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Grade 10 Quiz: Ratios & Proportions — Easy Version 1
Grade 10 · 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
Triangle Proportionality & Angle Bisector Theorems: DE ∥ BC. Find x.
Answer: 3
Not quite. The answer is
💡 By the Triangle Proportionality Theorem, DE ∥ BC divides the sides proportionally: AD/DB = AE/EC, so 210 = x15. Cross-multiply: 10x = 2 × 15 = 30. Divide both sides by 10: x = 3.
✓ Correct!
Not quite. The answer is
💡 By the Triangle Proportionality Theorem, DE ∥ BC divides the sides proportionally: AD/DB = AE/EC, so 210 = x15. Cross-multiply: 10x = 2 × 15 = 30. Divide both sides by 10: x = 3.
💡 How to solve: Triangle Proportionality & Angle Bisector Theorems
If DE is parallel to BC, it divides the two sides proportionally: AD/DB = AE/EC. If AD bisects ∠A of △ABC, it divides BC in the ratio of the other two sides: BD/DC = AB/AC. Write the proportion, cross-multiply and solve.
Try a similar one
DE ∥ BC. Find x.
✓ 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 labelled edges are 3 and 9, so the scale factor from smaller to larger is k = 93 = 3. Surface areas grow by the square of the scale factor, k2 = 9. Larger surface area = 4 × 9 = 36.
✓ Correct!
Not quite. The answer is
💡 The labelled edges are 3 and 9, so the scale factor from smaller to larger is k = 93 = 3. Surface areas grow by the square of the scale factor, k2 = 9. Larger surface area = 4 × 9 = 36.
💡 How to solve: Scale Factor: Effect on Area & Volume
If the scale factor of lengths is ab, then the ratio of areas (including surface areas) is a2/b2 and the ratio of volumes is a3/b3. To go backwards, take the square root of an area ratio or the cube root of a volume ratio to get the length ratio. When every dimension is multiplied by k, area is multiplied by k2 and volume by k3.
Try a similar one
Every dimension of a rectangular prism is multiplied by 5. By what number is its surface area multiplied?
✓ 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
💡 By the Triangle Proportionality Theorem, DE ∥ BC divides the sides proportionally: AD/DB = AE/EC, so 13 = x6. Cross-multiply: 3x = 1 × 6 = 6. Divide both sides by 3: x = 2.
✓ Correct!
Not quite. The answer is
💡 By the Triangle Proportionality Theorem, DE ∥ BC divides the sides proportionally: AD/DB = AE/EC, so 13 = x6. Cross-multiply: 3x = 1 × 6 = 6. Divide both sides by 3: x = 2.
💡 How to solve: Triangle Proportionality & Angle Bisector Theorems
If DE is parallel to BC, it divides the two sides proportionally: AD/DB = AE/EC. If AD bisects ∠A of △ABC, it divides BC in the ratio of the other two sides: BD/DC = AB/AC. Write the proportion, cross-multiply and solve.
Try a similar one
DE ∥ BC. Find x.
✓ 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 labelled edges are 1 and 3, so the scale factor from smaller to larger is k = 31 = 3. Volumes grow by the cube of the scale factor, k3 = 27. Larger volume = 4 × 27 = 108.
✓ Correct!
Not quite. The answer is
💡 The labelled edges are 1 and 3, so the scale factor from smaller to larger is k = 31 = 3. Volumes grow by the cube of the scale factor, k3 = 27. Larger volume = 4 × 27 = 108.
💡 How to solve: Scale Factor: Effect on Area & Volume
If the scale factor of lengths is ab, then the ratio of areas (including surface areas) is a2/b2 and the ratio of volumes is a3/b3. To go backwards, take the square root of an area ratio or the cube root of a volume ratio to get the length ratio. When every dimension is multiplied by k, area is multiplied by k2 and volume by k3.
Try a similar one
Every dimension of a rectangular prism is multiplied by 4. By what number is its surface area multiplied?
✓ 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
💡 By the Triangle Angle Bisector Theorem, AD divides BC in the ratio of the other two sides: BD/DC = AB/AC, so 9x = 1216. Cross-multiply: 12x = 9 × 16 = 144. Divide both sides by 12: x = 12.
✓ Correct!
Not quite. The answer is
💡 By the Triangle Angle Bisector Theorem, AD divides BC in the ratio of the other two sides: BD/DC = AB/AC, so 9x = 1216. Cross-multiply: 12x = 9 × 16 = 144. Divide both sides by 12: x = 12.
💡 How to solve: Triangle Proportionality & Angle Bisector Theorems
If DE is parallel to BC, it divides the two sides proportionally: AD/DB = AE/EC. If AD bisects ∠A of △ABC, it divides BC in the ratio of the other two sides: BD/DC = AB/AC. Write the proportion, cross-multiply and solve.
Try a similar one
DE ∥ BC. Find x.
✓ 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 labelled edges are 2 and 3, so the scale factor from smaller to larger is k = 32. Volumes grow by the cube of the scale factor, k3 = 278. Larger volume = 48 × 278 = 162.
✓ Correct!
Not quite. The answer is
💡 The labelled edges are 2 and 3, so the scale factor from smaller to larger is k = 32. Volumes grow by the cube of the scale factor, k3 = 278. Larger volume = 48 × 278 = 162.
💡 How to solve: Scale Factor: Effect on Area & Volume
If the scale factor of lengths is ab, then the ratio of areas (including surface areas) is a2/b2 and the ratio of volumes is a3/b3. To go backwards, take the square root of an area ratio or the cube root of a volume ratio to get the length ratio. When every dimension is multiplied by k, area is multiplied by k2 and volume by k3.
Try a similar one
Every dimension of a rectangular prism is multiplied by 2. By what number is its surface area multiplied?
✓ 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
💡 By the Triangle Angle Bisector Theorem, AD divides BC in the ratio of the other two sides: BD/DC = AB/AC, so x4 = 1512. Cross-multiply: 12x = 4 × 15 = 60. Divide both sides by 12: x = 5.
✓ Correct!
Not quite. The answer is
💡 By the Triangle Angle Bisector Theorem, AD divides BC in the ratio of the other two sides: BD/DC = AB/AC, so x4 = 1512. Cross-multiply: 12x = 4 × 15 = 60. Divide both sides by 12: x = 5.
💡 How to solve: Triangle Proportionality & Angle Bisector Theorems
If DE is parallel to BC, it divides the two sides proportionally: AD/DB = AE/EC. If AD bisects ∠A of △ABC, it divides BC in the ratio of the other two sides: BD/DC = AB/AC. Write the proportion, cross-multiply and solve.
Try a similar one
DE ∥ BC. Find x.
✓ 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 labelled edges are 4 and 6, so the scale factor from smaller to larger is k = 64 = 32. Surface areas grow by the square of the scale factor, k2 = 94. Larger surface area = 24 × 94 = 54.
✓ Correct!
Not quite. The answer is
💡 The labelled edges are 4 and 6, so the scale factor from smaller to larger is k = 64 = 32. Surface areas grow by the square of the scale factor, k2 = 94. Larger surface area = 24 × 94 = 54.
💡 How to solve: Scale Factor: Effect on Area & Volume
If the scale factor of lengths is ab, then the ratio of areas (including surface areas) is a2/b2 and the ratio of volumes is a3/b3. To go backwards, take the square root of an area ratio or the cube root of a volume ratio to get the length ratio. When every dimension is multiplied by k, area is multiplied by k2 and volume by k3.
Try a similar one
Every dimension of a rectangular prism is multiplied by 3. By what number is its surface area multiplied?
✓ 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
💡 By the Triangle Proportionality Theorem, DE ∥ BC divides the sides proportionally: AD/DB = AE/EC, so 4x = 82. Cross-multiply: 8x = 4 × 2 = 8. Divide both sides by 8: x = 1.
✓ Correct!
Not quite. The answer is
💡 By the Triangle Proportionality Theorem, DE ∥ BC divides the sides proportionally: AD/DB = AE/EC, so 4x = 82. Cross-multiply: 8x = 4 × 2 = 8. Divide both sides by 8: x = 1.
💡 How to solve: Triangle Proportionality & Angle Bisector Theorems
If DE is parallel to BC, it divides the two sides proportionally: AD/DB = AE/EC. If AD bisects ∠A of △ABC, it divides BC in the ratio of the other two sides: BD/DC = AB/AC. Write the proportion, cross-multiply and solve.
Try a similar one
DE ∥ BC. Find x.
✓ 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 scale factor is 2. Volume grows by the cube of the scale factor: 23 = 2 × 2 × 2 = 8. The volume is multiplied by 8.
✓ Correct!
Not quite. The answer is
💡 The scale factor is 2. Volume grows by the cube of the scale factor: 23 = 2 × 2 × 2 = 8. The volume is multiplied by 8.
💡 How to solve: Scale Factor: Effect on Area & Volume
If the scale factor of lengths is ab, then the ratio of areas (including surface areas) is a2/b2 and the ratio of volumes is a3/b3. To go backwards, take the square root of an area ratio or the cube root of a volume ratio to get the length ratio. When every dimension is multiplied by k, area is multiplied by k2 and volume by k3.
Try a similar one
Every dimension of a rectangular prism is multiplied by 5. By what number is its surface area multiplied?
✓ 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 10 Quiz: Ratios & Proportions — Easy Version 1
Answer every question. The lesson name before each question tells you which skill it checks — open that lesson if you need a reminder.