC.8.EE, NC.8.EE.4] multiply, divide, add, and subtract without losing the exponent
• Order of Operations with Radicals — [8.EE.2] where the radical bar fits in PEMDAS — it groups like parentheses

Linear Equations and Inequalities

• Graphing Proportional Relationships — [NC.8.EE, NC.8.EE.1] read the unit rate straight off a proportional graph
• Slope as a Rate of Change — [NC.8.F, NC.8.F.5] slope is just rise over run — a real-world rate
• Slope and the Equations of a Line — [NC.8.G, NC.8.G.8] build y = mx + b from a slope and a point
• Solving Linear Equations in One Variable — [NC.8.EE, NC.8.EE.8] multi-step solving: distribute, combine, isolate
• Solving Systems of Two Equations — [NC.8.EE, NC.8.EE.8] find the point two lines share by substitution or elimination
• Solving Real Problems with Systems — [NC.8.EE, NC.8.EE.7] turn a word problem into two equations and solve it
• Solving Linear Inequalities — [NC.8.EE, NC.8.EE.7] solve like an equation — but flip the sign when you divide by a negative
• Multiplying Linear Expressions and Factoring — [8.EE.1] distribute to expand, pull out a common factor to undo it
• Graphing Linear Inequalities in Two Variables — [8.EE.8] boundary line, solid or dashed, then shade the right side
• Parallel and Perpendicular Lines — [8.EE.6] equal slopes for parallel, negative reciprocals for perpendicular
• Point-Slope and Standard Form — [8.EE.6] two more ways to write a line — and when each one helps
• Literal Equations — [8.EE.7] solve a formula for a different letter
• Absolute Value Equations and Inequalities — [8.EE.7] split into two cases — and read ‘and’ vs ‘or’ correctly
• Equations with Special Solutions — [8.EE.7] spot ‘no solution’ and ‘all real numbers’ before you waste time

Functions and Sequences

• What Is a Function? — [NC.8.F, NC.8.F.1] every input gets exactly one output — and how to check
• Reading Function Values — [NC.8.F, NC.8.F.3] evaluate f(x) and read values from tables and graphs
• Comparing Two Functions — [NC.8.F, NC.8.F.2] compare functions given as equations, tables, and graphs
• Linear vs. Nonlinear Functions — [NC.8.F, NC.8.F.3, NC.8.F.4] constant rate of change means linear — everything else does not
• Building Linear Functions — [NC.8.F, NC.8.F.5] write the function from a description, a table, or two points
• Sketching and Describing Function Graphs — [NC.8.F, NC.8.F.5] match a graph’s shape to a story: increasing, flat, falling
• Domain and Range of a Function — [8.F.1] the inputs you may use and the outputs you get back
• Arithmetic Sequences — [8.F.4] add the same step each time — and find the nth term
• Geometric Sequences — [8.F.4] multiply by the same ratio each time — and find the nth term

Geometry

• Rotations, Reflections, and Translations — [NC.8.G, NC.8.G.6] the three rigid motions and what each does to a figure
• Congruent Figures — [NC.8.G, NC.8.G.9] same size and shape — and the moves that prove it
• Transformations on the Coordinate Plane — [NC.8.G, NC.8.G.2, NC.8.G.3] apply transformation rules to coordinates
• Similarity and Dilations — [NC.8.G, NC.8.G.4, NC.8.G.9] scale a figure up or down and keep its shape
• Angles in Triangles and Parallel Lines — [NC.8.G.5] the angle sum and the parallel-line angle pairs
• Pythagorean Theorem — [NC.8.G, NC.8.G.6, NC.8.G.7] a² + b² = c² for any right triangle
• Distance with the Pythagorean Theorem — [NC.8.G, NC.8.G.8] find the distance between two points on the plane
• Volume of Cylinders, Cones, and Spheres — [NC.8.G.9] the three curved-solid volume formulas, side by side
• Angle Relationships — [NC.8.G, NC.8.G.5] complementary, supplementary, vertical, and adjacent angles
• Surface Area of Prisms, Cylinders, and Pyramids — [8.G.9] add up every face — nets make it visible
• Volume of Pyramids — [8.G.9] one-third of the matching prism
• Composite Figures: Area and Perimeter — [8.G.9] break an odd shape into shapes you already know
• Interior Angles of Polygons — [8.G.5] the (n − 2) × 180° rule for any polygon
• Triangle Inequality Theorem — [8.G.5] which three lengths can actually close into a triangle
• Surface Area of Spheres — [8.G.9] the 4πr² formula and where it shows up
• Arc Length and Area of Sectors — [8.G.9] a slice of a circle — its curved edge and its area
• Cross Sections of 3D Figures — [8.G.9] the 2D shape you get when you slice a solid
• Parallel Lines and Transversals — [8.G.5] name and use every angle pair a transversal creates
• Applying the Pythagorean Theorem — [8.G.7] real-world right-triangle problems: ladders, ramps, diagonals
• Volume of Cones and Spheres — [NC.8.G.9] focused practice on the two trickiest volume formulas

Statistics and Probability

• Scatter Plots — [NC.8.SP, NC.8.SP.1, NC.8.SP.2] read clustering, outliers, and the direction of a trend
• Fitting a Line to Data — [NC.8.SP, NC.8.SP.3] draw a trend line and find its slope and intercept
• Using a Linear Model — [NC.8.SP, NC.8.SP.3] use the trend line to predict and to interpret slope
• Two-Way Tables — [NC.8.SP, NC.8.SP.4] organize categorical data and read relative frequencies
• Mean Absolute Deviation — [8.SP.4] measure how spread out a data set really is
• Probability: Simple and Compound — [8.SP.4] single-event probability and combining events
• Counting Principle and Permutations — [8.SP.4] count outcomes by multiplying — and when order matters
• Box Plots and IQR — [8.SP.4] the five-number summary, the box, and the spread of the middle
• Random Sampling — [8.SP.4] why a fair sample beats a biased one, and how to scale up
• Effect of Data Changes — [8.SP.4] what adding or scaling values does to mean, median, and range
• Probability of Compound Events — [8.SP.4] and/or events, with and without replacement

Financial Literacy

• Simple Interest — [8.PFL.1] I = Prt — interest that grows on the original amount only
• Compound Interest — [8.PFL.2] interest that earns interest, period after period
• Percents: Tax, Discount, and Markup — [8.PFL.3] the everyday percent problems behind every receipt
• Cost of Credit and Loans — [8.PFL.4] what borrowing really costs once interest is counted
• Payment Methods — [8.PFL.5] cash, debit, credit, and checks — the math and the trade-offs
• Saving for College — [8.PFL.6] set a goal, plan a monthly amount, and let growth help

How to use these worksheets at home

You do not need a plan that stretches across the whole semester. A dependable weekly rhythm does more than a frantic weekend ever will. Choose two afternoons — maybe a weeknight after school and a slow Saturday morning — and treat each PDF as one sitting. Most take fifteen to twenty minutes, short enough that a tired eighth grader will actually start.

A pairing worth trying: do a skill, then do the skill built on top of it. Run Slope as a Rate of Change one day and Slope and the Equations of a Line the next, and the second sheet feels like a continuation, not a new climb. The same goes for Pythagorean Theorem before Distance with the Pythagorean Theorem, or Scatter Plots before Fitting a Line to Data. Skills that connect should be practiced in order.

North Carolina runs from the mountains to the coast, and homework happens all the way across it — at a table in a Charlotte apartment, on a porch in the Piedmont, in the last quiet hour before a Friday night game in a small eastern town. Print what you need the night before, keep the answer key aside until the work is finished, and let your student check their own thinking. That final step — reading the explanations — is where the learning actually settles in.

A note about the EOG at Grade 8

North Carolina eighth graders take the End-of-Grade (EOG) Mathematics Test in the spring. It is built on the North Carolina Standard Course of Study in Mathematics, so the skills on these worksheets and the skills on the test come from the same place.

The Grade 8 EOG asks students to do real mathematical thinking, not just calculation. They have to read a graph and say what it means, set up an equation from a word problem, reason about a transformed figure, and pick the strategy that fits the question. The test leans hard on the algebra-and-functions strand — linear equations, systems, slope, and the function concept — that sits at the center of eighth-grade math.

Because every PDF here is tied to one Grade 8 standard, the spring window becomes a checklist you can actually use. If functions are solid but the Pythagorean theorem is shaky, that gap is easy to see — and you can work just those PDFs instead of reviewing everything again.

A short closing

Eighth-grade math is a climb, but a steady one — a student gets to the top one skill, one afternoon at a time. Bookmark this page, print a single PDF tonight, and let your student start somewhere small. North Carolina kids do hard things well when the next step is clear, and a worksheet on the table is about as clear as it gets.

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