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Grade 11 Quiz: Geometry — Easy Version 2
Grade 11 · MathSheets Name: ____________________ Date: __________
Answer every question. The lesson name before each question tells you which skill it checks — open that lesson if you need a reminder.
How to solve
This quiz mixes questions from different lessons, like a real test. Read each question carefully: the lesson name in front tells you what kind of problem it is. Check your answers, then practise the lessons where you made mistakes.
Example
Factoring Sums & Differences of Cubes: Factor: x³ - 8
Answer: (x - 2)(x² + 2x + 4)
Not quite. The answer is
💡 Compare with (x − h)2 + (y − k)2 = r2: (x + 1)2 = (x − (-1))2, so h = -1. y2 = (y − 0)2, so k = 0. The center is (-1, 0).
✓ Correct!
Not quite. The answer is
💡 Compare with (x − h)2 + (y − k)2 = r2: (x + 1)2 = (x − (-1))2, so h = -1. y2 = (y − 0)2, so k = 0. The center is (-1, 0).
💡 How to solve: Equations of Circles
A circle with center (h, k) and radius r has the equation (x - h)2 + (y - k)2 = r2. Watch the signs: (x + 3)2 means h = -3. If the equation is expanded, group the x-terms and the y-terms and complete the square for each one.
Try a similar one
Find the center of the circle (x + 5)² + (y + 4)² = 1. Write it as (h, k).
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Write each term as a cube: x3 is already a cube and 64 = 43. Use the sum of cubes A3 + B3 = (A + B)(A2 − AB + B2) with A = x and B = 4: A2 = x2, AB = 4x and B2 = 16. So the answer is (x + 4)(x2 - 4x + 16).
✓ Correct!
Not quite. The answer is
💡 Write each term as a cube: x3 is already a cube and 64 = 43. Use the sum of cubes A3 + B3 = (A + B)(A2 − AB + B2) with A = x and B = 4: A2 = x2, AB = 4x and B2 = 16. So the answer is (x + 4)(x2 - 4x + 16).
💡 How to solve: Factoring Sums & Differences of Cubes
Use a3 + b3 = (a + b)(a2 - ab + b2) and a3 - b3 = (a - b)(a2 + ab + b2). First take out any common factor, then write each term as a cube, for example 8x3 = (2x)3 and 27 = 33.
Try a similar one
Factor: x³ - 216
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The right side is r2 = 16, so r = √16 = 4.
✓ Correct!
Not quite. The answer is
💡 The right side is r2 = 16, so r = √16 = 4.
💡 How to solve: Equations of Circles
A circle with center (h, k) and radius r has the equation (x - h)2 + (y - k)2 = r2. Watch the signs: (x + 3)2 means h = -3. If the equation is expanded, group the x-terms and the y-terms and complete the square for each one.
Try a similar one
Find the center of the circle x² + (y + 5)² = 1. Write it as (h, k).
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Write each term as a cube: x3 is already a cube and 125 = 53. Use the sum of cubes A3 + B3 = (A + B)(A2 − AB + B2) with A = x and B = 5: A2 = x2, AB = 5x and B2 = 25. So the answer is (x + 5)(x2 - 5x + 25).
✓ Correct!
Not quite. The answer is
💡 Write each term as a cube: x3 is already a cube and 125 = 53. Use the sum of cubes A3 + B3 = (A + B)(A2 − AB + B2) with A = x and B = 5: A2 = x2, AB = 5x and B2 = 25. So the answer is (x + 5)(x2 - 5x + 25).
💡 How to solve: Factoring Sums & Differences of Cubes
Use a3 + b3 = (a + b)(a2 - ab + b2) and a3 - b3 = (a - b)(a2 + ab + b2). First take out any common factor, then write each term as a cube, for example 8x3 = (2x)3 and 27 = 33.
Try a similar one
Factor: x³ - 8
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Compare with (x − h)2 + (y − k)2 = r2: (x − 3)2 gives h = 3. (y − 4)2 gives k = 4. The center is (3, 4).
✓ Correct!
Not quite. The answer is
💡 Compare with (x − h)2 + (y − k)2 = r2: (x − 3)2 gives h = 3. (y − 4)2 gives k = 4. The center is (3, 4).
💡 How to solve: Equations of Circles
A circle with center (h, k) and radius r has the equation (x - h)2 + (y - k)2 = r2. Watch the signs: (x + 3)2 means h = -3. If the equation is expanded, group the x-terms and the y-terms and complete the square for each one.
Try a similar one
Find the center of the circle (x + 2)² + (y - 3)² = 1. Write it as (h, k).
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Write each term as a cube: x3 is already a cube and 8 = 23. Use the sum of cubes A3 + B3 = (A + B)(A2 − AB + B2) with A = x and B = 2: A2 = x2, AB = 2x and B2 = 4. So the answer is (x + 2)(x2 - 2x + 4).
✓ Correct!
Not quite. The answer is
💡 Write each term as a cube: x3 is already a cube and 8 = 23. Use the sum of cubes A3 + B3 = (A + B)(A2 − AB + B2) with A = x and B = 2: A2 = x2, AB = 2x and B2 = 4. So the answer is (x + 2)(x2 - 2x + 4).
💡 How to solve: Factoring Sums & Differences of Cubes
Use a3 + b3 = (a + b)(a2 - ab + b2) and a3 - b3 = (a - b)(a2 + ab + b2). First take out any common factor, then write each term as a cube, for example 8x3 = (2x)3 and 27 = 33.
Try a similar one
Factor: x³ - 27
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Put h = 4, k = -2 and r = 5 into (x − h)2 + (y − k)2 = r2. Then x − 4 stays as it is, y − (-2) = y + 2, and r2 = 52 = 25. So the equation is (x - 4)2 + (y + 2)2 = 25.
✓ Correct!
Not quite. The answer is
💡 Put h = 4, k = -2 and r = 5 into (x − h)2 + (y − k)2 = r2. Then x − 4 stays as it is, y − (-2) = y + 2, and r2 = 52 = 25. So the equation is (x - 4)2 + (y + 2)2 = 25.
💡 How to solve: Equations of Circles
A circle with center (h, k) and radius r has the equation (x - h)2 + (y - k)2 = r2. Watch the signs: (x + 3)2 means h = -3. If the equation is expanded, group the x-terms and the y-terms and complete the square for each one.
Try a similar one
Find the center of the circle (x + 3)² + (y + 3)² = 36. Write it as (h, k).
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Write each term as a cube: x3 is already a cube and 1 = 13. Use the difference of cubes A3 − B3 = (A − B)(A2 + AB + B2) with A = x and B = 1: A2 = x2, AB = x and B2 = 1. So the answer is (x - 1)(x2 + x + 1).
✓ Correct!
Not quite. The answer is
💡 Write each term as a cube: x3 is already a cube and 1 = 13. Use the difference of cubes A3 − B3 = (A − B)(A2 + AB + B2) with A = x and B = 1: A2 = x2, AB = x and B2 = 1. So the answer is (x - 1)(x2 + x + 1).
💡 How to solve: Factoring Sums & Differences of Cubes
Use a3 + b3 = (a + b)(a2 - ab + b2) and a3 - b3 = (a - b)(a2 + ab + b2). First take out any common factor, then write each term as a cube, for example 8x3 = (2x)3 and 27 = 33.
Try a similar one
Factor: x³ - 125
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The marked center is (-1, 2). The circle passes through (2, 2), 3 units to the right of the center, so r = 3. Put h = -1, k = 2 and r = 3 into (x − h)2 + (y − k)2 = r2. Then x − (-1) = x + 1, y − 2 stays as it is, and r2 = 32 = 9. So the equation is (x + 1)2 + (y - 2)2 = 9.
✓ Correct!
Not quite. The answer is
💡 The marked center is (-1, 2). The circle passes through (2, 2), 3 units to the right of the center, so r = 3. Put h = -1, k = 2 and r = 3 into (x − h)2 + (y − k)2 = r2. Then x − (-1) = x + 1, y − 2 stays as it is, and r2 = 32 = 9. So the equation is (x + 1)2 + (y - 2)2 = 9.
💡 How to solve: Equations of Circles
A circle with center (h, k) and radius r has the equation (x - h)2 + (y - k)2 = r2. Watch the signs: (x + 3)2 means h = -3. If the equation is expanded, group the x-terms and the y-terms and complete the square for each one.
Try a similar one
Find the center of the circle (x + 4)² + (y - 2)² = 16. Write it as (h, k).
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Write each term as a cube: x3 is already a cube and 27 = 33. Use the difference of cubes A3 − B3 = (A − B)(A2 + AB + B2) with A = x and B = 3: A2 = x2, AB = 3x and B2 = 9. So the answer is (x - 3)(x2 + 3x + 9).
✓ Correct!
Not quite. The answer is
💡 Write each term as a cube: x3 is already a cube and 27 = 33. Use the difference of cubes A3 − B3 = (A − B)(A2 + AB + B2) with A = x and B = 3: A2 = x2, AB = 3x and B2 = 9. So the answer is (x - 3)(x2 + 3x + 9).
💡 How to solve: Factoring Sums & Differences of Cubes
Use a3 + b3 = (a + b)(a2 - ab + b2) and a3 - b3 = (a - b)(a2 + ab + b2). First take out any common factor, then write each term as a cube, for example 8x3 = (2x)3 and 27 = 33.
Try a similar one
Factor: x³ + 27
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Grade 11 Quiz: Geometry — Easy Version 2
Answer every question. The lesson name before each question tells you which skill it checks — open that lesson if you need a reminder.