StudyBrixFree worksheets, study guides and courses

Grade 11 · Maths · curriculum collection

Grade 11 Maths, Common Core conceptual categories

8 units for Grade 11 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
All worksheets (PDF)All answer keys (PDF)Take a diagnostic first

Answer-checked and approved on 29 October 2026

What was checked
  • Every answer is present and well formed: numeric answers parse, choice answers are one of the choices, written questions include a sample answer.
  • Every question is marked correct by the site’s own grader when given its answer, and no wrong choice is marked correct.
  • Every question’s grade range includes the collection’s grade.
  • Every question belongs to its unit’s topic and domain.
  • No question appears twice in a collection.
  • Every worksheet has 10 to 15 questions, and every worksheet and answer key renders.

These checks run automatically on every question before the owner approves a collection. If any question changes, the collection is hidden until it passes the checks and is approved again.

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

Systems of two linear equations.

Short lesson: Simultaneous equations

Study guide for Grades 9 to 11: 2 worked examples and 2 practice questions. Add the equations to eliminate y, then solve for x.

x + y = s; x − y = d → x = (s + d)/2

Add the equations to eliminate y, then solve for x.

Worked example

Solve for x: x + y = 39 and x − y = 11.

2x = 50 → x = 25

Answer: 25

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: x + y = 28 and x − y = -8.

  2. Solve for x: x + y = 21 and x − y = -15.

  3. Solve for x: x + y = 53 and x − y = 15.

  4. Solve for x: x + y = 33 and x − y = 29.

  5. Solve for x: x + y = 40 and x − y = 32.

  6. Solve for x: x + y = 25 and x − y = 21.

  7. Solve for x: x + y = 20 and x − y = 2.

  8. Solve for x: x + y = 41 and x − y = 21.

  9. Solve for x: x + y = 20 and x − y = -12.

  10. Solve for x: x + y = 55 and x − y = 21.

  11. Solve for x: x + y = 13 and x − y = -3.

  12. Solve for x: x + y = 36 and x − y = -2.

Answer key
  1. 10 2x = 20 → x = 10
  2. 3 2x = 6 → x = 3
  3. 34 2x = 68 → x = 34
  4. 31 2x = 62 → x = 31
  5. 36 2x = 72 → x = 36
  6. 23 2x = 46 → x = 23
  7. 11 2x = 22 → x = 11
  8. 31 2x = 62 → x = 31
  9. 4 2x = 8 → x = 4
  10. 38 2x = 76 → x = 38
  11. 5 2x = 10 → x = 5
  12. 17 2x = 34 → x = 17
Review worksheet: 12 questions

  1. Solve for x: x + y = 10 and x − y = -4.

  2. Solve for x: x + y = 30 and x − y = 6.

  3. Solve for x: x + y = 55 and x − y = 19.

  4. Solve for x: x + y = 41 and x − y = 11.

  5. Solve for x: x + y = 5 and x − y = -1.

  6. Solve for x: x + y = 36 and x − y = 22.

  7. Solve for x: x + y = 43 and x − y = 9.

  8. Solve for x: x + y = 43 and x − y = 21.

  9. Solve for x: x + y = 46 and x − y = 22.

  10. Solve for x: x + y = 24 and x − y = -8.

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

  12. Solve for x: x + y = 44 and x − y = 34.

Answer key
  1. 3 2x = 6 → x = 3
  2. 18 2x = 36 → x = 18
  3. 37 2x = 74 → x = 37
  4. 26 2x = 52 → x = 26
  5. 2 2x = 4 → x = 2
  6. 29 2x = 58 → x = 29
  7. 26 2x = 52 → x = 26
  8. 32 2x = 64 → x = 32
  9. 34 2x = 68 → x = 34
  10. 8 2x = 16 → x = 8
  11. 3 2x = 6 → x = 3
  12. 39 2x = 78 → x = 39

Related ready-made worksheets: Grade 11 Algebra worksheet

02

HS.A Algebra

Quadratic expressions and equations

The discriminant, 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. Find the discriminant of 7x² + 12x + 1 = 0.

  2. Find the smaller root of (x − 10)(x − 23) = 0.

  3. Expand (12x + 9)². What is the coefficient of x?

  4. Complete x² + 6x + □ = (x + 3)².

  5. Find the discriminant of 6x² + 8x + 2 = 0.

  6. Find the smaller root of (x − 17)(x − 20) = 0.

  7. Expand (9x + 15)². What is the coefficient of x?

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

  9. Find the discriminant of 5x² + 7x + 2 = 0.

  10. Find the smaller root of (x − 21)(x − 26) = 0.

  11. Expand (11x + 16)². What is the coefficient of x?

  12. Complete x² + 58x + □ = (x + 29)².

Answer key
  1. 116 12² − 4 × 7 × 1 = 116
  2. 10 x = 10 or x = 23; 10 < 23
  3. 216 2 × 12 × 9 = 216
  4. 9 (6 ÷ 2)² = 9
  5. 16 8² − 4 × 6 × 2 = 16
  6. 17 x = 17 or x = 20; 17 < 20
  7. 270 2 × 9 × 15 = 270
  8. 484 (44 ÷ 2)² = 484
  9. 9 7² − 4 × 5 × 2 = 9
  10. 21 x = 21 or x = 26; 21 < 26
  11. 352 2 × 11 × 16 = 352
  12. 841 (58 ÷ 2)² = 841
Review worksheet: 12 questions

  1. Find the discriminant of 8x² + 6x + 11 = 0.

  2. Find the smaller root of (x − 18)(x − 23) = 0.

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

  4. Complete x² + 22x + □ = (x + 11)².

  5. Find the discriminant of 1x² + 11x + 9 = 0.

  6. Find the smaller root of (x − 25)(x − 38) = 0.

  7. Expand (6x + 28)². What is the coefficient of x?

  8. Complete x² + 16x + □ = (x + 8)².

  9. Find the discriminant of 2x² + 19x + 19 = 0.

  10. Find the smaller root of (x − 4)(x − 19) = 0.

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

  12. Complete x² + 2x + □ = (x + 1)².

Answer key
  1. -316 6² − 4 × 8 × 11 = -316
  2. 18 x = 18 or x = 23; 18 < 23
  3. 176 2 × 8 × 11 = 176
  4. 121 (22 ÷ 2)² = 121
  5. 85 11² − 4 × 1 × 9 = 85
  6. 25 x = 25 or x = 38; 25 < 38
  7. 336 2 × 6 × 28 = 336
  8. 64 (16 ÷ 2)² = 64
  9. 209 19² − 4 × 2 × 19 = 209
  10. 4 x = 4 or x = 19; 4 < 19
  11. 288 2 × 6 × 24 = 288
  12. 1 (2 ÷ 2)² = 1

Related ready-made worksheets: Grade 11 Quadratic equations worksheet

03

HS.A Algebra

Geometric series

Sums of geometric series.

Short lesson: Finite geometric sums

Study guide for Grades 10 to 12: 2 worked examples and 2 practice questions. Use n terms, starting with the first term a.

Sₙ = a(rⁿ − 1)/(r − 1), r ≠ 1

Use n terms, starting with the first term a.

Worked example

Find the sum of the first 4 terms of a geometric sequence with first term 4 and ratio 4.

4 × (4^4 − 1) ÷ (4 − 1) = 340

Answer: 340

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 the sum of the first 4 terms of a geometric sequence with first term 4 and ratio 2.

  2. Find the sum of the first 5 terms of a geometric sequence with first term 6 and ratio 5.

  3. Find the sum of the first 3 terms of a geometric sequence with first term 6 and ratio 4.

  4. Find the sum of the first 3 terms of a geometric sequence with first term 12 and ratio 4.

  5. Find the sum of the first 6 terms of a geometric sequence with first term 11 and ratio 3.

  6. Find the sum of the first 6 terms of a geometric sequence with first term 2 and ratio 4.

  7. Find the sum of the first 7 terms of a geometric sequence with first term 7 and ratio 4.

  8. Find the sum of the first 7 terms of a geometric sequence with first term 14 and ratio 3.

  9. Find the sum of the first 3 terms of a geometric sequence with first term 6 and ratio 5.

  10. Find the sum of the first 3 terms of a geometric sequence with first term 12 and ratio 2.

  11. Find the sum of the first 4 terms of a geometric sequence with first term 13 and ratio 2.

  12. Find the sum of the first 6 terms of a geometric sequence with first term 4 and ratio 4.

Answer key
  1. 60 4 × (2^4 − 1) ÷ (2 − 1) = 60
  2. 4686 6 × (5^5 − 1) ÷ (5 − 1) = 4686
  3. 126 6 × (4^3 − 1) ÷ (4 − 1) = 126
  4. 252 12 × (4^3 − 1) ÷ (4 − 1) = 252
  5. 4004 11 × (3^6 − 1) ÷ (3 − 1) = 4004
  6. 2730 2 × (4^6 − 1) ÷ (4 − 1) = 2730
  7. 38227 7 × (4^7 − 1) ÷ (4 − 1) = 38227
  8. 15302 14 × (3^7 − 1) ÷ (3 − 1) = 15302
  9. 186 6 × (5^3 − 1) ÷ (5 − 1) = 186
  10. 84 12 × (2^3 − 1) ÷ (2 − 1) = 84
  11. 195 13 × (2^4 − 1) ÷ (2 − 1) = 195
  12. 5460 4 × (4^6 − 1) ÷ (4 − 1) = 5460
Review worksheet: 12 questions

  1. Find the sum of the first 7 terms of a geometric sequence with first term 10 and ratio 5.

  2. Find the sum of the first 3 terms of a geometric sequence with first term 4 and ratio 5.

  3. Find the sum of the first 5 terms of a geometric sequence with first term 14 and ratio 2.

  4. Find the sum of the first 6 terms of a geometric sequence with first term 2 and ratio 2.

  5. Find the sum of the first 6 terms of a geometric sequence with first term 5 and ratio 5.

  6. Find the sum of the first 6 terms of a geometric sequence with first term 2 and ratio 3.

  7. Find the sum of the first 6 terms of a geometric sequence with first term 4 and ratio 3.

  8. Find the sum of the first 6 terms of a geometric sequence with first term 13 and ratio 2.

  9. Find the sum of the first 5 terms of a geometric sequence with first term 7 and ratio 2.

  10. Find the sum of the first 4 terms of a geometric sequence with first term 15 and ratio 4.

  11. Find the sum of the first 4 terms of a geometric sequence with first term 14 and ratio 5.

  12. Find the sum of the first 5 terms of a geometric sequence with first term 13 and ratio 3.

Answer key
  1. 195310 10 × (5^7 − 1) ÷ (5 − 1) = 195310
  2. 124 4 × (5^3 − 1) ÷ (5 − 1) = 124
  3. 434 14 × (2^5 − 1) ÷ (2 − 1) = 434
  4. 126 2 × (2^6 − 1) ÷ (2 − 1) = 126
  5. 19530 5 × (5^6 − 1) ÷ (5 − 1) = 19530
  6. 728 2 × (3^6 − 1) ÷ (3 − 1) = 728
  7. 1456 4 × (3^6 − 1) ÷ (3 − 1) = 1456
  8. 819 13 × (2^6 − 1) ÷ (2 − 1) = 819
  9. 217 7 × (2^5 − 1) ÷ (2 − 1) = 217
  10. 1275 15 × (4^4 − 1) ÷ (4 − 1) = 1275
  11. 2184 14 × (5^4 − 1) ÷ (5 − 1) = 2184
  12. 1573 13 × (3^5 − 1) ÷ (3 − 1) = 1573

Related ready-made worksheets: Grade 11 Sequences & series worksheet

04

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(t) = 8t + (-5); g(t) = 2t + (-5). Find f(g(6)).

  2. f(x) = 5x + (10). Find f⁻¹(-30).

  3. f(t) = 2t + (6); g(t) = 8t + (-4). Find f(g(-2)).

  4. f(x) = 3x + (12). Find f⁻¹(-21).

  5. f(t) = 6t + (-7); g(t) = 2t + (-1). Find f(g(-3)).

  6. f(x) = 4x + (21). Find f⁻¹(89).

  7. f(t) = 9t + (7); g(t) = 6t + (-8). Find f(g(2)).

  8. f(x) = 3x + (21). Find f⁻¹(57).

  9. f(t) = 8t + (-4); g(t) = 3t + (2). Find f(g(0)).

  10. f(x) = 6x + (20). Find f⁻¹(-4).

  11. f(t) = 3t + (10); g(t) = 7t + (-2). Find f(g(-2)).

  12. f(x) = 10x + (29). Find f⁻¹(279).

Answer key
  1. 51 g(6) = 7; f(7) = 51
  2. -8 (-30 − (10)) ÷ 5 = -8
  3. -34 g(-2) = -20; f(-20) = -34
  4. -11 (-21 − (12)) ÷ 3 = -11
  5. -49 g(-3) = -7; f(-7) = -49
  6. 17 (89 − (21)) ÷ 4 = 17
  7. 43 g(2) = 4; f(4) = 43
  8. 12 (57 − (21)) ÷ 3 = 12
  9. 12 g(0) = 2; f(2) = 12
  10. -4 (-4 − (20)) ÷ 6 = -4
  11. -38 g(-2) = -16; f(-16) = -38
  12. 25 (279 − (29)) ÷ 10 = 25
Review worksheet: 12 questions

  1. f(t) = 5t + (-10); g(t) = 5t + (-3). Find f(g(-5)).

  2. f(x) = 15x + (-16). Find f⁻¹(299).

  3. f(t) = 6t + (1); g(t) = 7t + (-8). Find f(g(3)).

  4. f(x) = 12x + (7). Find f⁻¹(91).

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

  6. f(x) = 10x + (24). Find f⁻¹(-176).

  7. f(t) = 9t + (-3); g(t) = 2t + (-6). Find f(g(2)).

  8. f(x) = 8x + (16). Find f⁻¹(192).

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

  10. f(x) = 2x + (-7). Find f⁻¹(-31).

  11. f(t) = 4t + (0); g(t) = 1t + (-1). Find f(g(0)).

  12. f(x) = 5x + (-16). Find f⁻¹(44).

Answer key
  1. -150 g(-5) = -28; f(-28) = -150
  2. 21 (299 − (-16)) ÷ 15 = 21
  3. 79 g(3) = 13; f(13) = 79
  4. 7 (91 − (7)) ÷ 12 = 7
  5. 315 g(7) = 44; f(44) = 315
  6. -20 (-176 − (24)) ÷ 10 = -20
  7. -21 g(2) = -2; f(-2) = -21
  8. 22 (192 − (16)) ÷ 8 = 22
  9. 56 g(1) = 9; f(9) = 56
  10. -12 (-31 − (-7)) ÷ 2 = -12
  11. -4 g(0) = -1; f(-1) = -4
  12. 12 (44 − (-16)) ÷ 5 = 12

Related ready-made worksheets: Grade 11 Algebra worksheet

05

HS.F Functions

Quadratic functions

The axis of symmetry of a parabola and 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. The graph y = 5x² + 21x + 19 has axis x = k. Find k.

  2. Find f(-1) if f(x) = 5x² + 4x + 7.

  3. The graph y = 6x² + 32x + 6 has axis x = k. Find k.

  4. Find f(7) if f(x) = 3x² + 12x + 12.

  5. The graph y = 9x² + 37x + 19 has axis x = k. Find k.

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

  7. The graph y = 1x² + 18x + 8 has axis x = k. Find k.

  8. Find f(4) if f(x) = 6x² + 12x + 7.

  9. The graph y = 2x² + 6x + 6 has axis x = k. Find k.

  10. Find f(8) if f(x) = 4x² + 11x + 5.

  11. The graph y = 1x² + 21x + 10 has axis x = k. Find k.

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

Answer key
  1. -21/10 k = −21/(2 × 5) = -21/10
  2. 8 5 × (-1)² + 4 × (-1) + 7 = 8
  3. -8/3 k = −32/(2 × 6) = -8/3
  4. 243 3 × (7)² + 12 × (7) + 12 = 243
  5. -37/18 k = −37/(2 × 9) = -37/18
  6. 75 3 × (-6)² + 6 × (-6) + 3 = 75
  7. -9 k = −18/(2 × 1) = -9
  8. 151 6 × (4)² + 12 × (4) + 7 = 151
  9. -3/2 k = −6/(2 × 2) = -3/2
  10. 349 4 × (8)² + 11 × (8) + 5 = 349
  11. -21/2 k = −21/(2 × 1) = -21/2
  12. 9 4 × (0)² + 12 × (0) + 9 = 9
Review worksheet: 12 questions

  1. Find f(-2) if f(x) = 3x² + 12x + 10.

  2. The graph y = 3x² + 35x + 10 has axis x = k. Find k.

  3. Find f(2) if f(x) = 1x² + 9x + 9.

  4. The graph y = 4x² + 32x + 3 has axis x = k. Find k.

  5. Find f(5) if f(x) = 5x² + 12x + 15.

  6. The graph y = 3x² + 39x + 18 has axis x = k. Find k.

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

  8. The graph y = 6x² + 6x + 7 has axis x = k. Find k.

  9. Find f(5) if f(x) = 3x² + 1x + 15.

  10. The graph y = 3x² + 30x + 13 has axis x = k. Find k.

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

  12. The graph y = 8x² + 33x + 3 has axis x = k. Find k.

Answer key
  1. -2 3 × (-2)² + 12 × (-2) + 10 = -2
  2. -35/6 k = −35/(2 × 3) = -35/6
  3. 31 1 × (2)² + 9 × (2) + 9 = 31
  4. -4 k = −32/(2 × 4) = -4
  5. 200 5 × (5)² + 12 × (5) + 15 = 200
  6. -13/2 k = −39/(2 × 3) = -13/2
  7. 46 1 × (4)² + 5 × (4) + 10 = 46
  8. -1/2 k = −6/(2 × 6) = -1/2
  9. 95 3 × (5)² + 1 × (5) + 15 = 95
  10. -5 k = −30/(2 × 3) = -5
  11. 18 1 × (2)² + 2 × (2) + 10 = 18
  12. -33/16 k = −33/(2 × 8) = -33/16

Related ready-made worksheets: Grade 11 Quadratic equations worksheet

06

HS.G Geometry

Geometry

Volume of cones.

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 22 cm and height 45 cm. Use π = 3.14. Find its volume in cm³.

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

  3. A cone has radius 18 cm and height 72 cm. Use π = 3.14. Find its volume in cm³.

  4. A cone has radius 19 cm and height 54 cm. Use π = 3.14. Find its volume in cm³.

  5. A cone has radius 6 cm and height 36 cm. Use π = 3.14. Find its volume in cm³.

  6. A cone has radius 20 cm and height 12 cm. Use π = 3.14. Find its volume in cm³.

  7. A cone has radius 18 cm and height 60 cm. Use π = 3.14. Find its volume in cm³.

  8. A cone has radius 17 cm and height 84 cm. Use π = 3.14. Find its volume in cm³.

  9. A cone has radius 21 cm and height 63 cm. Use π = 3.14. Find its volume in cm³.

  10. A cone has radius 14 cm and height 75 cm. Use π = 3.14. Find its volume in cm³.

  11. A cone has radius 6 cm and height 51 cm. Use π = 3.14. Find its volume in cm³.

  12. A cone has radius 2 cm and height 21 cm. Use π = 3.14. Find its volume in cm³.

Answer key
  1. 22796.4 cm³ 3.14 × 22² × 45 ÷ 3 = 22796.4
  2. 17232.32 cm³ 3.14 × 14² × 84 ÷ 3 = 17232.32
  3. 24416.64 cm³ 3.14 × 18² × 72 ÷ 3 = 24416.64
  4. 20403.72 cm³ 3.14 × 19² × 54 ÷ 3 = 20403.72
  5. 1356.48 cm³ 3.14 × 6² × 36 ÷ 3 = 1356.48
  6. 5024 cm³ 3.14 × 20² × 12 ÷ 3 = 5024
  7. 20347.2 cm³ 3.14 × 18² × 60 ÷ 3 = 20347.2
  8. 25408.88 cm³ 3.14 × 17² × 84 ÷ 3 = 25408.88
  9. 29079.54 cm³ 3.14 × 21² × 63 ÷ 3 = 29079.54
  10. 15386 cm³ 3.14 × 14² × 75 ÷ 3 = 15386
  11. 1921.68 cm³ 3.14 × 6² × 51 ÷ 3 = 1921.68
  12. 87.92 cm³ 3.14 × 2² × 21 ÷ 3 = 87.92
Review worksheet: 12 questions

  1. A cone has radius 23 cm and height 60 cm. Use π = 3.14. Find its volume in cm³.

  2. A cone has radius 19 cm and height 72 cm. Use π = 3.14. Find its volume in cm³.

  3. A cone has radius 18 cm and height 36 cm. Use π = 3.14. Find its volume in cm³.

  4. A cone has radius 2 cm and height 48 cm. Use π = 3.14. Find its volume in cm³.

  5. A cone has radius 25 cm and height 90 cm. Use π = 3.14. Find its volume in cm³.

  6. A cone has radius 20 cm and height 63 cm. Use π = 3.14. Find its volume in cm³.

  7. A cone has radius 4 cm and height 57 cm. Use π = 3.14. Find its volume in cm³.

  8. A cone has radius 25 cm and height 54 cm. Use π = 3.14. Find its volume in cm³.

  9. A cone has radius 23 cm and height 33 cm. Use π = 3.14. Find its volume in cm³.

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

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

  12. A cone has radius 13 cm and height 36 cm. Use π = 3.14. Find its volume in cm³.

Answer key
  1. 33221.2 cm³ 3.14 × 23² × 60 ÷ 3 = 33221.2
  2. 27204.96 cm³ 3.14 × 19² × 72 ÷ 3 = 27204.96
  3. 12208.32 cm³ 3.14 × 18² × 36 ÷ 3 = 12208.32
  4. 200.96 cm³ 3.14 × 2² × 48 ÷ 3 = 200.96
  5. 58875 cm³ 3.14 × 25² × 90 ÷ 3 = 58875
  6. 26376 cm³ 3.14 × 20² × 63 ÷ 3 = 26376
  7. 954.56 cm³ 3.14 × 4² × 57 ÷ 3 = 954.56
  8. 35325 cm³ 3.14 × 25² × 54 ÷ 3 = 35325
  9. 18271.66 cm³ 3.14 × 23² × 33 ÷ 3 = 18271.66
  10. 769.3 cm³ 3.14 × 7² × 15 ÷ 3 = 769.3
  11. 10173.6 cm³ 3.14 × 18² × 30 ÷ 3 = 10173.6
  12. 6367.92 cm³ 3.14 × 13² × 36 ÷ 3 = 6367.92
07

HS.G Geometry

Right-triangle trigonometry

The tangent ratio and the sine ratio.

Short lesson: Sine in a right triangle

Study guide for Grades 9 to 12: 2 worked examples and 2 practice questions. Name the angle first; opposite is the side across from that angle.

sin θ = opposite / hypotenuse

Name the angle first; opposite is the side across from that angle.

Worked example

In a right triangle, the side opposite θ is 165 cm and the hypotenuse is 429 cm. Find sin θ as a fraction.

165/429 = 5/13

Answer: 5/13

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. In a right triangle, the side opposite θ is 144 cm and the hypotenuse is 306 cm. Find sin θ as a fraction.

  2. In a right triangle, the legs opposite and adjacent to θ are 4 cm and 35 cm. Find tan θ as a fraction.

  3. In a right triangle, the side opposite θ is 105 cm and the hypotenuse is 175 cm. Find sin θ as a fraction.

  4. In a right triangle, the legs opposite and adjacent to θ are 27 cm and 34 cm. Find tan θ as a fraction.

  5. In a right triangle, the side opposite θ is 10 cm and the hypotenuse is 26 cm. Find sin θ as a fraction.

  6. In a right triangle, the legs opposite and adjacent to θ are 14 cm and 23 cm. Find tan θ as a fraction.

  7. In a right triangle, the side opposite θ is 75 cm and the hypotenuse is 195 cm. Find sin θ as a fraction.

  8. In a right triangle, the legs opposite and adjacent to θ are 37 cm and 24 cm. Find tan θ as a fraction.

  9. In a right triangle, the side opposite θ is 190 cm and the hypotenuse is 494 cm. Find sin θ as a fraction.

  10. In a right triangle, the legs opposite and adjacent to θ are 40 cm and 27 cm. Find tan θ as a fraction.

  11. In a right triangle, the side opposite θ is 30 cm and the hypotenuse is 78 cm. Find sin θ as a fraction.

  12. In a right triangle, the legs opposite and adjacent to θ are 2 cm and 32 cm. Find tan θ as a fraction.

Answer key
  1. 8/17 144/306 = 8/17
  2. 4/35 4/35 = 4/35
  3. 3/5 105/175 = 3/5
  4. 27/34 27/34 = 27/34
  5. 5/13 10/26 = 5/13
  6. 14/23 14/23 = 14/23
  7. 5/13 75/195 = 5/13
  8. 37/24 37/24 = 37/24
  9. 5/13 190/494 = 5/13
  10. 40/27 40/27 = 40/27
  11. 5/13 30/78 = 5/13
  12. 1/16 2/32 = 1/16
Review worksheet: 12 questions

  1. In a right triangle, the legs opposite and adjacent to θ are 7 cm and 34 cm. Find tan θ as a fraction.

  2. In a right triangle, the side opposite θ is 93 cm and the hypotenuse is 155 cm. Find sin θ as a fraction.

  3. In a right triangle, the legs opposite and adjacent to θ are 38 cm and 31 cm. Find tan θ as a fraction.

  4. In a right triangle, the side opposite θ is 51 cm and the hypotenuse is 85 cm. Find sin θ as a fraction.

  5. In a right triangle, the legs opposite and adjacent to θ are 16 cm and 40 cm. Find tan θ as a fraction.

  6. In a right triangle, the side opposite θ is 33 cm and the hypotenuse is 55 cm. Find sin θ as a fraction.

  7. In a right triangle, the legs opposite and adjacent to θ are 16 cm and 30 cm. Find tan θ as a fraction.

  8. In a right triangle, the side opposite θ is 240 cm and the hypotenuse is 510 cm. Find sin θ as a fraction.

  9. In a right triangle, the legs opposite and adjacent to θ are 40 cm and 26 cm. Find tan θ as a fraction.

  10. In a right triangle, the side opposite θ is 96 cm and the hypotenuse is 204 cm. Find sin θ as a fraction.

  11. In a right triangle, the legs opposite and adjacent to θ are 18 cm and 39 cm. Find tan θ as a fraction.

  12. In a right triangle, the side opposite θ is 224 cm and the hypotenuse is 476 cm. Find sin θ as a fraction.

Answer key
  1. 7/34 7/34 = 7/34
  2. 3/5 93/155 = 3/5
  3. 38/31 38/31 = 38/31
  4. 3/5 51/85 = 3/5
  5. 2/5 16/40 = 2/5
  6. 3/5 33/55 = 3/5
  7. 8/15 16/30 = 8/15
  8. 8/17 240/510 = 8/17
  9. 20/13 40/26 = 20/13
  10. 8/17 96/204 = 8/17
  11. 6/13 18/39 = 6/13
  12. 8/17 224/476 = 8/17

Related ready-made worksheets: Grade 11 Trigonometry worksheet

08

HS.S Statistics and Probability

Statistics & probability

The mean of a frequency table, conditional probability from a table, variance, interquartile range, combinations and permutations.

Short lesson: Conditional probability from counts

Study guide for Grades 9 to 12: 2 worked examples and 2 practice questions. Restrict the denominator to the group named in the condition.

P(A | B) = count(A and B) / count(B)

Restrict the denominator to the group named in the condition.

Worked example

Club A has 6 bus users and 19 walkers. Club B has 16 bus users. Given that a student is in Club A, what is the probability they use the bus? Give a simplified fraction.

6/(6 + 19) = 6/25

Answer: 6/25

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 the population variance of 51, 60, 69, 78, 87. Divide by 5.

  2. Club A has 15 bus users and 18 walkers. Club B has 18 bus users. Given that a student is in Club A, what is the probability they use the bus? Give a simplified fraction.

  3. A score of 28 occurs 4 times; a score of 4 occurs 9 times. Find the mean as a fraction or decimal.

  4. Data: 49, 53, 57, 61, 65, 69, 73, 77. Using medians of the lower four and upper four values, find the interquartile range.

  5. How many different groups of 5 can be chosen from 13 distinct people, if order does not matter?

  6. How many ordered selections of 2 distinct items can be made from 10 items without repetition?

  7. Find the population variance of 48, 57, 66, 75, 84. Divide by 5.

  8. Club A has 18 bus users and 16 walkers. Club B has 8 bus users. Given that a student is in Club A, what is the probability they use the bus? Give a simplified fraction.

  9. A score of 10 occurs 7 times; a score of 17 occurs 5 times. Find the mean as a fraction or decimal.

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

  11. How many different groups of 2 can be chosen from 8 distinct people, if order does not matter?

  12. How many ordered selections of 2 distinct items can be made from 8 items without repetition?

Answer key
  1. 162 μ = 69; (324 + 81 + 0 + 81 + 324)/5 = 162
  2. 5/11 15/(15 + 18) = 5/11
  3. 148/13 (28 × 4 + 4 × 9)/(4 + 9) = 148/13
  4. 16 Q₁ = 55; Q₃ = 71; IQR = 16
  5. 1287 13!/(5! × 8!) = 1287
  6. 90 10!/8! = 90
  7. 162 μ = 66; (324 + 81 + 0 + 81 + 324)/5 = 162
  8. 9/17 18/(18 + 16) = 9/17
  9. 155/12 (10 × 7 + 17 × 5)/(7 + 5) = 155/12
  10. 44 Q₁ = 50.5; Q₃ = 94.5; IQR = 44
  11. 28 8!/(2! × 6!) = 28
  12. 56 8!/6! = 56
Review worksheet: 12 questions

  1. Find the population variance of 16, 18, 20, 22, 24. Divide by 5.

  2. A score of 28 occurs 7 times; a score of 29 occurs 2 times. Find the mean as a fraction or decimal.

  3. Club A has 5 bus users and 19 walkers. Club B has 4 bus users. Given that a student is in Club A, what is the probability they use the bus? Give a simplified fraction.

  4. Data: 21, 28, 35, 42, 49, 56, 63, 70. Using medians of the lower four and upper four values, find the interquartile range.

  5. How many different groups of 3 can be chosen from 12 distinct people, if order does not matter?

  6. How many ordered selections of 4 distinct items can be made from 7 items without repetition?

  7. Find the population variance of 29, 34, 39, 44, 49. Divide by 5.

  8. A score of 28 occurs 1 times; a score of 18 occurs 6 times. Find the mean as a fraction or decimal.

  9. Club A has 8 bus users and 12 walkers. Club B has 17 bus users. Given that a student is in Club A, what is the probability they use the bus? Give a simplified fraction.

  10. Data: 34, 40, 46, 52, 58, 64, 70, 76. Using medians of the lower four and upper four values, find the interquartile range.

  11. How many different groups of 2 can be chosen from 11 distinct people, if order does not matter?

  12. How many ordered selections of 3 distinct items can be made from 15 items without repetition?

Answer key
  1. 8 μ = 20; (16 + 4 + 0 + 4 + 16)/5 = 8
  2. 254/9 (28 × 7 + 29 × 2)/(7 + 2) = 254/9
  3. 5/24 5/(5 + 19) = 5/24
  4. 28 Q₁ = 31.5; Q₃ = 59.5; IQR = 28
  5. 220 12!/(3! × 9!) = 220
  6. 840 7!/3! = 840
  7. 50 μ = 39; (100 + 25 + 0 + 25 + 100)/5 = 50
  8. 136/7 (28 × 1 + 18 × 6)/(1 + 6) = 136/7
  9. 2/5 8/(8 + 12) = 2/5
  10. 24 Q₁ = 43; Q₃ = 67; IQR = 24
  11. 55 11!/(2! × 9!) = 55
  12. 2730 15!/12! = 2730

Related ready-made worksheets: Grade 11 Statistics & probability worksheet