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Grade 9 Quiz: Expressions & Equations — Easy Version 2
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
Quadratic Expressions: Expand: (x + 2)(x + 3)
Answer: x² + 5x + 6
Not quite. The answer is
💡 Substitute x = 3 and y = 0 into each inequality. First: −3 − 1 = −4, and 0 > −4 is true. Second: 3 − 2 = 1, and 0 > 1 is false. P must make both true to be a solution, so no.
✓ Correct!
Not quite. The answer is
💡 Substitute x = 3 and y = 0 into each inequality. First: −3 − 1 = −4, and 0 > −4 is true. Second: 3 − 2 = 1, and 0 > 1 is false. P must make both true to be a solution, so no.
💡 How to solve: Systems of Linear Inequalities
A point is a solution of a system only if it makes every inequality true. Substitute its x- and y-values into each inequality and check. On a graph, the solutions are in the region where the shadings overlap; points on a dashed line are not included.
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Is P(1, 7) a solution of the system y > x and y > -x + 1? Answer yes or no.
✓ 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
💡 Find two numbers that multiply to c = 8 and add to b = −6: −2 and −4, because −2 × (−4) = 8 and −2 + (−4) = −6. So the factors are (x − 2)(x − 4). Check with FOIL: (x − 2)(x − 4) = x² − 4x − 2x + 8 = x² − 6x + 8.
✓ Correct!
Not quite. The answer is
💡 Find two numbers that multiply to c = 8 and add to b = −6: −2 and −4, because −2 × (−4) = 8 and −2 + (−4) = −6. So the factors are (x − 2)(x − 4). Check with FOIL: (x − 2)(x − 4) = x² − 4x − 2x + 8 = x² − 6x + 8.
💡 How to solve: Factoring Quadratic Trinomials
Find two numbers that multiply to the constant term and add to the middle coefficient. If the numbers are p and q, write the answer as (x + p)(x + q), using minus signs for negative numbers.
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Factor: x² + 10x + 25
✓ 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
💡 Both terms have √11, so they are like radicals. Combine the numbers in front, the way you combine like terms: 7 + 9 = 16. The answer is 16√11.
✓ Correct!
Not quite. The answer is
💡 Both terms have √11, so they are like radicals. Combine the numbers in front, the way you combine like terms: 7 + 9 = 16. The answer is 16√11.
💡 How to solve: Operations with Radicals
Simplify each radical first (√12 = 2√3). Add or subtract only like radicals, the way you combine like terms: 2√3 + 5√3 = 7√3. To multiply, multiply the numbers outside and the numbers inside: 2√3 · 4√5 = 8√15, then simplify. To rationalize, multiply the top and bottom by the radical in the denominator.
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3√7 + 3√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
💡 Product rule: when you multiply powers of the same base, add the exponents. x7 × x7 = x7+7 = x14. The answer is 14.
✓ Correct!
Not quite. The answer is
💡 Product rule: when you multiply powers of the same base, add the exponents. x7 × x7 = x7+7 = x14. The answer is 14.
💡 How to solve: Exponent Rules
When multiplying powers with the same base, add the exponents: xa × xb = xa+b. When dividing, subtract them: xa ÷ xb = xa-b. For a power of a power, multiply them: (xa)b = xab. Write only the missing exponent.
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x4 × x6 = 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
💡 Coefficients: 15 = 3 × 5 and 24 = 3 × 8. 5 and 8 have no common factor except 1, so the GCF of 15 and 24 is 3. Both terms have x² = x × x, so the GCF of the variable parts is x². So the GCF is 3x².
✓ Correct!
Not quite. The answer is
💡 Coefficients: 15 = 3 × 5 and 24 = 3 × 8. 5 and 8 have no common factor except 1, so the GCF of 15 and 24 is 3. Both terms have x² = x × x, so the GCF of the variable parts is x². So the GCF is 3x².
💡 How to solve: GCF of Monomials
Find the greatest common factor of the coefficients. Then take the variable with the smaller exponent that appears in both terms (x if either term has just x). Write the answer as the number times the variable, like 4x or 3x².
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Find the GCF of 9x and 15x².
✓ 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
💡 Add the like terms. x² terms: 3 + 4 = 7, giving 7x². x terms: 5 + 5 = 10, giving 10x. So the answer is 7x² + 10x.
✓ Correct!
Not quite. The answer is
💡 Add the like terms. x² terms: 3 + 4 = 7, giving 7x². x terms: 5 + 5 = 10, giving 10x. So the answer is 7x² + 10x.
💡 How to solve: Polynomial Operations
For subtraction, first change the sign of every term in the second parentheses. Then combine like terms: add the x² coefficients together and the x coefficients together. Write the answer with the x² term first.
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Simplify: (2x² + 5x) + (5x² + 4x)
✓ 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
💡 Use FOIL. First: 3x × 3x = 9x². Outer: 3x × (−4) = −12x. Inner: 4 × 3x = 12x. Last: 4 × (−4) = −16. The outer and inner terms are opposites, so they cancel. Add them and combine like terms: 9x² − 12x + 12x − 16 = 9x² − 16.
✓ Correct!
Not quite. The answer is
💡 Use FOIL. First: 3x × 3x = 9x². Outer: 3x × (−4) = −12x. Inner: 4 × 3x = 12x. Last: 4 × (−4) = −16. The outer and inner terms are opposites, so they cancel. Add them and combine like terms: 9x² − 12x + 12x − 16 = 9x² − 16.
💡 How to solve: Multiplying Polynomials & Special Products
Multiply every term of the first polynomial by every term of the second, then combine like terms. Special products: (a + b)2 = a2 + 2ab + b2, (a - b)2 = a2 - 2ab + b2, and (a + b)(a - b) = a2 - b2.
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4x(x² + 3x + 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
💡 The graph is shaded to the left of 3 and to the right of 8, so x is less than 3 or greater than 8. Both circles are open, so 3 and 8 are not included: x < 3 or x > 8.
✓ Correct!
Not quite. The answer is
💡 The graph is shaded to the left of 3 and to the right of 8, so x is less than 3 or greater than 8. Both circles are open, so 3 and 8 are not included: x < 3 or x > 8.
💡 How to solve: Compound Inequalities
For an "and" inequality like -3 < 2x + 1 < 7, do the same step to all three parts until x is alone in the middle. For an "or" inequality, solve each part separately and join them with "or". Dividing or multiplying by a negative number flips the inequality signs.
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-5 < 3x - 5 < 19
✓ 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
💡 x² is the square of x and 49 is the square of 7, and the terms are subtracted, so this is a difference of squares. Use A² − B² = (A + B)(A − B) with A = x and B = 7: (x + 7)(x − 7). Check with FOIL: (x + 7)(x − 7) = x² − 7x + 7x − 49 = x² − 49; the middle terms cancel.
✓ Correct!
Not quite. The answer is
💡 x² is the square of x and 49 is the square of 7, and the terms are subtracted, so this is a difference of squares. Use A² − B² = (A + B)(A − B) with A = x and B = 7: (x + 7)(x − 7). Check with FOIL: (x + 7)(x − 7) = x² − 7x + 7x − 49 = x² − 49; the middle terms cancel.
💡 How to solve: Factoring Special Products
Difference of two squares: a2 - b2 = (a + b)(a - b). Perfect-square trinomial: a2 + 2ab + b2 = (a + b)2 and a2 - 2ab + b2 = (a - b)2. Check that the first and last terms are perfect squares and, for a trinomial, that the middle term is 2ab.
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Factor: x² - 36
✓ 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
💡 Find the largest perfect-square factor of 27: 27 = 9 × 3. So √27 = √9 × √3 = 3√3, because √9 = 3. The answer is 3√3.
✓ Correct!
Not quite. The answer is
💡 Find the largest perfect-square factor of 27: 27 = 9 × 3. So √27 = √9 × √3 = 3√3, because √9 = 3. The answer is 3√3.
💡 How to solve: Simplifying Radicals
Find the largest perfect square that divides the number under the radical (4, 9, 16, 25, 36, ...). Rewrite √n as √(square × rest), take the square root of the square outside, and write the answer as a√b.
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Simplify: √40
✓ 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: Expressions & Equations — 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.