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Grade 8 · Maths · curriculum collection

Grade 8 Maths, Common Core domains

4 units for Grade 8 maths, organised by Common Core domain: Expressions and Equations, Geometry. Each unit has a short lesson, a practice worksheet and a review worksheet, both with answer keys.

4 units8 worksheets96 questions with answers
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Answer-checked and approved on 29 October 2026

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Aligned by StudyBrix at domain level. Not an official publication of, or endorsed by, the standards' authors. Framework: Common Core State Standards for Mathematics.

Units in teaching order

01

8.EE Expressions and Equations

Algebra

Two-step equations, equations with the unknown on both sides and one-step equations.

Short lesson: Equations with x on both sides

Study guide for Grades 8 to 10: 2 worked examples and 2 practice questions. Perform the same operation on both sides. Here a is different from c.

ax + b = cx + d → (a − c)x = d − b

Perform the same operation on both sides. Here a is different from c.

Worked example

Solve: 9x + 19 = 2x + 68.

7x = 49 → x = 7

Answer: 7

Read the full study guide

Worksheets

A practice worksheet and a review worksheet, 12 and 12 questions.

Worksheets (PDF)Answer keys (PDF)
Practice worksheet: 12 questions

  1. Solve for x: 6x + 42 = 192

  2. Solve for x: 15x = 570

  3. Solve: 14x + 4 = 2x + 136.

  4. Solve for x: 4x + 36 = 76

  5. Solve for x: 21x = 798

  6. Solve: 14x + 7 = 3x + 161.

  7. Solve for x: 19x + 4 = 669

  8. Solve for x: 20x = 200

  9. Solve: 15x + 17 = 2x + 173.

  10. Solve for x: 14x + 80 = 724

  11. Solve for x: 10x = -130

  12. Solve: 15x + 12 = 2x + 155.

Answer key
  1. 25 6x = 192 − 42 = 150; x = 25
  2. 38 x = 570 ÷ 15 = 38
  3. 11 12x = 132 → x = 11
  4. 10 4x = 76 − 36 = 40; x = 10
  5. 38 x = 798 ÷ 21 = 38
  6. 14 11x = 154 → x = 14
  7. 35 19x = 669 − 4 = 665; x = 35
  8. 10 x = 200 ÷ 20 = 10
  9. 12 13x = 156 → x = 12
  10. 46 14x = 724 − 80 = 644; x = 46
  11. -13 x = -130 ÷ 10 = -13
  12. 11 13x = 143 → x = 11
Review worksheet: 12 questions

  1. Solve: 13x + 10 = 4x + 46.

  2. Solve for x: 12x + 13 = 613

  3. Solve for x: 15x = -690

  4. Solve: 12x + 8 = 3x + 71.

  5. Solve for x: 10x + 55 = 345

  6. Solve for x: 25x = -125

  7. Solve: 14x + 6 = 1x + 214.

  8. Solve for x: 7x + 54 = -44

  9. Solve for x: 21x = -630

  10. Solve: 7x + 11 = 4x + 53.

  11. Solve for x: 17x + 4 = -64

  12. Solve for x: 9x = -216

Answer key
  1. 4 9x = 36 → x = 4
  2. 50 12x = 613 − 13 = 600; x = 50
  3. -46 x = -690 ÷ 15 = -46
  4. 7 9x = 63 → x = 7
  5. 29 10x = 345 − 55 = 290; x = 29
  6. -5 x = -125 ÷ 25 = -5
  7. 16 13x = 208 → x = 16
  8. -14 7x = -44 − 54 = -98; x = -14
  9. -30 x = -630 ÷ 21 = -30
  10. 14 3x = 42 → x = 14
  11. -4 17x = -64 − 4 = -68; x = -4
  12. -24 x = -216 ÷ 9 = -24

Related ready-made worksheets: Grade 8 Algebra worksheet

02

8.EE Expressions and Equations

Powers & roots

Dividing powers, multiplying powers, square roots, cube roots and whole-number exponents.

Short lesson: Multiply powers of one base

Study guide for Grades 8 to 10: 2 worked examples and 2 practice questions. Add exponents only when multiplying the same base.

aᵐ × aⁿ = aᵐ⁺ⁿ

Add exponents only when multiplying the same base.

Worked example

Find n: 10^10 × 10^3 = 10^n.

10 + 3 = 13

Answer: 13

Read the full study guide

Worksheets

A practice worksheet and a review worksheet, 12 and 12 questions.

Worksheets (PDF)Answer keys (PDF)
Practice worksheet: 12 questions

  1. Find n: 14^5 ÷ 14^4 = 14^n.

  2. Find n: 19^5 × 19^4 = 19^n.

  3. ∛(0) = ?

  4. √1089 = ?

  5. 6^4 = ?

  6. Find n: 9^2 ÷ 9^12 = 9^n.

  7. Find n: 17^9 × 17^5 = 17^n.

  8. ∛(4913) = ?

  9. √6084 = ?

  10. 5^3 = ?

  11. Find n: 6^4 ÷ 6^6 = 6^n.

  12. Find n: 12^2 × 12^4 = 12^n.

Answer key
  1. 1 5 − 4 = 1
  2. 9 5 + 4 = 9
  3. 0 (0)³ = 0
  4. 33 33 × 33 = 1089
  5. 1296 6 × 6 × 6 × 6 = 1296
  6. -10 2 − 12 = -10
  7. 14 9 + 5 = 14
  8. 17 (17)³ = 4913
  9. 78 78 × 78 = 6084
  10. 125 5 × 5 × 5 = 125
  11. -2 4 − 6 = -2
  12. 6 2 + 4 = 6
Review worksheet: 12 questions

  1. Find n: 20^8 ÷ 20^9 = 20^n.

  2. Find n: 6^3 × 6^7 = 6^n.

  3. ∛(10648) = ?

  4. √625 = ?

  5. 9^4 = ?

  6. Find n: 2^2 ÷ 2^12 = 2^n.

  7. Find n: 20^2 × 20^6 = 20^n.

  8. ∛(1) = ?

  9. √1681 = ?

  10. 3^2 = ?

  11. Find n: 20^8 ÷ 20^5 = 20^n.

  12. Find n: 4^8 × 4^9 = 4^n.

Answer key
  1. -1 8 − 9 = -1
  2. 10 3 + 7 = 10
  3. 22 (22)³ = 10648
  4. 25 25 × 25 = 625
  5. 6561 9 × 9 × 9 × 9 = 6561
  6. -10 2 − 12 = -10
  7. 8 2 + 6 = 8
  8. 1 (1)³ = 1
  9. 41 41 × 41 = 1681
  10. 9 3 × 3 = 9
  11. 3 8 − 5 = 3
  12. 17 8 + 9 = 17
03

8.G Geometry

Transformations

Reflections and rotations.

Short lesson: Reflection in a vertical line

Study guide for Grades 6 to 9: 2 worked examples and 2 practice questions. The image is the same distance on the opposite side of the mirror line.

x′ = 2h − x; reflection in x = h

The image is the same distance on the opposite side of the mirror line.

Worked example

Reflect (9, -5) in x = -2. What is the new x-coordinate?

2 × (-2) − (9) = -13

Answer: -13

Read the full study guide

Worksheets

A practice worksheet and a review worksheet, 12 and 12 questions.

Worksheets (PDF)Answer keys (PDF)
Practice worksheet: 12 questions

  1. Reflect (5, -8) in x = 8. What is the new x-coordinate?

  2. Rotate (25, 11) 90° counterclockwise about the origin. Give the new x-coordinate.

  3. Reflect (-16, -8) in x = 7. What is the new x-coordinate?

  4. Rotate (29, 23) 90° counterclockwise about the origin. Give the new x-coordinate.

  5. Reflect (-14, -9) in x = 6. What is the new x-coordinate?

  6. Rotate (4, 13) 90° counterclockwise about the origin. Give the new x-coordinate.

  7. Reflect (-9, 0) in x = -3. What is the new x-coordinate?

  8. Rotate (-8, -15) 90° counterclockwise about the origin. Give the new x-coordinate.

  9. Reflect (-11, -7) in x = -8. What is the new x-coordinate?

  10. Rotate (18, -19) 90° counterclockwise about the origin. Give the new x-coordinate.

  11. Reflect (15, 4) in x = 10. What is the new x-coordinate?

  12. Rotate (21, -15) 90° counterclockwise about the origin. Give the new x-coordinate.

Answer key
  1. 11 2 × (8) − (5) = 11
  2. -11 (25, 11) → (-11, 25)
  3. 30 2 × (7) − (-16) = 30
  4. -23 (29, 23) → (-23, 29)
  5. 26 2 × (6) − (-14) = 26
  6. -13 (4, 13) → (-13, 4)
  7. 3 2 × (-3) − (-9) = 3
  8. 15 (-8, -15) → (15, -8)
  9. -5 2 × (-8) − (-11) = -5
  10. 19 (18, -19) → (19, 18)
  11. 5 2 × (10) − (15) = 5
  12. 15 (21, -15) → (15, 21)
Review worksheet: 12 questions

  1. Reflect (4, 6) in x = -6. What is the new x-coordinate?

  2. Rotate (-18, 10) 90° counterclockwise about the origin. Give the new x-coordinate.

  3. Reflect (7, 3) in x = -8. What is the new x-coordinate?

  4. Rotate (-1, -11) 90° counterclockwise about the origin. Give the new x-coordinate.

  5. Reflect (-7, -8) in x = -8. What is the new x-coordinate?

  6. Rotate (-6, -4) 90° counterclockwise about the origin. Give the new x-coordinate.

  7. Reflect (16, -5) in x = 0. What is the new x-coordinate?

  8. Rotate (-28, 16) 90° counterclockwise about the origin. Give the new x-coordinate.

  9. Reflect (-4, 4) in x = -8. What is the new x-coordinate?

  10. Rotate (-3, 8) 90° counterclockwise about the origin. Give the new x-coordinate.

  11. Reflect (18, -4) in x = 1. What is the new x-coordinate?

  12. Rotate (13, -12) 90° counterclockwise about the origin. Give the new x-coordinate.

Answer key
  1. -16 2 × (-6) − (4) = -16
  2. -10 (-18, 10) → (-10, -18)
  3. -23 2 × (-8) − (7) = -23
  4. 11 (-1, -11) → (11, -1)
  5. -9 2 × (-8) − (-7) = -9
  6. 4 (-6, -4) → (4, -6)
  7. -16 2 × (0) − (16) = -16
  8. -16 (-28, 16) → (-16, -28)
  9. -12 2 × (-8) − (-4) = -12
  10. -8 (-3, 8) → (-8, -3)
  11. -16 2 × (1) − (18) = -16
  12. 12 (13, -12) → (12, 13)

Related ready-made worksheets: Grade 8 Coordinate geometry worksheet

04

8.G Geometry

Geometry

Angles in a triangle, volume of cylinders, volume of cones and the Pythagorean theorem.

Short lesson: Volume of a cone

Study guide for Grades 8 to 12: 2 worked examples and 2 practice questions. Use the perpendicular height and radius, not the diameter.

V = πr²h/3

Use the perpendicular height and radius, not the diameter.

Worked example

A cone has radius 2 cm and height 90 cm. Use π = 3.14. Find its volume in cm³.

3.14 × 2² × 90 ÷ 3 = 376.8

Answer: 376.8 cm³

Read the full study guide

Worksheets

A practice worksheet and a review worksheet, 12 and 12 questions.

Worksheets (PDF)Answer keys (PDF)
Practice worksheet: 12 questions

  1. A cylinder has radius 19 cm and height 27 cm. Its volume is kπ cm³. Find k.

  2. A cone has radius 22 cm and height 51 cm. Use π = 3.14. Find its volume in cm³.

  3. Two interior angles of a triangle are 45° and 90°. Find the third angle in degrees.

  4. A right triangle has legs 130 cm and 312 cm. Find the hypotenuse in cm.

  5. A cylinder has radius 11 cm and height 5 cm. Its volume is kπ cm³. Find k.

  6. A cone has radius 18 cm and height 69 cm. Use π = 3.14. Find its volume in cm³.

  7. Two interior angles of a triangle are 100° and 33°. Find the third angle in degrees.

  8. A right triangle has legs 240 cm and 450 cm. Find the hypotenuse in cm.

  9. A cylinder has radius 10 cm and height 16 cm. Its volume is kπ cm³. Find k.

  10. A cone has radius 8 cm and height 42 cm. Use π = 3.14. Find its volume in cm³.

  11. Two interior angles of a triangle are 91° and 36°. Find the third angle in degrees.

  12. A right triangle has legs 135 cm and 324 cm. Find the hypotenuse in cm.

Answer key
  1. 9747 V = π × 19² × 27 = 9747π
  2. 25835.92 cm³ 3.14 × 22² × 51 ÷ 3 = 25835.92
  3. 45 ° 180 − 45 − 90 = 45°
  4. 338 cm √(130² + 312²) = √114244 = 338
  5. 605 V = π × 11² × 5 = 605π
  6. 23399.28 cm³ 3.14 × 18² × 69 ÷ 3 = 23399.28
  7. 47 ° 180 − 100 − 33 = 47°
  8. 510 cm √(240² + 450²) = √260100 = 510
  9. 1600 V = π × 10² × 16 = 1600π
  10. 2813.44 cm³ 3.14 × 8² × 42 ÷ 3 = 2813.44
  11. 53 ° 180 − 91 − 36 = 53°
  12. 351 cm √(135² + 324²) = √123201 = 351
Review worksheet: 12 questions

  1. Two interior angles of a triangle are 87° and 20°. Find the third angle in degrees.

  2. A cylinder has radius 10 cm and height 19 cm. Its volume is kπ cm³. Find k.

  3. A cone has radius 18 cm and height 30 cm. Use π = 3.14. Find its volume in cm³.

  4. A right triangle has legs 24 cm and 32 cm. Find the hypotenuse in cm.

  5. Two interior angles of a triangle are 83° and 60°. Find the third angle in degrees.

  6. A cylinder has radius 7 cm and height 12 cm. Its volume is kπ cm³. Find k.

  7. A cone has radius 4 cm and height 6 cm. Use π = 3.14. Find its volume in cm³.

  8. A right triangle has legs 30 cm and 40 cm. Find the hypotenuse in cm.

  9. Two interior angles of a triangle are 79° and 52°. Find the third angle in degrees.

  10. A cylinder has radius 25 cm and height 13 cm. Its volume is kπ cm³. Find k.

  11. A cone has radius 10 cm and height 72 cm. Use π = 3.14. Find its volume in cm³.

  12. A right triangle has legs 55 cm and 132 cm. Find the hypotenuse in cm.

Answer key
  1. 73 ° 180 − 87 − 20 = 73°
  2. 1900 V = π × 10² × 19 = 1900π
  3. 10173.6 cm³ 3.14 × 18² × 30 ÷ 3 = 10173.6
  4. 40 cm √(24² + 32²) = √1600 = 40
  5. 37 ° 180 − 83 − 60 = 37°
  6. 588 V = π × 7² × 12 = 588π
  7. 100.48 cm³ 3.14 × 4² × 6 ÷ 3 = 100.48
  8. 50 cm √(30² + 40²) = √2500 = 50
  9. 49 ° 180 − 79 − 52 = 49°
  10. 8125 V = π × 25² × 13 = 8125π
  11. 7536 cm³ 3.14 × 10² × 72 ÷ 3 = 7536
  12. 143 cm √(55² + 132²) = √20449 = 143

Related ready-made worksheets: Grade 8 Geometry worksheet