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Grade 10 · Maths · curriculum collection

Grade 10 Maths, Common Core conceptual categories

8 units for Grade 10 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

Equations with the unknown on both sides 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: 11x + 7 = 3x + 95.

  2. Solve for x: x + y = 15 and x − y = 5.

  3. Solve: 14x + 4 = 2x + 76.

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

  5. Solve: 14x + 9 = 4x + 99.

  6. Solve for x: x + y = 58 and x − y = 22.

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

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

  9. Solve: 9x + 9 = 3x + 81.

  10. Solve for x: x + y = 33 and x − y = 25.

  11. Solve: 6x + 14 = 3x + 53.

  12. Solve for x: x + y = 31 and x − y = 29.

Answer key
  1. 11 8x = 88 → x = 11
  2. 10 2x = 20 → x = 10
  3. 6 12x = 72 → x = 6
  4. 18 2x = 36 → x = 18
  5. 9 10x = 90 → x = 9
  6. 40 2x = 80 → x = 40
  7. 2 3x = 6 → x = 2
  8. 7 2x = 14 → x = 7
  9. 12 6x = 72 → x = 12
  10. 29 2x = 58 → x = 29
  11. 13 3x = 39 → x = 13
  12. 30 2x = 60 → x = 30
Review worksheet: 12 questions

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

  2. Solve: 10x + 5 = 3x + 61.

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

  4. Solve: 8x + 10 = 4x + 46.

  5. Solve for x: x + y = 45 and x − y = 33.

  6. Solve: 10x + 19 = 2x + 83.

  7. Solve for x: x + y = 17 and x − y = 3.

  8. Solve: 9x + 6 = 1x + 14.

  9. Solve for x: x + y = 28 and x − y = 0.

  10. Solve: 12x + 5 = 2x + 25.

  11. Solve for x: x + y = 25 and x − y = 1.

  12. Solve: 13x + 19 = 3x + 49.

Answer key
  1. 34 2x = 68 → x = 34
  2. 8 7x = 56 → x = 8
  3. 8 2x = 16 → x = 8
  4. 9 4x = 36 → x = 9
  5. 39 2x = 78 → x = 39
  6. 8 8x = 64 → x = 8
  7. 10 2x = 20 → x = 10
  8. 1 8x = 8 → x = 1
  9. 14 2x = 28 → x = 14
  10. 2 10x = 20 → x = 2
  11. 13 2x = 26 → x = 13
  12. 3 10x = 30 → x = 3

Related ready-made worksheets: Grade 10 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 smaller root of (x − 20)(x − 21) = 0.

  2. Expand (12x + 14)². What is the coefficient of x?

  3. Complete x² + 78x + □ = (x + 39)².

  4. Find the discriminant of 8x² + 2x + 19 = 0.

  5. Find the smaller root of (x − 24)(x − 29) = 0.

  6. Expand (11x + 7)². What is the coefficient of x?

  7. Complete x² + 36x + □ = (x + 18)².

  8. Find the discriminant of 6x² + 16x + 11 = 0.

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

  10. Expand (7x + 21)². What is the coefficient of x?

  11. Complete x² + 64x + □ = (x + 32)².

  12. Find the discriminant of 1x² + 8x + 7 = 0.

Answer key
  1. 20 x = 20 or x = 21; 20 < 21
  2. 336 2 × 12 × 14 = 336
  3. 1521 (78 ÷ 2)² = 1521
  4. -604 2² − 4 × 8 × 19 = -604
  5. 24 x = 24 or x = 29; 24 < 29
  6. 154 2 × 11 × 7 = 154
  7. 324 (36 ÷ 2)² = 324
  8. -8 16² − 4 × 6 × 11 = -8
  9. 6 x = 6 or x = 20; 6 < 20
  10. 294 2 × 7 × 21 = 294
  11. 1024 (64 ÷ 2)² = 1024
  12. 36 8² − 4 × 1 × 7 = 36
Review worksheet: 12 questions

  1. Find the smaller root of (x − 23)(x − 38) = 0.

  2. Find the discriminant of 1x² + 13x + 1 = 0.

  3. Expand (4x + 28)². What is the coefficient of x?

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

  5. Find the smaller root of (x − 23)(x − 31) = 0.

  6. Find the discriminant of 1x² + 4x + 12 = 0.

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

  8. Complete x² + 26x + □ = (x + 13)².

  9. Find the smaller root of (x − 25)(x − 28) = 0.

  10. Find the discriminant of 2x² + 1x + 6 = 0.

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

  12. Complete x² + 60x + □ = (x + 30)².

Answer key
  1. 23 x = 23 or x = 38; 23 < 38
  2. 165 13² − 4 × 1 × 1 = 165
  3. 224 2 × 4 × 28 = 224
  4. 1156 (68 ÷ 2)² = 1156
  5. 23 x = 23 or x = 31; 23 < 31
  6. -32 4² − 4 × 1 × 12 = -32
  7. 552 2 × 12 × 23 = 552
  8. 169 (26 ÷ 2)² = 169
  9. 25 x = 25 or x = 28; 25 < 28
  10. -47 1² − 4 × 2 × 6 = -47
  11. 36 2 × 2 × 9 = 36
  12. 900 (60 ÷ 2)² = 900

Related ready-made worksheets: Grade 10 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 7 terms of a geometric sequence with first term 1 and ratio 5.

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

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

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

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

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

  7. Find the sum of the first 7 terms of a geometric sequence with first term 2 and ratio 4.

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

  9. Find the sum of the first 6 terms of a geometric sequence with first term 1 and ratio 5.

  10. Find the sum of the first 6 terms of a geometric sequence with first term 11 and ratio 4.

  11. Find the sum of the first 7 terms of a geometric sequence with first term 10 and ratio 3.

  12. Find the sum of the first 7 terms of a geometric sequence with first term 10 and ratio 2.

Answer key
  1. 19531 1 × (5^7 − 1) ÷ (5 − 1) = 19531
  2. 16380 12 × (4^6 − 1) ÷ (4 − 1) = 16380
  3. 165 11 × (2^4 − 1) ÷ (2 − 1) = 165
  4. 14 2 × (2^3 − 1) ÷ (2 − 1) = 14
  5. 147 7 × (4^3 − 1) ÷ (4 − 1) = 147
  6. 97655 5 × (5^7 − 1) ÷ (5 − 1) = 97655
  7. 10922 2 × (4^7 − 1) ÷ (4 − 1) = 10922
  8. 75 5 × (2^4 − 1) ÷ (2 − 1) = 75
  9. 3906 1 × (5^6 − 1) ÷ (5 − 1) = 3906
  10. 15015 11 × (4^6 − 1) ÷ (4 − 1) = 15015
  11. 10930 10 × (3^7 − 1) ÷ (3 − 1) = 10930
  12. 1270 10 × (2^7 − 1) ÷ (2 − 1) = 1270
Review worksheet: 12 questions

  1. Find the sum of the first 3 terms of a geometric sequence with first term 11 and ratio 4.

  2. Find the sum of the first 6 terms of a geometric sequence with first term 1 and ratio 4.

  3. Find the sum of the first 4 terms of a geometric sequence with first term 6 and ratio 5.

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

  5. Find the sum of the first 6 terms of a geometric sequence with first term 13 and ratio 4.

  6. Find the sum of the first 4 terms of a geometric sequence with first term 12 and ratio 2.

  7. Find the sum of the first 7 terms of a geometric sequence with first term 12 and ratio 3.

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

  9. Find the sum of the first 5 terms of a geometric sequence with first term 8 and ratio 2.

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

  11. Find the sum of the first 7 terms of a geometric sequence with first term 14 and ratio 2.

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

Answer key
  1. 231 11 × (4^3 − 1) ÷ (4 − 1) = 231
  2. 1365 1 × (4^6 − 1) ÷ (4 − 1) = 1365
  3. 936 6 × (5^4 − 1) ÷ (5 − 1) = 936
  4. 16383 3 × (4^7 − 1) ÷ (4 − 1) = 16383
  5. 17745 13 × (4^6 − 1) ÷ (4 − 1) = 17745
  6. 180 12 × (2^4 − 1) ÷ (2 − 1) = 180
  7. 13116 12 × (3^7 − 1) ÷ (3 − 1) = 13116
  8. 5467 7 × (5^5 − 1) ÷ (5 − 1) = 5467
  9. 248 8 × (2^5 − 1) ÷ (2 − 1) = 248
  10. 2184 6 × (3^6 − 1) ÷ (3 − 1) = 2184
  11. 1778 14 × (2^7 − 1) ÷ (2 − 1) = 1778
  12. 169 13 × (3^3 − 1) ÷ (3 − 1) = 169

Related ready-made worksheets: Grade 10 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) = 7t + (1); g(t) = 1t + (5). Find f(g(4)).

  2. f(x) = 14x + (-6). Find f⁻¹(330).

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

  4. f(x) = 9x + (24). Find f⁻¹(-30).

  5. f(t) = 5t + (-8); g(t) = 6t + (4). Find f(g(8)).

  6. f(x) = 5x + (-20). Find f⁻¹(95).

  7. f(t) = 8t + (10); g(t) = 3t + (-2). Find f(g(3)).

  8. f(x) = 8x + (-17). Find f⁻¹(79).

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

  10. f(x) = 10x + (18). Find f⁻¹(218).

  11. f(t) = 3t + (-9); g(t) = 1t + (-3). Find f(g(6)).

  12. f(x) = 9x + (22). Find f⁻¹(-5).

Answer key
  1. 64 g(4) = 9; f(9) = 64
  2. 24 (330 − (-6)) ÷ 14 = 24
  3. 142 g(4) = 27; f(27) = 142
  4. -6 (-30 − (24)) ÷ 9 = -6
  5. 252 g(8) = 52; f(52) = 252
  6. 23 (95 − (-20)) ÷ 5 = 23
  7. 66 g(3) = 7; f(7) = 66
  8. 12 (79 − (-17)) ÷ 8 = 12
  9. -4 g(-5) = 0; f(0) = -4
  10. 20 (218 − (18)) ÷ 10 = 20
  11. 0 g(6) = 3; f(3) = 0
  12. -3 (-5 − (22)) ÷ 9 = -3
Review worksheet: 12 questions

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

  2. f(x) = 6x + (20). Find f⁻¹(-4).

  3. f(t) = 9t + (7); g(t) = 5t + (-5). Find f(g(3)).

  4. f(x) = 9x + (-2). Find f⁻¹(7).

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

  6. f(x) = 9x + (30). Find f⁻¹(57).

  7. f(t) = 3t + (-10); g(t) = 1t + (-4). Find f(g(4)).

  8. f(x) = 11x + (0). Find f⁻¹(253).

  9. f(t) = 4t + (10); g(t) = 4t + (-6). Find f(g(5)).

  10. f(x) = 12x + (28). Find f⁻¹(376).

  11. f(t) = 5t + (-4); g(t) = 6t + (-5). Find f(g(-5)).

  12. f(x) = 8x + (22). Find f⁻¹(126).

Answer key
  1. -42 g(-4) = -13; f(-13) = -42
  2. -4 (-4 − (20)) ÷ 6 = -4
  3. 97 g(3) = 10; f(10) = 97
  4. 1 (7 − (-2)) ÷ 9 = 1
  5. -28 g(-4) = -5; f(-5) = -28
  6. 3 (57 − (30)) ÷ 9 = 3
  7. -10 g(4) = 0; f(0) = -10
  8. 23 (253 − (0)) ÷ 11 = 23
  9. 66 g(5) = 14; f(14) = 66
  10. 29 (376 − (28)) ÷ 12 = 29
  11. -179 g(-5) = -35; f(-35) = -179
  12. 13 (126 − (22)) ÷ 8 = 13

Related ready-made worksheets: Grade 10 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. Find f(-2) if f(x) = 6x² + 1x + 6.

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

  3. Find f(-4) if f(x) = 2x² + 10x + 9.

  4. The graph y = 10x² + 27x + 10 has axis x = k. Find k.

  5. Find f(-3) if f(x) = 5x² + 1x + 7.

  6. The graph y = 3x² + 25x + 3 has axis x = k. Find k.

  7. Find f(7) if f(x) = 3x² + 2x + 14.

  8. The graph y = 9x² + 8x + 12 has axis x = k. Find k.

  9. Find f(3) if f(x) = 6x² + 9x + 7.

  10. The graph y = 8x² + 21x + 18 has axis x = k. Find k.

  11. Find f(7) if f(x) = 2x² + 8x + 6.

  12. The graph y = 10x² + 24x + 14 has axis x = k. Find k.

Answer key
  1. 28 6 × (-2)² + 1 × (-2) + 6 = 28
  2. -3/4 k = −3/(2 × 2) = -3/4
  3. 1 2 × (-4)² + 10 × (-4) + 9 = 1
  4. -27/20 k = −27/(2 × 10) = -27/20
  5. 49 5 × (-3)² + 1 × (-3) + 7 = 49
  6. -25/6 k = −25/(2 × 3) = -25/6
  7. 175 3 × (7)² + 2 × (7) + 14 = 175
  8. -4/9 k = −8/(2 × 9) = -4/9
  9. 88 6 × (3)² + 9 × (3) + 7 = 88
  10. -21/16 k = −21/(2 × 8) = -21/16
  11. 160 2 × (7)² + 8 × (7) + 6 = 160
  12. -6/5 k = −24/(2 × 10) = -6/5
Review worksheet: 12 questions

  1. Find f(-7) if f(x) = 6x² + 3x + 14.

  2. The graph y = 1x² + 20x + 13 has axis x = k. Find k.

  3. Find f(6) if f(x) = 5x² + 5x + 8.

  4. The graph y = 2x² + 5x + 8 has axis x = k. Find k.

  5. Find f(-4) if f(x) = 3x² + 7x + 11.

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

  7. Find f(-5) if f(x) = 6x² + 6x + 6.

  8. The graph y = 2x² + 20x + 15 has axis x = k. Find k.

  9. Find f(6) if f(x) = 1x² + 7x + 9.

  10. The graph y = 8x² + 34x + 10 has axis x = k. Find k.

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

  12. The graph y = 5x² + 10x + 18 has axis x = k. Find k.

Answer key
  1. 287 6 × (-7)² + 3 × (-7) + 14 = 287
  2. -10 k = −20/(2 × 1) = -10
  3. 218 5 × (6)² + 5 × (6) + 8 = 218
  4. -5/4 k = −5/(2 × 2) = -5/4
  5. 31 3 × (-4)² + 7 × (-4) + 11 = 31
  6. -1/14 k = −1/(2 × 7) = -1/14
  7. 126 6 × (-5)² + 6 × (-5) + 6 = 126
  8. -5 k = −20/(2 × 2) = -5
  9. 87 1 × (6)² + 7 × (6) + 9 = 87
  10. -17/8 k = −34/(2 × 8) = -17/8
  11. 2 2 × (0)² + 11 × (0) + 2 = 2
  12. -1 k = −10/(2 × 5) = -1

Related ready-made worksheets: Grade 10 Quadratic equations worksheet

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

  2. Find only the x-coordinate of the midpoint of (5, 15) and (-11, -13).

  3. Rotate (-14, -20) 90° counterclockwise about the origin. Give the new x-coordinate.

  4. Find only the x-coordinate of the midpoint of (-5, 18) and (-24, -14).

  5. Rotate (18, -23) 90° counterclockwise about the origin. Give the new x-coordinate.

  6. Find only the x-coordinate of the midpoint of (27, 4) and (-4, -4).

  7. Rotate (0, 10) 90° counterclockwise about the origin. Give the new x-coordinate.

  8. Find only the x-coordinate of the midpoint of (15, -7) and (-11, 10).

  9. Rotate (-26, -2) 90° counterclockwise about the origin. Give the new x-coordinate.

  10. Find only the x-coordinate of the midpoint of (27, 19) and (12, 5).

  11. Rotate (-20, -22) 90° counterclockwise about the origin. Give the new x-coordinate.

  12. Find only the x-coordinate of the midpoint of (25, -1) and (24, 7).

Answer key
  1. 27 (3, -27) → (27, 3)
  2. -3 (5 + (-11))/2 = -3
  3. 20 (-14, -20) → (20, -14)
  4. -14.5 (-5 + (-24))/2 = -14.5
  5. 23 (18, -23) → (23, 18)
  6. 11.5 (27 + (-4))/2 = 11.5
  7. -10 (0, 10) → (-10, 0)
  8. 2 (15 + (-11))/2 = 2
  9. 2 (-26, -2) → (2, -26)
  10. 19.5 (27 + (12))/2 = 19.5
  11. 22 (-20, -22) → (22, -20)
  12. 24.5 (25 + (24))/2 = 24.5
Review worksheet: 12 questions

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

  2. Find only the x-coordinate of the midpoint of (-5, -17) and (-26, 10).

  3. Rotate (1, -29) 90° counterclockwise about the origin. Give the new x-coordinate.

  4. Find only the x-coordinate of the midpoint of (-8, -15) and (-4, -9).

  5. Rotate (-9, -14) 90° counterclockwise about the origin. Give the new x-coordinate.

  6. Find only the x-coordinate of the midpoint of (19, 3) and (18, -8).

  7. Rotate (9, -29) 90° counterclockwise about the origin. Give the new x-coordinate.

  8. Find only the x-coordinate of the midpoint of (3, 19) and (2, -20).

  9. Rotate (23, 27) 90° counterclockwise about the origin. Give the new x-coordinate.

  10. Find only the x-coordinate of the midpoint of (30, 0) and (-18, -20).

  11. Rotate (22, -6) 90° counterclockwise about the origin. Give the new x-coordinate.

  12. Find only the x-coordinate of the midpoint of (6, -10) and (27, 6).

Answer key
  1. -22 (-22, 22) → (-22, -22)
  2. -15.5 (-5 + (-26))/2 = -15.5
  3. 29 (1, -29) → (29, 1)
  4. -6 (-8 + (-4))/2 = -6
  5. 14 (-9, -14) → (14, -9)
  6. 18.5 (19 + (18))/2 = 18.5
  7. 29 (9, -29) → (29, 9)
  8. 2.5 (3 + (2))/2 = 2.5
  9. -27 (23, 27) → (-27, 23)
  10. 6 (30 + (-18))/2 = 6
  11. 6 (22, -6) → (6, 22)
  12. 16.5 (6 + (27))/2 = 16.5

Related ready-made worksheets: Grade 10 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 cylinder has radius 1 cm and height 30 cm. Its volume is kπ cm³. Find k.

  2. A right triangle has legs 72 cm and 96 cm. Find the hypotenuse in cm.

  3. A cone has radius 8 cm and height 72 cm. Use π = 3.14. Find its volume in cm³.

  4. A cylinder has radius 17 cm and height 19 cm. Its volume is kπ cm³. Find k.

  5. A right triangle has legs 88 cm and 165 cm. Find the hypotenuse in cm.

  6. A cone has radius 22 cm and height 87 cm. Use π = 3.14. Find its volume in cm³.

  7. A cylinder has radius 24 cm and height 40 cm. Its volume is kπ cm³. Find k.

  8. A right triangle has legs 168 cm and 576 cm. Find the hypotenuse in cm.

  9. A cone has radius 18 cm and height 48 cm. Use π = 3.14. Find its volume in cm³.

  10. A cylinder has radius 20 cm and height 34 cm. Its volume is kπ cm³. Find k.

  11. A right triangle has legs 75 cm and 180 cm. Find the hypotenuse in cm.

  12. A cone has radius 8 cm and height 63 cm. Use π = 3.14. Find its volume in cm³.

Answer key
  1. 30 V = π × 1² × 30 = 30π
  2. 120 cm √(72² + 96²) = √14400 = 120
  3. 4823.04 cm³ 3.14 × 8² × 72 ÷ 3 = 4823.04
  4. 5491 V = π × 17² × 19 = 5491π
  5. 187 cm √(88² + 165²) = √34969 = 187
  6. 44073.04 cm³ 3.14 × 22² × 87 ÷ 3 = 44073.04
  7. 23040 V = π × 24² × 40 = 23040π
  8. 600 cm √(168² + 576²) = √360000 = 600
  9. 16277.76 cm³ 3.14 × 18² × 48 ÷ 3 = 16277.76
  10. 13600 V = π × 20² × 34 = 13600π
  11. 195 cm √(75² + 180²) = √38025 = 195
  12. 4220.16 cm³ 3.14 × 8² × 63 ÷ 3 = 4220.16
Review worksheet: 12 questions

  1. A cylinder has radius 7 cm and height 5 cm. Its volume is kπ cm³. Find k.

  2. A cone has radius 16 cm and height 15 cm. Use π = 3.14. Find its volume in cm³.

  3. A right triangle has legs 192 cm and 360 cm. Find the hypotenuse in cm.

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

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

  6. A right triangle has legs 42 cm and 144 cm. Find the hypotenuse in cm.

  7. A cylinder has radius 22 cm and height 14 cm. Its volume is kπ cm³. Find k.

  8. A cone has radius 15 cm and height 21 cm. Use π = 3.14. Find its volume in cm³.

  9. A right triangle has legs 224 cm and 420 cm. Find the hypotenuse in cm.

  10. A cylinder has radius 25 cm and height 32 cm. Its volume is kπ cm³. Find k.

  11. A cone has radius 24 cm and height 90 cm. Use π = 3.14. Find its volume in cm³.

  12. A right triangle has legs 18 cm and 24 cm. Find the hypotenuse in cm.

Answer key
  1. 245 V = π × 7² × 5 = 245π
  2. 4019.2 cm³ 3.14 × 16² × 15 ÷ 3 = 4019.2
  3. 408 cm √(192² + 360²) = √166464 = 408
  4. 275 V = π × 5² × 11 = 275π
  5. 226.08 cm³ 3.14 × 6² × 6 ÷ 3 = 226.08
  6. 150 cm √(42² + 144²) = √22500 = 150
  7. 6776 V = π × 22² × 14 = 6776π
  8. 4945.5 cm³ 3.14 × 15² × 21 ÷ 3 = 4945.5
  9. 476 cm √(224² + 420²) = √226576 = 476
  10. 20000 V = π × 25² × 32 = 20000π
  11. 54259.2 cm³ 3.14 × 24² × 90 ÷ 3 = 54259.2
  12. 30 cm √(18² + 24²) = √900 = 30

Related ready-made worksheets: Grade 10 Geometry worksheet

08

HS.S Statistics and Probability

Statistics & probability

The mean of a frequency table, conditional probability from a table, variance, probability of an event not happening, interquartile range and probability of two events.

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. Club A has 15 bus users and 11 walkers. Club B has 2 bus users. Given that a student is in Club A, what is the probability they use the bus? Give a simplified fraction.

  2. Data: 38, 43, 48, 53, 58, 63, 68, 73. Using medians of the lower four and upper four values, find the interquartile range.

  3. A score of 9 occurs 5 times; a score of 15 occurs 8 times. Find the mean as a fraction or decimal.

  4. Find the population variance of 41, 42, 43, 44, 45. Divide by 5.

  5. A bag has 12 red and 10 blue counters. Draw twice, replacing the first counter. What is the probability both are red? Give a simplified fraction.

  6. P(A) = 4/6. Find P(not A).

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

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

  9. Club A has 24 bus users and 4 walkers. Club B has 19 bus users. Given that a student is in Club A, what is the probability they use the bus? Give a simplified fraction.

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

  11. A score of 17 occurs 9 times; a score of 4 occurs 3 times. Find the mean as a fraction or decimal.

  12. Find the population variance of 42, 46, 50, 54, 58. Divide by 5.

Answer key
  1. 15/26 15/(15 + 11) = 15/26
  2. 20 Q₁ = 45.5; Q₃ = 65.5; IQR = 20
  3. 165/13 (9 × 5 + 15 × 8)/(5 + 8) = 165/13
  4. 2 μ = 43; (4 + 1 + 0 + 1 + 4)/5 = 2
  5. 36/121 12/22 × 12/22 = 36/121
  6. 1/3 1 − 4/6 = 1/3
  7. 1287 13!/(5! × 8!) = 1287
  8. 360 6!/2! = 360
  9. 6/7 24/(24 + 4) = 6/7
  10. 16 Q₁ = 55; Q₃ = 71; IQR = 16
  11. 55/4 (17 × 9 + 4 × 3)/(9 + 3) = 55/4
  12. 32 μ = 50; (64 + 16 + 0 + 16 + 64)/5 = 32
Review worksheet: 12 questions

  1. Data: 5, 16, 27, 38, 49, 60, 71, 82. Using medians of the lower four and upper four values, find the interquartile range.

  2. Find the population variance of 74, 75, 76, 77, 78. Divide by 5.

  3. A bag has 1 red and 5 blue counters. Draw twice, replacing the first counter. What is the probability both are red? Give a simplified fraction.

  4. P(A) = 19/36. Find P(not A).

  5. A score of 23 occurs 9 times; a score of 19 occurs 8 times. Find the mean as a fraction or decimal.

  6. Club A has 6 bus users and 25 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.

  7. How many different groups of 4 can be chosen from 15 distinct people, if order does not matter?

  8. How many ordered selections of 2 distinct items can be made from 11 items without repetition?

  9. Data: 16, 19, 22, 25, 28, 31, 34, 37. Using medians of the lower four and upper four values, find the interquartile range.

  10. Find the population variance of 38, 39, 40, 41, 42. Divide by 5.

  11. A bag has 8 red and 15 blue counters. Draw twice, replacing the first counter. What is the probability both are red? Give a simplified fraction.

  12. P(A) = 9/20. Find P(not A).

Answer key
  1. 44 Q₁ = 21.5; Q₃ = 65.5; IQR = 44
  2. 2 μ = 76; (4 + 1 + 0 + 1 + 4)/5 = 2
  3. 1/36 1/6 × 1/6 = 1/36
  4. 17/36 1 − 19/36 = 17/36
  5. 359/17 (23 × 9 + 19 × 8)/(9 + 8) = 359/17
  6. 6/31 6/(6 + 25) = 6/31
  7. 1365 15!/(4! × 11!) = 1365
  8. 110 11!/9! = 110
  9. 12 Q₁ = 20.5; Q₃ = 32.5; IQR = 12
  10. 2 μ = 40; (4 + 1 + 0 + 1 + 4)/5 = 2
  11. 64/529 8/23 × 8/23 = 64/529
  12. 11/20 1 − 9/20 = 11/20

Related ready-made worksheets: Grade 10 Statistics & probability worksheet