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Grade 9 Quiz: Integers & Real Numbers — Easy Version 1
Grade 9 · 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
Solving Quadratic Equations Using Square Roots: x2 = 25
Answer: x = -5 or x = 5
Not quite. The answer is
💡 |x + 2| = 7 means x + 2 is 7 units from 0, so x + 2 = 7 or x + 2 = −7. Subtract 2 from both sides: x = 7 − 2 = 5 or x = −7 − 2 = −9. So x = 5 or x = −9.
✓ Correct!
Not quite. The answer is
💡 |x + 2| = 7 means x + 2 is 7 units from 0, so x + 2 = 7 or x + 2 = −7. Subtract 2 from both sides: x = 7 − 2 = 5 or x = −7 − 2 = −9. So x = 5 or x = −9.
💡 How to solve: Absolute Value Equations
An absolute value equals k when the inside equals k or -k. Write two equations, x - h = k and x - h = -k, and solve each one. Write both solutions as x = a or x = b.
Try a similar one
|x - 2| = 3
✓ 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
💡 Subtract 15 from both sides: 5x² = 140 − 15 = 125. Divide both sides by 5: x² = 125 ÷ 5 = 25. Take the square root of both sides, using both the positive and the negative root: x = ±√25 = ±5, because 5 × 5 = 25 and (−5) × (−5) = 25. So x = −5 or x = 5.
✓ Correct!
Not quite. The answer is
💡 Subtract 15 from both sides: 5x² = 140 − 15 = 125. Divide both sides by 5: x² = 125 ÷ 5 = 25. Take the square root of both sides, using both the positive and the negative root: x = ±√25 = ±5, because 5 × 5 = 25 and (−5) × (−5) = 25. So x = −5 or x = 5.
💡 How to solve: Solving Quadratic Equations Using Square Roots
Get the squared expression alone on one side. Then take the square root of both sides, remembering both the positive and the negative root: if x2 = 25, then x = 5 or x = -5. For (x - 3)2 = 16, x - 3 = ±4, so x = 7 or x = -1.
Try a similar one
x2 = 1
✓ 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
💡 |x − 2| < 1 means x − 2 is less than 1 unit from 0, so −1 < x − 2 < 1. Add 2 to all three parts: 1 < x < 3.
✓ Correct!
Not quite. The answer is
💡 |x − 2| < 1 means x − 2 is less than 1 unit from 0, so −1 < x − 2 < 1. Add 2 to all three parts: 1 < x < 3.
💡 How to solve: Absolute Value Inequalities
First isolate the absolute value. If |A| < c, then -c < A < c (an "and" inequality). If |A| > c, then A < -c or A > c (an "or" inequality). Then solve for x.
Try a similar one
|x - 2| < 2
✓ 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
💡 |x + 5| = 1 means x + 5 is 1 unit from 0, so x + 5 = 1 or x + 5 = −1. Subtract 5 from both sides: x = 1 − 5 = −4 or x = −1 − 5 = −6. So x = −4 or x = −6.
✓ Correct!
Not quite. The answer is
💡 |x + 5| = 1 means x + 5 is 1 unit from 0, so x + 5 = 1 or x + 5 = −1. Subtract 5 from both sides: x = 1 − 5 = −4 or x = −1 − 5 = −6. So x = −4 or x = −6.
💡 How to solve: Absolute Value Equations
An absolute value equals k when the inside equals k or -k. Write two equations, x - h = k and x - h = -k, and solve each one. Write both solutions as x = a or x = b.
Try a similar one
|x + 1| = 4
✓ 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
💡 Take the square root of both sides, using both the positive and the negative root: x = ±√16 = ±4, because 4 × 4 = 16 and (−4) × (−4) = 16. So x = −4 or x = 4.
✓ Correct!
Not quite. The answer is
💡 Take the square root of both sides, using both the positive and the negative root: x = ±√16 = ±4, because 4 × 4 = 16 and (−4) × (−4) = 16. So x = −4 or x = 4.
💡 How to solve: Solving Quadratic Equations Using Square Roots
Get the squared expression alone on one side. Then take the square root of both sides, remembering both the positive and the negative root: if x2 = 25, then x = 5 or x = -5. For (x - 3)2 = 16, x - 3 = ±4, so x = 7 or x = -1.
Try a similar one
x2 = 9
✓ 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
💡 |x + 1| > 4 means x + 1 is more than 4 units from 0, so x + 1 < −4 or x + 1 > 4. Subtract 1 from both sides of each part: x < −5 or x > 3.
✓ Correct!
Not quite. The answer is
💡 |x + 1| > 4 means x + 1 is more than 4 units from 0, so x + 1 < −4 or x + 1 > 4. Subtract 1 from both sides of each part: x < −5 or x > 3.
💡 How to solve: Absolute Value Inequalities
First isolate the absolute value. If |A| < c, then -c < A < c (an "and" inequality). If |A| > c, then A < -c or A > c (an "or" inequality). Then solve for x.
Try a similar one
|x + 8| < 6
✓ 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
💡 |x + 1| = 4 means x + 1 is 4 units from 0, so x + 1 = 4 or x + 1 = −4. Subtract 1 from both sides: x = 4 − 1 = 3 or x = −4 − 1 = −5. So x = 3 or x = −5.
✓ Correct!
Not quite. The answer is
💡 |x + 1| = 4 means x + 1 is 4 units from 0, so x + 1 = 4 or x + 1 = −4. Subtract 1 from both sides: x = 4 − 1 = 3 or x = −4 − 1 = −5. So x = 3 or x = −5.
💡 How to solve: Absolute Value Equations
An absolute value equals k when the inside equals k or -k. Write two equations, x - h = k and x - h = -k, and solve each one. Write both solutions as x = a or x = b.
Try a similar one
|x + 2| = 7
✓ 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
💡 Take the square root of both sides, using both the positive and the negative root: x = ±√1 = ±1, because 1 × 1 = 1 and (−1) × (−1) = 1. So x = −1 or x = 1.
✓ Correct!
Not quite. The answer is
💡 Take the square root of both sides, using both the positive and the negative root: x = ±√1 = ±1, because 1 × 1 = 1 and (−1) × (−1) = 1. So x = −1 or x = 1.
💡 How to solve: Solving Quadratic Equations Using Square Roots
Get the squared expression alone on one side. Then take the square root of both sides, remembering both the positive and the negative root: if x2 = 25, then x = 5 or x = -5. For (x - 3)2 = 16, x - 3 = ±4, so x = 7 or x = -1.
Try a similar one
x2 = 16
✓ 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
💡 |x − 4| > 4 means x − 4 is more than 4 units from 0, so x − 4 < −4 or x − 4 > 4. Add 4 to both sides of each part: x < 0 or x > 8.
✓ Correct!
Not quite. The answer is
💡 |x − 4| > 4 means x − 4 is more than 4 units from 0, so x − 4 < −4 or x − 4 > 4. Add 4 to both sides of each part: x < 0 or x > 8.
💡 How to solve: Absolute Value Inequalities
First isolate the absolute value. If |A| < c, then -c < A < c (an "and" inequality). If |A| > c, then A < -c or A > c (an "or" inequality). Then solve for x.
Try a similar one
|x| < 3
✓ 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
💡 |x + 4| = 2 means x + 4 is 2 units from 0, so x + 4 = 2 or x + 4 = −2. Subtract 4 from both sides: x = 2 − 4 = −2 or x = −2 − 4 = −6. So x = −2 or x = −6.
✓ Correct!
Not quite. The answer is
💡 |x + 4| = 2 means x + 4 is 2 units from 0, so x + 4 = 2 or x + 4 = −2. Subtract 4 from both sides: x = 2 − 4 = −2 or x = −2 − 4 = −6. So x = −2 or x = −6.
💡 How to solve: Absolute Value Equations
An absolute value equals k when the inside equals k or -k. Write two equations, x - h = k and x - h = -k, and solve each one. Write both solutions as x = a or x = b.
Try a similar one
|x - 2| = 6
✓ 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 9 Quiz: Integers & Real Numbers — 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.