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Grade 9 · Maths · curriculum collection

Grade 9 Maths, Common Core conceptual categories

8 units for Grade 9 maths, organised by Common Core conceptual category: Algebra, Functions, Geometry, Statistics and Probability. Each unit has a short lesson, a practice worksheet and a review worksheet, both with answer keys.

8 units16 worksheets192 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

HS.A Algebra

Equations and systems

Two-step equations, equations with the unknown on both sides, one-step equations and systems of two linear 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: 10x = 460

  2. Solve for x: 14x + 9 = 457

  3. Solve: 10x + 18 = 1x + 63.

  4. Solve for x: x + y = 28 and x − y = 12.

  5. Solve for x: 6x = 234

  6. Solve for x: 14x + 33 = -79

  7. Solve: 15x + 7 = 4x + 29.

  8. Solve for x: x + y = 17 and x − y = -11.

  9. Solve for x: 21x = -1029

  10. Solve for x: 19x + 42 = -224

  11. Solve: 7x + 10 = 3x + 86.

  12. Solve for x: x + y = 35 and x − y = 9.

Answer key
  1. 46 x = 460 ÷ 10 = 46
  2. 32 14x = 457 − 9 = 448; x = 32
  3. 5 9x = 45 → x = 5
  4. 20 2x = 40 → x = 20
  5. 39 x = 234 ÷ 6 = 39
  6. -8 14x = -79 − 33 = -112; x = -8
  7. 2 11x = 22 → x = 2
  8. 3 2x = 6 → x = 3
  9. -49 x = -1029 ÷ 21 = -49
  10. -14 19x = -224 − 42 = -266; x = -14
  11. 19 4x = 76 → x = 19
  12. 22 2x = 44 → x = 22
Review worksheet: 12 questions

  1. Solve for x: 4x = -196

  2. Solve: 10x + 10 = 3x + 24.

  3. Solve for x: 16x + 52 = 132

  4. Solve for x: x + y = 34 and x − y = 30.

  5. Solve for x: 30x = -90

  6. Solve: 7x + 10 = 4x + 16.

  7. Solve for x: 10x + 28 = 348

  8. Solve for x: x + y = 27 and x − y = 23.

  9. Solve for x: 4x = 128

  10. Solve: 11x + 16 = 1x + 36.

  11. Solve for x: 19x + 15 = 224

  12. Solve for x: x + y = 41 and x − y = 39.

Answer key
  1. -49 x = -196 ÷ 4 = -49
  2. 2 7x = 14 → x = 2
  3. 5 16x = 132 − 52 = 80; x = 5
  4. 32 2x = 64 → x = 32
  5. -3 x = -90 ÷ 30 = -3
  6. 2 3x = 6 → x = 2
  7. 32 10x = 348 − 28 = 320; x = 32
  8. 25 2x = 50 → x = 25
  9. 32 x = 128 ÷ 4 = 32
  10. 2 10x = 20 → x = 2
  11. 11 19x = 224 − 15 = 209; x = 11
  12. 40 2x = 80 → x = 40

Related ready-made worksheets: Grade 9 Algebra worksheet

02

HS.A Algebra

Quadratic expressions and equations

Solving factored quadratics, expanding binomials and completing the square.

Short lesson: Expand a binomial square

Study guide for Grades 8 to 11: 2 worked examples and 2 practice questions. The middle term is twice the product, not zero.

(x + a)² = x² + 2ax + a²

The middle term is twice the product, not zero.

Worked example

Expand (6x + 24)². What is the coefficient of x?

2 × 6 × 24 = 288

Answer: 288

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. Expand (5x + 6)². What is the coefficient of x?

  2. Find the smaller root of (x − 21)(x − 33) = 0.

  3. Complete x² + 38x + □ = (x + 19)².

  4. Expand (4x + 3)². What is the coefficient of x?

  5. Find the smaller root of (x − 8)(x − 16) = 0.

  6. Complete x² + 56x + □ = (x + 28)².

  7. Expand (12x + 10)². What is the coefficient of x?

  8. Find the smaller root of (x − 21)(x − 23) = 0.

  9. Complete x² + 44x + □ = (x + 22)².

  10. Expand (12x + 23)². What is the coefficient of x?

  11. Find the smaller root of (x − 14)(x − 23) = 0.

  12. Complete x² + 68x + □ = (x + 34)².

Answer key
  1. 60 2 × 5 × 6 = 60
  2. 21 x = 21 or x = 33; 21 < 33
  3. 361 (38 ÷ 2)² = 361
  4. 24 2 × 4 × 3 = 24
  5. 8 x = 8 or x = 16; 8 < 16
  6. 784 (56 ÷ 2)² = 784
  7. 240 2 × 12 × 10 = 240
  8. 21 x = 21 or x = 23; 21 < 23
  9. 484 (44 ÷ 2)² = 484
  10. 552 2 × 12 × 23 = 552
  11. 14 x = 14 or x = 23; 14 < 23
  12. 1156 (68 ÷ 2)² = 1156
Review worksheet: 12 questions

  1. Expand (1x + 16)². What is the coefficient of x?

  2. Find the smaller root of (x − 3)(x − 13) = 0.

  3. Complete x² + 10x + □ = (x + 5)².

  4. Expand (11x + 8)². What is the coefficient of x?

  5. Find the smaller root of (x − 1)(x − 16) = 0.

  6. Complete x² + 18x + □ = (x + 9)².

  7. Expand (2x + 16)². What is the coefficient of x?

  8. Find the smaller root of (x − 20)(x − 34) = 0.

  9. Complete x² + 70x + □ = (x + 35)².

  10. Expand (2x + 26)². What is the coefficient of x?

  11. Find the smaller root of (x − 22)(x − 28) = 0.

  12. Complete x² + 62x + □ = (x + 31)².

Answer key
  1. 32 2 × 1 × 16 = 32
  2. 3 x = 3 or x = 13; 3 < 13
  3. 25 (10 ÷ 2)² = 25
  4. 176 2 × 11 × 8 = 176
  5. 1 x = 1 or x = 16; 1 < 16
  6. 81 (18 ÷ 2)² = 81
  7. 64 2 × 2 × 16 = 64
  8. 20 x = 20 or x = 34; 20 < 34
  9. 1225 (70 ÷ 2)² = 1225
  10. 104 2 × 2 × 26 = 104
  11. 22 x = 22 or x = 28; 22 < 28
  12. 961 (62 ÷ 2)² = 961

Related ready-made worksheets: Grade 9 Quadratic equations worksheet

03

HS.F Functions

Inverse and composite functions

Composing functions and inverse functions.

Short lesson: Compose two functions

Study guide for Grades 9 to 12: 2 worked examples and 2 practice questions. Apply the inside function first.

(f ∘ g)(x) = f(g(x))

Apply the inside function first.

Worked example

f(t) = 4t + (-3); g(t) = 5t + (-5). Find f(g(7)).

g(7) = 30; f(30) = 117

Answer: 117

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. f(x) = 7x + (-13). Find f⁻¹(-132).

  2. f(t) = 5t + (-1); g(t) = 5t + (5). Find f(g(7)).

  3. f(x) = 13x + (9). Find f⁻¹(61).

  4. f(t) = 7t + (-7); g(t) = 1t + (8). Find f(g(1)).

  5. f(x) = 7x + (8). Find f⁻¹(120).

  6. f(t) = 6t + (-8); g(t) = 1t + (1). Find f(g(-2)).

  7. f(x) = 12x + (-2). Find f⁻¹(202).

  8. f(t) = 6t + (10); g(t) = 3t + (8). Find f(g(-3)).

  9. f(x) = 14x + (15). Find f⁻¹(435).

  10. f(t) = 2t + (9); g(t) = 4t + (5). Find f(g(-1)).

  11. f(x) = 5x + (30). Find f⁻¹(145).

  12. f(t) = 9t + (9); g(t) = 4t + (0). Find f(g(4)).

Answer key
  1. -17 (-132 − (-13)) ÷ 7 = -17
  2. 199 g(7) = 40; f(40) = 199
  3. 4 (61 − (9)) ÷ 13 = 4
  4. 56 g(1) = 9; f(9) = 56
  5. 16 (120 − (8)) ÷ 7 = 16
  6. -14 g(-2) = -1; f(-1) = -14
  7. 17 (202 − (-2)) ÷ 12 = 17
  8. 4 g(-3) = -1; f(-1) = 4
  9. 30 (435 − (15)) ÷ 14 = 30
  10. 11 g(-1) = 1; f(1) = 11
  11. 23 (145 − (30)) ÷ 5 = 23
  12. 153 g(4) = 16; f(16) = 153
Review worksheet: 12 questions

  1. f(x) = 12x + (-3). Find f⁻¹(-3).

  2. f(t) = 6t + (-6); g(t) = 2t + (-1). Find f(g(2)).

  3. f(x) = 14x + (19). Find f⁻¹(159).

  4. f(t) = 4t + (-8); g(t) = 5t + (3). Find f(g(4)).

  5. f(x) = 14x + (-18). Find f⁻¹(-256).

  6. f(t) = 9t + (9); g(t) = 4t + (-8). Find f(g(-1)).

  7. f(x) = 3x + (-15). Find f⁻¹(-63).

  8. f(t) = 2t + (1); g(t) = 1t + (1). Find f(g(-4)).

  9. f(x) = 9x + (-2). Find f⁻¹(7).

  10. f(t) = 2t + (-2); g(t) = 4t + (-4). Find f(g(3)).

  11. f(x) = 15x + (-9). Find f⁻¹(441).

  12. f(t) = 4t + (6); g(t) = 1t + (8). Find f(g(3)).

Answer key
  1. 0 (-3 − (-3)) ÷ 12 = 0
  2. 12 g(2) = 3; f(3) = 12
  3. 10 (159 − (19)) ÷ 14 = 10
  4. 84 g(4) = 23; f(23) = 84
  5. -17 (-256 − (-18)) ÷ 14 = -17
  6. -99 g(-1) = -12; f(-12) = -99
  7. -16 (-63 − (-15)) ÷ 3 = -16
  8. -5 g(-4) = -3; f(-3) = -5
  9. 1 (7 − (-2)) ÷ 9 = 1
  10. 14 g(3) = 8; f(8) = 14
  11. 30 (441 − (-9)) ÷ 15 = 30
  12. 50 g(3) = 11; f(11) = 50

Related ready-made worksheets: Grade 9 Algebra worksheet

04

HS.F Functions

Quadratic functions

Evaluating quadratic functions.

Short lesson: Evaluate a quadratic

Study guide for Grades 9 to 11: 2 worked examples and 2 practice questions. Square the input before multiplying by its coefficient.

f(x) = ax² + bx + c

Square the input before multiplying by its coefficient.

Worked example

Find f(-5) if f(x) = 6x² + 1x + 7.

6 × (-5)² + 1 × (-5) + 7 = 152

Answer: 152

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 f(6) if f(x) = 1x² + 7x + 9.

  2. Find f(1) if f(x) = 5x² + 5x + 10.

  3. Find f(7) if f(x) = 5x² + 11x + 13.

  4. Find f(5) if f(x) = 4x² + 2x + 5.

  5. Find f(3) if f(x) = 1x² + 12x + 10.

  6. Find f(-1) if f(x) = 4x² + 2x + 4.

  7. Find f(-8) if f(x) = 1x² + 2x + 8.

  8. Find f(-2) if f(x) = 6x² + 10x + 5.

  9. Find f(0) if f(x) = 3x² + 3x + 3.

  10. Find f(-1) if f(x) = 4x² + 6x + 5.

  11. Find f(-3) if f(x) = 5x² + 7x + 10.

  12. Find f(6) if f(x) = 4x² + 12x + 9.

Answer key
  1. 87 1 × (6)² + 7 × (6) + 9 = 87
  2. 20 5 × (1)² + 5 × (1) + 10 = 20
  3. 335 5 × (7)² + 11 × (7) + 13 = 335
  4. 115 4 × (5)² + 2 × (5) + 5 = 115
  5. 55 1 × (3)² + 12 × (3) + 10 = 55
  6. 6 4 × (-1)² + 2 × (-1) + 4 = 6
  7. 56 1 × (-8)² + 2 × (-8) + 8 = 56
  8. 9 6 × (-2)² + 10 × (-2) + 5 = 9
  9. 3 3 × (0)² + 3 × (0) + 3 = 3
  10. 3 4 × (-1)² + 6 × (-1) + 5 = 3
  11. 34 5 × (-3)² + 7 × (-3) + 10 = 34
  12. 225 4 × (6)² + 12 × (6) + 9 = 225
Review worksheet: 12 questions

  1. Find f(0) if f(x) = 1x² + 12x + 1.

  2. Find f(-5) if f(x) = 4x² + 11x + 10.

  3. Find f(-7) if f(x) = 3x² + 7x + 11.

  4. Find f(3) if f(x) = 6x² + 11x + 4.

  5. Find f(0) if f(x) = 2x² + 11x + 2.

  6. Find f(6) if f(x) = 6x² + 12x + 11.

  7. Find f(0) if f(x) = 4x² + 12x + 9.

  8. Find f(7) if f(x) = 2x² + 12x + 11.

  9. Find f(7) if f(x) = 6x² + 2x + 14.

  10. Find f(2) if f(x) = 5x² + 5x + 5.

  11. Find f(-6) if f(x) = 4x² + 6x + 13.

  12. Find f(2) if f(x) = 6x² + 2x + 8.

Answer key
  1. 1 1 × (0)² + 12 × (0) + 1 = 1
  2. 55 4 × (-5)² + 11 × (-5) + 10 = 55
  3. 109 3 × (-7)² + 7 × (-7) + 11 = 109
  4. 91 6 × (3)² + 11 × (3) + 4 = 91
  5. 2 2 × (0)² + 11 × (0) + 2 = 2
  6. 299 6 × (6)² + 12 × (6) + 11 = 299
  7. 9 4 × (0)² + 12 × (0) + 9 = 9
  8. 193 2 × (7)² + 12 × (7) + 11 = 193
  9. 322 6 × (7)² + 2 × (7) + 14 = 322
  10. 35 5 × (2)² + 5 × (2) + 5 = 35
  11. 121 4 × (-6)² + 6 × (-6) + 13 = 121
  12. 36 6 × (2)² + 2 × (2) + 8 = 36

Related ready-made worksheets: Grade 9 Quadratic equations worksheet

05

HS.F Functions

Sequences, logarithms and radians

Arithmetic sequences.

Short lesson: Arithmetic sequences

Study guide for Grades 9 to 12: 2 worked examples and 2 practice questions. The first term is n = 1. Use one fewer step than the term number.

aₙ = a₁ + (n − 1)d

The first term is n = 1. Use one fewer step than the term number.

Worked example

An arithmetic sequence has first term 17 and common difference 2. Find term 24.

17 + (24 − 1) × 2 = 63

Answer: 63

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. An arithmetic sequence has first term 30 and common difference 9. Find term 20.

  2. An arithmetic sequence has first term 36 and common difference 9. Find term 6.

  3. An arithmetic sequence has first term 32 and common difference 15. Find term 6.

  4. An arithmetic sequence has first term 32 and common difference 5. Find term 15.

  5. An arithmetic sequence has first term 36 and common difference 14. Find term 14.

  6. An arithmetic sequence has first term 21 and common difference 6. Find term 19.

  7. An arithmetic sequence has first term 40 and common difference 11. Find term 21.

  8. An arithmetic sequence has first term 13 and common difference 15. Find term 23.

  9. An arithmetic sequence has first term 3 and common difference 14. Find term 13.

  10. An arithmetic sequence has first term 1 and common difference 15. Find term 28.

  11. An arithmetic sequence has first term 18 and common difference 2. Find term 25.

  12. An arithmetic sequence has first term 33 and common difference 7. Find term 11.

Answer key
  1. 201 30 + (20 − 1) × 9 = 201
  2. 81 36 + (6 − 1) × 9 = 81
  3. 107 32 + (6 − 1) × 15 = 107
  4. 102 32 + (15 − 1) × 5 = 102
  5. 218 36 + (14 − 1) × 14 = 218
  6. 129 21 + (19 − 1) × 6 = 129
  7. 260 40 + (21 − 1) × 11 = 260
  8. 343 13 + (23 − 1) × 15 = 343
  9. 171 3 + (13 − 1) × 14 = 171
  10. 406 1 + (28 − 1) × 15 = 406
  11. 66 18 + (25 − 1) × 2 = 66
  12. 103 33 + (11 − 1) × 7 = 103
Review worksheet: 12 questions

  1. An arithmetic sequence has first term 10 and common difference 11. Find term 11.

  2. An arithmetic sequence has first term 31 and common difference 14. Find term 16.

  3. An arithmetic sequence has first term 29 and common difference 6. Find term 29.

  4. An arithmetic sequence has first term 8 and common difference 11. Find term 18.

  5. An arithmetic sequence has first term 1 and common difference 9. Find term 30.

  6. An arithmetic sequence has first term 20 and common difference 10. Find term 27.

  7. An arithmetic sequence has first term 15 and common difference 2. Find term 11.

  8. An arithmetic sequence has first term 28 and common difference 8. Find term 28.

  9. An arithmetic sequence has first term 4 and common difference 13. Find term 7.

  10. An arithmetic sequence has first term 1 and common difference 12. Find term 12.

  11. An arithmetic sequence has first term 16 and common difference 15. Find term 24.

  12. An arithmetic sequence has first term 3 and common difference 11. Find term 6.

Answer key
  1. 120 10 + (11 − 1) × 11 = 120
  2. 241 31 + (16 − 1) × 14 = 241
  3. 197 29 + (29 − 1) × 6 = 197
  4. 195 8 + (18 − 1) × 11 = 195
  5. 262 1 + (30 − 1) × 9 = 262
  6. 280 20 + (27 − 1) × 10 = 280
  7. 35 15 + (11 − 1) × 2 = 35
  8. 244 28 + (28 − 1) × 8 = 244
  9. 82 4 + (7 − 1) × 13 = 82
  10. 133 1 + (12 − 1) × 12 = 133
  11. 361 16 + (24 − 1) × 15 = 361
  12. 58 3 + (6 − 1) × 11 = 58
06

HS.G Geometry

Coordinates and transformations

Midpoints and rotations.

Short lesson: Quarter-turn rotations

Study guide for Grades 7 to 10: 2 worked examples and 2 practice questions. This rule rotates around the origin in the coordinate plane.

90° counterclockwise: (x,y) → (−y,x)

This rule rotates around the origin in the coordinate plane.

Worked example

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

(-12, -21) → (21, -12)

Answer: 21

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. Rotate (0, -17) 90° counterclockwise about the origin. Give the new x-coordinate.

  2. Find only the x-coordinate of the midpoint of (14, -19) and (1, -16).

  3. Rotate (6, 27) 90° counterclockwise about the origin. Give the new x-coordinate.

  4. Find only the x-coordinate of the midpoint of (-15, -8) and (-6, -12).

  5. Rotate (-22, 13) 90° counterclockwise about the origin. Give the new x-coordinate.

  6. Find only the x-coordinate of the midpoint of (26, -15) and (-6, -3).

  7. Rotate (3, 28) 90° counterclockwise about the origin. Give the new x-coordinate.

  8. Find only the x-coordinate of the midpoint of (30, 14) and (18, -13).

  9. Rotate (24, -13) 90° counterclockwise about the origin. Give the new x-coordinate.

  10. Find only the x-coordinate of the midpoint of (12, -3) and (13, -8).

  11. Rotate (14, 1) 90° counterclockwise about the origin. Give the new x-coordinate.

  12. Find only the x-coordinate of the midpoint of (19, -2) and (-9, -1).

Answer key
  1. 17 (0, -17) → (17, 0)
  2. 7.5 (14 + (1))/2 = 7.5
  3. -27 (6, 27) → (-27, 6)
  4. -10.5 (-15 + (-6))/2 = -10.5
  5. -13 (-22, 13) → (-13, -22)
  6. 10 (26 + (-6))/2 = 10
  7. -28 (3, 28) → (-28, 3)
  8. 24 (30 + (18))/2 = 24
  9. 13 (24, -13) → (13, 24)
  10. 12.5 (12 + (13))/2 = 12.5
  11. -1 (14, 1) → (-1, 14)
  12. 5 (19 + (-9))/2 = 5
Review worksheet: 12 questions

  1. Find only the x-coordinate of the midpoint of (-16, 17) and (-20, -15).

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

  3. Find only the x-coordinate of the midpoint of (10, -18) and (-20, 4).

  4. Rotate (13, -5) 90° counterclockwise about the origin. Give the new x-coordinate.

  5. Find only the x-coordinate of the midpoint of (9, 8) and (26, -4).

  6. Rotate (-15, 1) 90° counterclockwise about the origin. Give the new x-coordinate.

  7. Find only the x-coordinate of the midpoint of (21, -8) and (22, 6).

  8. Rotate (-1, -13) 90° counterclockwise about the origin. Give the new x-coordinate.

  9. Find only the x-coordinate of the midpoint of (-29, 7) and (-8, 20).

  10. Rotate (14, -15) 90° counterclockwise about the origin. Give the new x-coordinate.

  11. Find only the x-coordinate of the midpoint of (1, -16) and (-22, 9).

  12. Rotate (4, 9) 90° counterclockwise about the origin. Give the new x-coordinate.

Answer key
  1. -18 (-16 + (-20))/2 = -18
  2. -13 (-4, 13) → (-13, -4)
  3. -5 (10 + (-20))/2 = -5
  4. 5 (13, -5) → (5, 13)
  5. 17.5 (9 + (26))/2 = 17.5
  6. -1 (-15, 1) → (-1, -15)
  7. 21.5 (21 + (22))/2 = 21.5
  8. 13 (-1, -13) → (13, -1)
  9. -18.5 (-29 + (-8))/2 = -18.5
  10. 15 (14, -15) → (15, 14)
  11. -10.5 (1 + (-22))/2 = -10.5
  12. -9 (4, 9) → (-9, 4)

Related ready-made worksheets: Grade 9 Coordinate geometry worksheet

07

HS.G Geometry

Geometry

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 cone has radius 12 cm and height 36 cm. Use π = 3.14. Find its volume in cm³.

  2. A right triangle has legs 6 cm and 8 cm. Find the hypotenuse in cm.

  3. A cylinder has radius 15 cm and height 22 cm. Its volume is kπ cm³. Find k.

  4. A cone has radius 20 cm and height 18 cm. Use π = 3.14. Find its volume in cm³.

  5. A right triangle has legs 105 cm and 360 cm. Find the hypotenuse in cm.

  6. A cylinder has radius 16 cm and height 24 cm. Its volume is kπ cm³. Find k.

  7. A cone has radius 15 cm and height 9 cm. Use π = 3.14. Find its volume in cm³.

  8. A right triangle has legs 64 cm and 120 cm. Find the hypotenuse in cm.

  9. A cylinder has radius 15 cm and height 23 cm. Its volume is kπ cm³. Find k.

  10. A cone has radius 14 cm and height 84 cm. Use π = 3.14. Find its volume in cm³.

  11. A right triangle has legs 152 cm and 285 cm. Find the hypotenuse in cm.

  12. A cylinder has radius 5 cm and height 8 cm. Its volume is kπ cm³. Find k.

Answer key
  1. 5425.92 cm³ 3.14 × 12² × 36 ÷ 3 = 5425.92
  2. 10 cm √(6² + 8²) = √100 = 10
  3. 4950 V = π × 15² × 22 = 4950π
  4. 7536 cm³ 3.14 × 20² × 18 ÷ 3 = 7536
  5. 375 cm √(105² + 360²) = √140625 = 375
  6. 6144 V = π × 16² × 24 = 6144π
  7. 2119.5 cm³ 3.14 × 15² × 9 ÷ 3 = 2119.5
  8. 136 cm √(64² + 120²) = √18496 = 136
  9. 5175 V = π × 15² × 23 = 5175π
  10. 17232.32 cm³ 3.14 × 14² × 84 ÷ 3 = 17232.32
  11. 323 cm √(152² + 285²) = √104329 = 323
  12. 200 V = π × 5² × 8 = 200π
Review worksheet: 12 questions

  1. A cone has radius 14 cm and height 60 cm. Use π = 3.14. Find its volume in cm³.

  2. A cylinder has radius 21 cm and height 19 cm. Its volume is kπ cm³. Find k.

  3. A right triangle has legs 80 cm and 150 cm. Find the hypotenuse in cm.

  4. A cone has radius 23 cm and height 66 cm. Use π = 3.14. Find its volume in cm³.

  5. A cylinder has radius 6 cm and height 40 cm. Its volume is kπ cm³. Find k.

  6. A right triangle has legs 147 cm and 504 cm. Find the hypotenuse in cm.

  7. A cone has radius 19 cm and height 90 cm. Use π = 3.14. Find its volume in cm³.

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

  9. A right triangle has legs 203 cm and 696 cm. Find the hypotenuse in cm.

  10. A cone has radius 8 cm and height 12 cm. Use π = 3.14. Find its volume in cm³.

  11. A cylinder has radius 13 cm and height 27 cm. Its volume is kπ cm³. Find k.

  12. A right triangle has legs 80 cm and 192 cm. Find the hypotenuse in cm.

Answer key
  1. 12308.8 cm³ 3.14 × 14² × 60 ÷ 3 = 12308.8
  2. 8379 V = π × 21² × 19 = 8379π
  3. 170 cm √(80² + 150²) = √28900 = 170
  4. 36543.32 cm³ 3.14 × 23² × 66 ÷ 3 = 36543.32
  5. 1440 V = π × 6² × 40 = 1440π
  6. 525 cm √(147² + 504²) = √275625 = 525
  7. 34006.2 cm³ 3.14 × 19² × 90 ÷ 3 = 34006.2
  8. 9747 V = π × 19² × 27 = 9747π
  9. 725 cm √(203² + 696²) = √525625 = 725
  10. 803.84 cm³ 3.14 × 8² × 12 ÷ 3 = 803.84
  11. 4563 V = π × 13² × 27 = 4563π
  12. 208 cm √(80² + 192²) = √43264 = 208

Related ready-made worksheets: Grade 9 Geometry worksheet

08

HS.S Statistics and Probability

Statistics & probability

The mean, the median, the mean of a frequency table, conditional probability from a table, probability of an event not happening and interquartile range.

Short lesson: Interquartile range

Study guide for Grades 8 to 12: 2 worked examples and 2 practice questions. Use medians of the lower and upper halves for this exercise.

IQR = Q₃ − Q₁

Use medians of the lower and upper halves for this exercise.

Worked example

Data: 34, 45, 56, 67, 78, 89, 100, 111. Using medians of the lower four and upper four values, find the interquartile range.

Q₁ = 50.5; Q₃ = 94.5; IQR = 44

Answer: 44

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. Data: 14, 20, 26, 32, 38, 44, 50, 56. Using medians of the lower four and upper four values, find the interquartile range.

  2. Club A has 9 bus users and 3 walkers. Club B has 3 bus users. Given that a student is in Club A, what is the probability they use the bus? Give a simplified fraction.

  3. Find the median of 85, 10, 47, 27, 69.

  4. P(A) = 27/32. Find P(not A).

  5. A bag has 14 red and 11 blue counters. Draw twice, replacing the first counter. What is the probability both are red? Give a simplified fraction.

  6. A score of 15 occurs 7 times; a score of 11 occurs 10 times. Find the mean as a fraction or decimal.

  7. Find the mean of 36, 15, 14, 25.

  8. Data: 4, 10, 16, 22, 28, 34, 40, 46. Using medians of the lower four and upper four values, find the interquartile range.

  9. Club A has 17 bus users and 5 walkers. Club B has 9 bus users. Given that a student is in Club A, what is the probability they use the bus? Give a simplified fraction.

  10. Find the median of 27, 62, 74, 6, 64.

  11. P(A) = 5/13. Find P(not A).

  12. A bag has 14 red and 15 blue counters. Draw twice, replacing the first counter. What is the probability both are red? Give a simplified fraction.

Answer key
  1. 24 Q₁ = 23; Q₃ = 47; IQR = 24
  2. 3/4 9/(9 + 3) = 3/4
  3. 47 10 ≤ 27 ≤ 47 ≤ 69 ≤ 85 → 47
  4. 5/32 1 − 27/32 = 5/32
  5. 196/625 14/25 × 14/25 = 196/625
  6. 215/17 (15 × 7 + 11 × 10)/(7 + 10) = 215/17
  7. 22.5 (36 + 15 + 14 + 25) ÷ 4 = 22.5
  8. 24 Q₁ = 13; Q₃ = 37; IQR = 24
  9. 17/22 17/(17 + 5) = 17/22
  10. 62 6 ≤ 27 ≤ 62 ≤ 64 ≤ 74 → 62
  11. 8/13 1 − 5/13 = 8/13
  12. 196/841 14/29 × 14/29 = 196/841
Review worksheet: 12 questions

  1. A score of 13 occurs 7 times; a score of 4 occurs 8 times. Find the mean as a fraction or decimal.

  2. P(A) = 2/6. Find P(not A).

  3. A bag has 7 red and 1 blue counters. Draw twice, replacing the first counter. What is the probability both are red? Give a simplified fraction.

  4. Find the median of 70, 72, 49, 31, 59.

  5. Data: 31, 36, 41, 46, 51, 56, 61, 66. Using medians of the lower four and upper four values, find the interquartile range.

  6. Find the mean of 45, 29, 11, 27.

  7. Club A has 15 bus users and 16 walkers. Club B has 14 bus users. Given that a student is in Club A, what is the probability they use the bus? Give a simplified fraction.

  8. A score of 15 occurs 9 times; a score of 11 occurs 4 times. Find the mean as a fraction or decimal.

  9. P(A) = 10/15. Find P(not A).

  10. A bag has 4 red and 1 blue counters. Draw twice, replacing the first counter. What is the probability both are red? Give a simplified fraction.

  11. Find the median of 95, 8, 12, 40, 71.

  12. Data: 35, 39, 43, 47, 51, 55, 59, 63. Using medians of the lower four and upper four values, find the interquartile range.

Answer key
  1. 41/5 (13 × 7 + 4 × 8)/(7 + 8) = 41/5
  2. 2/3 1 − 2/6 = 2/3
  3. 49/64 7/8 × 7/8 = 49/64
  4. 59 31 ≤ 49 ≤ 59 ≤ 70 ≤ 72 → 59
  5. 20 Q₁ = 38.5; Q₃ = 58.5; IQR = 20
  6. 28 (45 + 29 + 11 + 27) ÷ 4 = 28
  7. 15/31 15/(15 + 16) = 15/31
  8. 179/13 (15 × 9 + 11 × 4)/(9 + 4) = 179/13
  9. 1/3 1 − 10/15 = 1/3
  10. 16/25 4/5 × 4/5 = 16/25
  11. 40 8 ≤ 12 ≤ 40 ≤ 71 ≤ 95 → 40
  12. 16 Q₁ = 41; Q₃ = 57; IQR = 16

Related ready-made worksheets: Grade 9 Statistics & probability worksheet