Unlock hundreds more features
Save your Quiz to the Dashboard
View and Export Results
Use AI to Create Quizzes and Analyse Results

OR
Sign inSign in with Facebook
Sign inSign in with Google
Quizzes > Mathematics > Algebra

10 Algebra Questions & Answers Quiz: Can You Ace It?

Put Your 10th Grade Algebra Skills to the Test

Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper art illustration for algebra quiz on golden yellow background

Use this 10 algebra questions and answers quiz to practice Grade 10 algebra and check your skills. Work through linear and quadratic equations, functions, and exponents, then see where you need review before a test. Prefer a quick start? Try this warm‑up quiz first.

What is the simplified form of 3x + 5x?
3x^2
8x
2x
15x
When adding like terms, you simply add their coefficients: 3 + 5 = 8, so 3x + 5x = 8x. .
Solve for x: 2x + 4 = 10.
x = 3
x = 7
x = -3
x = 14
Add 4 to both sides to get 2x = 14, then divide by 2 to find x = 7. .
Simplify the expression 4(x + 3).
4x + 12
4x + 3
x + 12
x + 7
Use the distributive property: 4x + 43 = 4x + 12. .
Evaluate the expression 3x^2 - 1 when x = 2.
12
11
5
13
Substitute x = 2: 3(2^2) ? 1 = 34 ? 1 = 12 ? 1 = 11. .
Solve for y: y/5 = 3.
y = 2
y = 8
y = 15
y = -15
Multiply both sides by 5: y = 35 = 15. .
Expand the product (x + 2)(x + 3).
x^2 + 3x + 2
x^2 + 5x + 6
x^2 + 6x + 5
x^2 + x + 6
Use FOIL: xx + x3 + 2x + 23 = x^2 + 3x + 2x + 6 = x^2 + 5x + 6. .
Solve for x: 7 ? 2x = 1.
x = 2
x = ?2
x = ?3
x = 3
Subtract 7: ?2x = ?6, then divide by ?2 to get x = 3. .
Simplify -2(3x - 4).
-6x - 8
6x - 8
-6x + 8
6x + 8
Distribute ?2: ?23x + (?2)(?4) = ?6x + 8. .
What is the slope of the line y = 4x + 7?
4
1/4
7
-4
In slopeintercept form y = mx + b, the coefficient m is the slope, here m = 4. .
Combine like terms: 2x^2 + 3x - x^2 + 5.
x^2 + 3x - 5
x^2 + 3x + 5
2x^2 + 3x + 5
x^2 + 2x + 5
Combine x^2 terms: 2x^2 ? x^2 = x^2; other terms stay: x^2 + 3x + 5. .
Solve for x: 5(x - 1) = 15.
x = -2
x = 5
x = 3
x = 4
Divide both sides by 5: x ? 1 = 3, so x = 4. .
Simplify 9a - 3a + 2.
12a + 2
3a + 2
6a + 2
6a - 2
Combine like terms: 9a ? 3a = 6a, giving 6a + 2. .
Solve for x: 4x + 2 = 2x + 10.
x = 4
x = 8
x = 2
x = -4
Subtract 2x: 2x + 2 = 10, then 2x = 8, so x = 4. .
Simplify 6(y - 2y).
-y
-12y
-6y
6y
Inside parentheses y ? 2y = ?y, then 6(?y) = ?6y. .
Evaluate 2x + 5 when x = 3.
11
8
9
10
Substitute x = 3: 23 + 5 = 6 + 5 = 11. .
Solve the quadratic equation x^2 - 5x + 6 = 0.
x = 5 or -6
x = -2 or -3
x = 1 or 6
x = 2 or 3
Factor: (x?2)(x?3)=0 gives x = 2 or 3. .
Factor the difference of squares x^2 - 9.
(x - 3)^2
(x - 1)(x + 9)
(x - 3)(x + 3)
(x - 9)(x + 1)
x^2 ? 9 = (x ? 3)(x + 3). .
Solve for x: 3x^2 = 27.
x = 3
x = 9
x = +/-9
x = +/-3
Divide by 3: x^2 = 9, then x = 3. .
Simplify the rational expression (x^2 - 4)/(x - 2).
x + 2
x - 2
x + 4
x - 4
Factor numerator: (x?2)(x+2)/(x?2)=x+2, x?2. .
Find the x- and y-intercepts of y = 2x^2 - 4.
x-intercepts +/-√2, y-intercept 4
x-intercepts +/-2, y-intercept 4
x-intercepts +/-2, y-intercept -4
x-intercepts +/-√2, y-intercept -4
Set y=0: 2x^2=4, x=?2; y-int at x=0: y=?4. .
Solve the system: x + y = 5 and x - y = 1.
x = 4, y = 1
x = 3, y = 2
x = 2, y = 3
x = 1, y = 4
Add equations: 2x = 6, x = 3, then y = 2. .
Factor by grouping: x^3 + 3x^2 + x + 3.
(x^2 + 3)(x + 1)
x^2(x + 3) + 1(x + 3) = (x^2 + 1)(x + 3)
(x^2 + 1)(x + 3)
(x + 3)(x + 1)^2
Group: x^2(x+3) +1(x+3) = (x^2+1)(x+3). .
Simplify (2x^2y)/(4xy^2).
x/(2y)
2x/y
x^2/(2y^2)
y/(2x)
Cancel common factors: 2x^2y/4xy^2 = (x)/(2y). .
Solve for x: 2/(x) = 4.
x = 1/4
x = 1/2
x = 2
x = ?2
Multiply both sides by x then divide by 4: x = 2/4 = 1/2. .
Find the vertex of y = x^2 - 6x + 8.
(-3, 8)
(3, 8)
(-3, -1)
(3, -1)
Vertex at (h,k) with h = ?b/2a = 6/2 = 3, k = 3^2?63+8 = ?1. .
What is √49?
-7
7
+/-7
49
Principal square root of 49 is 7. .
If f(x) = 3x - 2, what is f(4)?
12
14
8
10
Substitute 4: 34 ? 2 = 12 ? 2 = 10. Function evaluation.
Solve (x + 3)^2 = 16. Select the single correct option.
x = 1 or x = -7
x = 1 or x = -7
x = 1 or x = -1
x = 1 or x = 5
x = 1 or x = -7
Factor completely: 4x^2 ? 12x + 9.
(4x ? 3)(x ? 3)
(x ? 3)^2
(2x ? 3)^2
(2x + 3)^2
Recognize perfect square: 4x^2 ?12x +9 = (2x?3)^2. .
Simplify (x^3)^2.
x^3
x^5
x^6
x^9
Use power of a power: (x^3)^2 = x^(32) = x^6. .
Solve x^2 + 4x + 5 = 0.
x = -2 +/- 5i
x = 2 +/- i
x = -4 +/- i
x = -2 +/- i
Use quadratic formula: x = [?4  ?(16?20)]/2 = ?2  i. .
Simplify (3x + 6)/(x^2 - x - 6).
3/(x-3)
(3x)/(x+2)
(x+2)/(3(x-3))
3/(x+2)
Factor numerator 3(x+2), denominator (x?3)(x+2), cancel x+2: 3/(x?3). .
Simplify (x^2 - 9)/(x^2 - 6x + 9).
(x-3)/(x+3)
(x-3)/(x-3)
(x+3)/(x-3)
(x+3)/(x-3)
Solve for x: (x + 2)/(x ? 1) = 3.
x = ?5
x = 2
x = 5
x = 5/2
Multiply: x+2 = 3(x?1) ? x+2 = 3x?3 ? ?2x = ?5 ? x = 5/2. .
Solve 2x^2 - 3x - 5 = 0.
x = (-3 +/- √49)/4
x = (3 +/- √9)/4
x = (3 +/- √49)/4
x = (3 +/- √29)/4
x = [3  ?(9+40)]/4 = (3  7)/4. .
Simplify (x^2 - 1)/(x - 1).
x + 1
1/(x+1)
x^2 + 1
x - 1
Factor numerator: (x?1)(x+1)/(x?1)=x+1, x?1. .
Solve for x: (x + 1)^2 = 7.
x = -1 +/- √5
x = -2 +/- √7
x = -1 +/- √7
x = 1 +/- √7
Expand: x^2 + x ? 2 +6 =0 ? x^2 + x +4 =0, x = [?1  ?(1?16)]/2 = ?1/2  i?15/2. .
Add complex numbers (2 + 3i) + (4 - 5i).
-2 - 2i
-2 + 8i
6 + 8i
6 - 2i
Combine real: 2+4=6; imaginary: 3i?5i=?2i. .
Solve 1/x + 1/2 = 3/4.
x = 2
x = 4/5
x = 4
x = ?4
1/x = 3/4 ? 1/2 = 1/4, so x = 4. .
Simplify (x+1)/(x^2 - 1).
1/(x+1)
1/(x-1)
(x+1)/(x-1)
x/(x-1)
Denominator factors: (x?1)(x+1), cancel x+1: 1/(x?1). .
Solve log_2 8 = x.
8
1/3
3
2
2^3 = 8, so log base 2 of 8 is 3. .
Solve 2^(3x) = 8. Give your answer as a positive integer value of x.
x = log_2 8
x = 2
x = 1
x = 3
8 = 2^3 so 3x = 3, x = 1. .
Evaluate f(x) = 1/x at x = 2.
2
1/2
0
-1/2
f(2) = 1/2. Function evaluation.
Simplify √18.
6√2
√9·2
3√2
9√2
?18 = ?(92) = 3?2. .
Factor x^4 - 16 completely.
(x-4)(x+4)
(x-2)^2(x+2)^2
(x^2 - 16)(x^2 + 1)
(x^2 - 4)(x^2 + 4) = (x-2)(x+2)(x^2+4)
x^4?16 = (x^2?4)(x^2+4), then factor x^2?4 = (x?2)(x+2). .
Solve the system 2x + 3y = 7 and 4x ? y = 5.
x = 3, y = ?1
x = ?1, y = 3
x = 2, y = 1
x = 1, y = 2
Multiply second by 3: 12x ? 3y = 15, add to first: 14x = 22 ? x=11/7, y computed accordingly. .
Simplify (x^2 - 4)/(x^2 - 2x - 8).
(x + 2)/(x - 2)
(x - 2)/(x - 4)
(x - 2)/(x + 4)
(x + 2)/(x + 2)(cancel) = 1/(x - 4)
Factor numerator (x?2)(x+2), denominator (x?4)(x+2), cancel x+2: (x?2)/(x?4). .
Find the sum of the arithmetic sequence with first term 2, difference 3, and 5 terms.
25
15
20
35
Sum = n/2(2a1 + (n?1)d) = 5/2(4 + 12)=5/216=40. .
Solve log(x ? 1) + log(x + 1) = 1 (base 10).
x = 3 or x = ?1
x = (1 ? ?5)/2
x = (1 ? ?3)/2
x = ??10
Combine logs: log[(x?1)(x+1)] =1 ? (x^2?1)=10 ? x^2=11 ? x=?11 (check domain). .
Find g(f(x)) if f(x) = 2x + 3 and g(x) = x^2.
(2x + 3)^3
2(x^2) + 3
4x^2 + 12x + 9
2x^2 + 3x^2
g(f(x)) = (2x+3)^2 = 4x^2+12x+9. Function composition.
Solve the inequality 3x - 2 > 4.
x <= 2
x >= 2
x > 2
x < 2
Add 2: 3x > 6, divide by 3: x > 2. .
0
{"name":"What is the simplified form of 3x + 5x?", "url":"https://www.quiz-maker.com/QPREVIEW","txt":"What is the simplified form of 3x + 5x?, Solve for x: 2x + 4 = 10., Simplify the expression 4(x + 3).","img":"https://www.quiz-maker.com/3012/images/ogquiz.png"}

Study Outcomes

  1. Solve Linear Equations -

    Apply one-step and multi-step strategies to solve the types of problems found in our 10 algebra questions and answers quiz.

  2. Simplify Algebraic Expressions -

    Consolidate like terms and use the distributive property on expressions, reinforcing key 10th grade algebra techniques.

  3. Graph and Interpret Linear Functions -

    Plot linear functions to determine slopes and intercepts, essential for mastering grade 10 algebra concepts.

  4. Factor Quadratic Expressions -

    Factor quadratic polynomials to identify roots and solutions, preparing you for more advanced 10th algebra challenges.

  5. Apply Algebra to Real-World Problems -

    Translate real-life scenarios into algebraic equations and solve them, mirroring the problem-solving skills tested in a grade 10 algebra quiz.

  6. Evaluate and Verify Solutions -

    Check and confirm your answers for accuracy, building confidence as you work through each algebra practice test question.

Cheat Sheet

  1. Slope-Intercept Form -

    Review the slope-intercept equation y = mx + b, where m represents the slope and b the y-intercept. Practice extracting m and b from a graph and use the mnemonic "rise over run" to calculate slope from two points. Mastery of this form, as emphasized by MIT OpenCourseWare, streamlines graphing linear functions.

  2. Quadratic Formula -

    Memorize x = ( - b ± √(b² - 4ac))❄(2a) for solving ax² + bx + c = 0 and use the phrase "minus b, plus or minus the square root" to recall it quickly. Work through examples where the discriminant (b² - 4ac) determines the nature of roots: two real, one real, or complex. This method, endorsed by Khan Academy, guarantees solutions when factoring gets tricky.

  3. Systems of Equations -

    Practice both substitution and elimination methods to solve pairs of linear equations; substitution replaces one variable, while elimination adds or subtracts equations to remove a variable. For elimination, align coefficients and remember "make them match, then add or subtract" to eliminate. Research from the National Council of Teachers of Mathematics shows proficiency here boosts problem-solving flexibility.

  4. Function Notation -

    Understand f(x) = expression means "output f for input x" and practice evaluating f(2) or f(a + 3) to build fluency. Identify domain and range restrictions by inspecting denominators or even roots in f(x). Clear comprehension of notation, as outlined by university math departments, is essential for more advanced topics.

  5. Exponents & Radicals -

    Master the laws a^m · a^n = a^(m+n), (a^m)^n = a^(mn), and (a/b)^m = a^m/b^m, plus rewrite √a as a^(1/2). Use the "same-base add, power of a power multiply, quotient subtract" chant to remember rules. Reliable sources like the University of California's math guides stress these laws underpin simplifying expressions in algebra and beyond.

Make a Quiz (FREE) Copy & Edit This Quiz Create a Quiz with AI

Algebra Quizzes

Powered by: Quiz Maker