Free Math Practice Test by Grade 2026 — Grades 1–8 (With Answers)
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Grade-by-grade math practice for grades 1–8 — with worked answers, 4-week study plans, key formulas, and free worksheets, from the team behind MathNotion’s math workbooks.
What’s on Each Grade’s Math?
Elementary and middle school math builds in a clear progression. Grades 1–2 focus on number sense, place value, and addition and subtraction. Grades 3–5 add multiplication, division, fractions, decimals, and the start of geometry and measurement. Grades 6–8 move into ratios, percents, integers, algebra, functions, and the Pythagorean theorem.
This page gives a quick, grade-appropriate practice quiz for each grade level (1 through 8), plus a study plan, the key topics, and the formulas students are expected to know — aligned to common national standards. Choose a grade in the tabs below to begin.
Math Practice by Grade (1–8)
Choose a grade below. Each grade includes its own overview, 4-week study plan, practice quiz, tips, topic list, key formulas, and free resources — all grouped in one tab.
Grade 1 Math
First grade math builds number sense: counting to 120, addition and subtraction within 20, comparing numbers, basic shapes, and measuring length.
Grade 1: 4-Week Study Plan
Grade 1: Practice Quiz
Addition
What is 7 + 5?
- 10
- 11
- 12
- 13
Show answer
Comparing
Which is greater, 8 or 5?
- 5
- 8
- They are equal
- Cannot tell
Show answer
Shapes
How many sides does a triangle have?
- 2
- 3
- 4
- 5
Show answer
Grade 1: Tips to Boost Your Score
- Count out loud using objects like coins or blocks.
- Practice number bonds — pairs that make 10.
- Read each question slowly before answering.
Grade 1: Practice by Topic
Counting & Number Sense
Counting, ordering, and comparing to 120.
Addition & Subtraction
Facts within 20 and simple word problems.
Shapes & Measurement
2-D/3-D shapes, length, and time.
Browse free Grade 1 worksheets →
Grade 1: Key Facts to Know
- A triangle has 3 sides; a square has 4.
- Count by 1s, 2s, 5s, and 10s.
- Addition means putting groups together; subtraction means taking away.
Grade 2 Math
Second grade focuses on place value to 1,000, addition and subtraction within 100, the start of multiplication, money, time, and measurement.
Grade 2: 4-Week Study Plan
Grade 2: Practice Quiz
Place value
How many tens are in 100?
- 1
- 10
- 100
- 1000
Show answer
Addition
What is 45 + 38?
- 73
- 82
- 83
- 93
Show answer
Money
How many cents are in a quarter?
- 10
- 20
- 25
- 50
Show answer
Grade 2: Tips to Boost Your Score
- Line up digits by place value when adding.
- Skip-count to get ready for multiplication.
- Use a number line to add and subtract.
Grade 2: Practice by Topic
Place Value to 1,000
Hundreds, tens, and ones.
Add & Subtract within 100
Regrouping and word problems.
Money, Time & Measurement
Coins, clocks, and length.
Browse free Grade 2 worksheets →
Grade 2: Key Facts to Know
- 100 = 10 tens = 100 ones.
- Even numbers end in 0, 2, 4, 6, or 8.
- Perimeter = add the lengths of all sides.
Grade 3 Math
Third grade introduces multiplication and division, fractions, area and perimeter, and rounding.
Grade 3: 4-Week Study Plan
Grade 3: Practice Quiz
Multiplication
What is 6 × 7?
- 36
- 42
- 48
- 49
Show answer
Fractions
What is 1/2 of 10?
- 2
- 5
- 10
- 20
Show answer
Area
Area of a 4 × 5 rectangle?
- 9
- 20
- 40
- 45
Show answer
Grade 3: Tips to Boost Your Score
- Memorize times tables up to 10.
- Draw fractions to picture equal parts.
- Label units (cm, in) in measurement answers.
Grade 3: Practice by Topic
Multiplication & Division
Facts, arrays, and word problems.
Fractions
Naming and comparing simple fractions.
Area & Perimeter
Rectangles and rounding.
Browse free Grade 3 worksheets →
Grade 3: Formulas to Know
- Area of a rectangle = length × width.
- Multiplication is repeated addition.
- A fraction shows equal parts of a whole.
Grade 4 Math
Fourth grade covers multi-digit multiplication and division, fractions and decimals, factors and multiples, and angles.
Grade 4: 4-Week Study Plan
Grade 4: Practice Quiz
Multiplication
What is 23 × 4?
- 82
- 84
- 92
- 96
Show answer
Decimals
0.5 is the same as which fraction?
- 1/5
- 1/4
- 1/2
- 1/3
Show answer
Factors
Which number is a factor of 12?
- 5
- 6
- 7
- 9
Show answer
Grade 4: Tips to Boost Your Score
- Estimate before multiplying to check your work.
- Convert between fractions and decimals.
- Learn your factor pairs.
Grade 4: Practice by Topic
Multiplication & Division
Multi-digit and long division.
Fractions & Decimals
Equivalence and comparing.
Factors, Multiples & Angles
Number theory and geometry.
Browse free Grade 4 worksheets →
Grade 4: Formulas to Know
- Area = length × width.
- 1/2 = 0.5 = 50%.
- A right angle measures 90°.
Grade 5 Math
Fifth grade works with decimal operations, adding, subtracting and multiplying fractions, volume, the coordinate plane, and order of operations.
Grade 5: 4-Week Study Plan
Grade 5: Practice Quiz
Fractions
What is 1/2 + 1/4?
- 1/6
- 2/6
- 1/3
- 3/4
Show answer
Decimals
What is 3.2 × 10?
- 0.32
- 3.2
- 32
- 320
Show answer
Order of ops
What is 2 + 3 × 4?
- 9
- 14
- 20
- 24
Show answer
Grade 5: Tips to Boost Your Score
- Follow the order of operations (PEMDAS).
- Find common denominators for fractions.
- Keep decimal points lined up.
Grade 5: Practice by Topic
Decimal Operations
Add, subtract, multiply, divide.
Fraction Operations
Add, subtract, and multiply.
Volume & Coordinate Plane
Boxes and plotting points.
Browse free Grade 5 worksheets →
Grade 5: Formulas to Know
- Order of operations: PEMDAS.
- Volume of a box = length × width × height.
- Mean = sum ÷ number of values.
Grade 6 Math
Sixth grade introduces ratios and rates, percents, integers, expressions and equations, area and surface area, and statistics.
Grade 6: 4-Week Study Plan
Grade 6: Practice Quiz
Percent
What is 25% of 80?
- 16
- 20
- 25
- 40
Show answer
Ratio
In a 2:3 ratio with 8 of the first, how many of the second?
- 6
- 10
- 12
- 15
Show answer
Integers
What is −5 + 8?
- −13
- −3
- 3
- 13
Show answer
Grade 6: Tips to Boost Your Score
- Learn fraction–decimal–percent equivalents.
- Use a number line for integers.
- Rewrite word problems as expressions.
Grade 6: Practice by Topic
Ratios, Rates & Percent
Proportional thinking.
Integers
Signed numbers and the number line.
Expressions & Equations
One-step equations.
Grade 6 Math Books
Browse free Grade 6 worksheets →
Grade 6: Formulas to Know
- Percent = (part ÷ whole) × 100.
- Area of a triangle = ½ × base × height.
- A ratio a:b compares two quantities.
Grade 7 Math
Seventh grade covers proportional relationships, rational numbers, expressions, equations and inequalities, geometry (scale, circles), and probability.
Grade 7: 4-Week Study Plan
Grade 7: Practice Quiz
Algebra
Solve: 3x = 21.
- 6
- 7
- 18
- 24
Show answer
Percent
What is 15% of 60?
- 6
- 9
- 12
- 15
Show answer
Geometry
Area of a circle with r = 3 (π ≈ 3.14)?
- 6.28
- 9.42
- 18.84
- 28.26
Show answer
Grade 7: Tips to Boost Your Score
- Set up proportions for scale and percent problems.
- Track negative signs carefully.
- Memorize the circle formulas.
Grade 7: Practice by Topic
Proportional Relationships
Rates, scale, and percent.
Equations & Inequalities
Two-step and inequalities.
Geometry & Probability
Circles, area, and chance.
Grade 7 Math Books
Browse free Grade 7 worksheets →
Grade 7: Formulas to Know
- Proportion: a/b = c/d → a × d = b × c.
- Circle: area = πr², circumference = 2πr.
- Probability = favorable ÷ total outcomes.
Grade 8 Math
Eighth grade focuses on linear equations and functions, exponents and scientific notation, the Pythagorean theorem, systems of equations, and transformations.
Grade 8: 4-Week Study Plan
Grade 8: Practice Quiz
Algebra
Solve: 2x − 3 = 11.
- 4
- 7
- 8
- 14
Show answer
Exponents
Simplify: x² · x³.
- x
- x⁵
- x⁶
- x⁸
Show answer
Geometry
Right triangle with legs 3 and 4 — hypotenuse?
- 5
- 6
- 7
- 12
Show answer
Grade 8: Tips to Boost Your Score
- Master slope = rise ÷ run.
- Add exponents when multiplying like bases.
- Use a² + b² = c² for right triangles.
Grade 8: Practice by Topic
Linear Equations & Functions
Slope, intercepts, and graphs.
Exponents & Notation
Powers and scientific notation.
Pythagorean & Systems
Right triangles and systems.
Grade 8 Math Books
Browse free Grade 8 worksheets →
Grade 8: Formulas to Know
- Slope = (y₂ − y₁) ÷ (x₂ − x₁).
- Pythagorean theorem: a² + b² = c².
- Exponents: xᵃ · xᵇ = xᵃ⁺ᵇ.
Frequently Asked Questions
What grades does this page cover?
It covers math for grades 1 through 8, with a separate tab and practice quiz for each grade level.
Is the practice aligned to standards?
Yes. The topics and formulas follow common national math standards for each grade.
Is it free?
Yes — every grade quiz, study plan, and resource here is 100% free with no signup.
Do students need a calculator?
No. The quizzes are designed to build mental math and written calculation skills.
How are the quizzes structured?
Each grade quiz shows one question at a time with four choices and a worked solution you can reveal after answering.
How should my child practice?
Use the 4-week study plan for the grade, do a little each day, and review every missed question.