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Algebra Test

Unofficial algebra questions in five rising levels, from order of operations to quadratics, each worked out.

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Evaluate −7 + (−5).

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All 120 questions with answers

Level 1: expressions and order of operations 24

  • A gym charges a $25 sign-up fee plus $15 a month. Which expression gives the cost, in dollars, of m months? Answer: 15m + 25. Source: Common Core State Standards for Mathematics, 6.EE.A.2.a: write expressions that record operations with numbers and with letters standing for numbers
  • Evaluate (1/2)x + 3 when x = 10. Answer: 8. Source: Common Core State Standards for Mathematics, 6.EE.A.2.c: evaluate expressions at specific values of their variables, in the conventional order of operations
  • Evaluate (−3)². Answer: 9. Source: Common Core State Standards for Mathematics, 7.NS.A.2: multiply and divide rational numbers
  • Evaluate (−4)(−6). Answer: 24. Source: Common Core State Standards for Mathematics, 7.NS.A.2: multiply and divide rational numbers
  • Evaluate 2(a + b) when a = 3 and b = −5. Answer: −4. Source: Common Core State Standards for Mathematics, 6.EE.A.2.c: evaluate expressions at specific values of their variables, in the conventional order of operations
  • Evaluate 2³ + 4². Answer: 24. Source: Common Core State Standards for Mathematics, 6.EE.A.1: write and evaluate numerical expressions involving whole-number exponents
  • Evaluate 3 + 4 · 5. Answer: 23. Source: Common Core State Standards for Mathematics, 6.EE.A.2.c: evaluate expressions at specific values of their variables, in the conventional order of operations
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Level 1: expressions and order of operations, continued

  • Evaluate 5x − 2 when x = 4. Answer: 18. Source: Common Core State Standards for Mathematics, 6.EE.A.2.c: evaluate expressions at specific values of their variables, in the conventional order of operations
  • Evaluate 18 − 3 · 2². Answer: 6. Source: Common Core State Standards for Mathematics, 6.EE.A.1: write and evaluate numerical expressions involving whole-number exponents
  • Evaluate 20 − 2 · (3 + 4). Answer: 6. Source: Common Core State Standards for Mathematics, 5.OA.A.1: evaluate numerical expressions with parentheses, brackets or braces
  • Evaluate 36 ÷ 4 · 3. Answer: 27. Source: Common Core State Standards for Mathematics, 6.EE.A.2.c: evaluate expressions at specific values of their variables, in the conventional order of operations
  • Evaluate x² − 3x when x = −2. Answer: 10. Source: Common Core State Standards for Mathematics, 6.EE.A.2.c: evaluate expressions at specific values of their variables, in the conventional order of operations
  • Evaluate |−8| − |3|. Answer: 5. Source: Common Core State Standards for Mathematics, 6.NS.C.7.c: absolute value as distance from 0 on the number line
  • Evaluate −6 − (−9). Answer: 3. Source: Common Core State Standards for Mathematics, 7.NS.A.1: add and subtract rational numbers
  • Evaluate −7 + (−5). Answer: −12. Source: Common Core State Standards for Mathematics, 7.NS.A.1: add and subtract rational numbers
  • Factor the greatest common factor out of 12x − 18. Answer: 6(2x − 3). Source: Common Core State Standards for Mathematics, 7.EE.A.1: add, subtract, factor and expand linear expressions with rational coefficients
  • Simplify 3x + 5x. Answer: 8x. Source: Common Core State Standards for Mathematics, 6.EE.A.3: apply the properties of operations to generate equivalent expressions
  • Simplify 5x − (2x − 4). Answer: 3x + 4. Source: Common Core State Standards for Mathematics, 7.EE.A.1: add, subtract, factor and expand linear expressions with rational coefficients
  • Simplify 7y − 2 + 3y + 9. Answer: 10y + 7. Source: Common Core State Standards for Mathematics, 7.EE.A.1: add, subtract, factor and expand linear expressions with rational coefficients
  • Simplify −2(3x − 5). Answer: −6x + 10. Source: Common Core State Standards for Mathematics, 7.EE.A.1: add, subtract, factor and expand linear expressions with rational coefficients
  • Use the distributive property to rewrite 4(x + 3). Answer: 4x + 12. Source: Common Core State Standards for Mathematics, 6.EE.A.3: apply the properties of operations to generate equivalent expressions
  • What is the coefficient of x in the expression 7 − 4x + x²? Answer: −4. Source: Common Core State Standards for Mathematics, HSA.SSE.A.1.a: interpret parts of an expression, such as terms, factors and coefficients
  • Which expression is equivalent to 6x + 9? Answer: 3(2x + 3). Source: Common Core State Standards for Mathematics, 6.EE.A.4: identify when two expressions are equivalent
  • Which expression means "6 less than twice a number n"? Answer: 2n − 6. Source: Common Core State Standards for Mathematics, 6.EE.A.2.a: write expressions that record operations with numbers and with letters standing for numbers

Level 2: linear equations and inequalities 24

  • A phone plan costs $30 a month plus $0.10 for each text. Dana's bill was $42.50. How many texts did she send? Answer: 125. Source: Common Core State Standards for Mathematics, HSA.CED.A.1: create equations and inequalities in one variable and use them to solve problems
  • A print shop charges $4 a poster plus a $6 setup fee. An order costs $46. How many posters were ordered? Answer: 10. Source: Common Core State Standards for Mathematics, HSA.CED.A.1: create equations and inequalities in one variable and use them to solve problems
  • How many solutions does 3(x + 4) = 3x + 12 have? Answer: Infinitely many. Source: Common Core State Standards for Mathematics, 8.EE.C.7.a: linear equations in one variable with one solution, infinitely many solutions or no solutions
  • Sam has $50 and saves $15 a week. Which inequality gives the number of weeks w until Sam has at least $200? Answer: 50 + 15w ≥ 200. Source: Common Core State Standards for Mathematics, HSA.CED.A.1: create equations and inequalities in one variable and use them to solve problems
  • Solve (2/3)x = 12. Answer: x = 18. Source: Common Core State Standards for Mathematics, 8.EE.C.7.b: solve linear equations with rational number coefficients, using the distributive property and collecting like terms
  • Solve 0.5x + 1.5 = 4. Answer: x = 5. Source: Common Core State Standards for Mathematics, 8.EE.C.7.b: solve linear equations with rational number coefficients, using the distributive property and collecting like terms
  • Solve 2x + 3 ≥ 5x − 9. Answer: x ≤ 4. Source: Common Core State Standards for Mathematics, HSA.REI.B.3: solve linear equations and inequalities in one variable
  • Solve 2x + 5 = 17. Answer: x = 6. Source: Common Core State Standards for Mathematics, 7.EE.B.4.a: solve equations of the form px + q = r and p(x + q) = r
  • Solve 3(x + 4) = 2x − 1. Answer: x = −13. Source: Common Core State Standards for Mathematics, 8.EE.C.7.b: solve linear equations with rational number coefficients, using the distributive property and collecting like terms
  • Solve 3x + 2y = 12 for y. Answer: y = 6 − (3/2)x. Source: Common Core State Standards for Mathematics, HSA.CED.A.4: rearrange formulas to highlight a quantity of interest
  • Solve 3x − 5 > 10. Answer: x > 5. Source: Common Core State Standards for Mathematics, 7.EE.B.4.b: solve inequalities of the form px + q > r or px + q < r
  • Solve 4 − x < 9. Answer: x > −5. Source: Common Core State Standards for Mathematics, 7.EE.B.4.b: solve inequalities of the form px + q > r or px + q < r
  • Solve 4x = −28. Answer: x = −7. Source: Common Core State Standards for Mathematics, HSA.REI.B.3: solve linear equations and inequalities in one variable
  • Solve 5(x − 2) = 20. Answer: x = 6. Source: Common Core State Standards for Mathematics, 7.EE.B.4.a: solve equations of the form px + q = r and p(x + q) = r
  • Solve 6 − 2(x − 1) = 4x. Answer: x = 4/3. Source: Common Core State Standards for Mathematics, 8.EE.C.7.b: solve linear equations with rational number coefficients, using the distributive property and collecting like terms
  • Solve 7x − 4 = 3x + 12. Answer: x = 4. Source: Common Core State Standards for Mathematics, 8.EE.C.7.b: solve linear equations with rational number coefficients, using the distributive property and collecting like terms
  • Solve A = (1/2)bh for h. Answer: h = 2A/b. Source: Common Core State Standards for Mathematics, HSA.CED.A.4: rearrange formulas to highlight a quantity of interest
  • Solve x + 9 = 4. Answer: x = −5. Source: Common Core State Standards for Mathematics, HSA.REI.B.3: solve linear equations and inequalities in one variable
  • Solve x/3 − 2 = 5. Answer: x = 21. Source: Common Core State Standards for Mathematics, 7.EE.B.4.a: solve equations of the form px + q = r and p(x + q) = r
  • Solve −2x ≤ 8. Answer: x ≥ −4. Source: Common Core State Standards for Mathematics, 7.EE.B.4.b: solve inequalities of the form px + q > r or px + q < r
  • Solve −3 < 2x + 1 ≤ 7. Answer: −2 < x ≤ 3. Source: Common Core State Standards for Mathematics, HSA.REI.B.3: solve linear equations and inequalities in one variable
  • The sum of a number and 12 is three times the number. What is the number? Answer: 6. Source: Common Core State Standards for Mathematics, HSA.CED.A.1: create equations and inequalities in one variable and use them to solve problems
  • Three consecutive integers add up to 72. What is the smallest of the three? Answer: 23. Source: Common Core State Standards for Mathematics, HSA.CED.A.1: create equations and inequalities in one variable and use them to solve problems
  • Which equation has no solution? Answer: 3x + 2 = 3x − 7. Source: Common Core State Standards for Mathematics, 8.EE.C.7.a: linear equations in one variable with one solution, infinitely many solutions or no solutions

Level 3: lines, slope and systems 24

  • A car travels 150 miles in 3 hours at a constant speed. In the equation d = kt, what is k? Answer: 50. Source: Common Core State Standards for Mathematics, 7.RP.A.2.b: identify the constant of proportionality (unit rate)
  • A line passes through (0, 3) and has slope 0. What is its equation? Answer: y = 3. Source: Common Core State Standards for Mathematics, 8.F.A.3: interpret the equation y = mx + b as defining a linear function
  • A tank holds 40 gallons and drains 2.5 gallons a minute. Which equation gives the gallons g left after t minutes? Answer: g = 40 − 2.5t. Source: Common Core State Standards for Mathematics, 8.F.B.4: determine the rate of change and initial value of a linear function
  • Adult tickets cost $9 and child tickets cost $5. A family buys 7 tickets for $47. How many adult tickets did they buy? Answer: 3. Source: Common Core State Standards for Mathematics, 8.EE.C.8.c: solve real-world problems leading to two linear equations in two variables
  • The cost in dollars of a taxi ride is C = 2.50m + 4, where m is the number of miles. What does a 6-mile ride cost? Answer: $19.00. Source: Common Core State Standards for Mathematics, 8.F.B.4: determine the rate of change and initial value of a linear function
  • How many solutions does the system x + y = 4 and 2x + 2y = 8 have? Answer: Infinitely many. Source: Common Core State Standards for Mathematics, 8.EE.C.8.b: solve systems of two linear equations in two variables algebraically
  • How many solutions does the system y = 2x + 3 and y = 2x − 1 have? Answer: None. Source: Common Core State Standards for Mathematics, 8.EE.C.8.b: solve systems of two linear equations in two variables algebraically
  • Solve the system 2x + 3y = 12 and x − y = 1. Answer: (3, 2). Source: Common Core State Standards for Mathematics, HSA.REI.C.6: solve systems of linear equations exactly and approximately
  • Solve the system 3x + y = 5 and 2x − y = 10. Answer: (3, −4). Source: Common Core State Standards for Mathematics, HSA.REI.C.6: solve systems of linear equations exactly and approximately
  • Solve the system x + y = 10 and x − y = 4. Answer: (7, 3). Source: Common Core State Standards for Mathematics, 8.EE.C.8.b: solve systems of two linear equations in two variables algebraically
  • Solve the system y = 2x and x + y = 12. Answer: (4, 8). Source: Common Core State Standards for Mathematics, 8.EE.C.8.b: solve systems of two linear equations in two variables algebraically
  • Two numbers add up to 30 and differ by 8. What is the larger number? Answer: 19. Source: Common Core State Standards for Mathematics, 8.EE.C.8.c: solve real-world problems leading to two linear equations in two variables
  • What is the slope of the line 3x + 2y = 8? Answer: −3/2. Source: Common Core State Standards for Mathematics, 8.F.A.3: interpret the equation y = mx + b as defining a linear function
  • What is the slope of the line in the graph? (Picture: A coordinate grid from −5 to 5 with one straight line that rises from left to right. It passes through the grid points (−2, −3), (0, 1) and (2, 5).) Answer: 2. Source: Common Core State Standards for Mathematics, 8.F.B.4: determine the rate of change and initial value of a linear function
  • What is the slope of the line through (2, 1) and (5, 13)? Answer: 4. Source: Common Core State Standards for Mathematics, 8.F.B.4: determine the rate of change and initial value of a linear function
  • What is the slope of the line through (−2, 5) and (4, −7)? Answer: −2. Source: Common Core State Standards for Mathematics, 8.F.B.4: determine the rate of change and initial value of a linear function
  • What is the slope of the line y = −4x + 7? Answer: −4. Source: Common Core State Standards for Mathematics, 8.F.A.3: interpret the equation y = mx + b as defining a linear function
  • What is the x-intercept of the line 2x − 5y = 20? Answer: (10, 0). Source: Common Core State Standards for Mathematics, HSF.IF.C.7.a: graph linear and quadratic functions and show intercepts, maxima and minima
  • Where does the line y = 2x − 9 cross the y-axis? Answer: (0, −9). Source: Common Core State Standards for Mathematics, 8.EE.B.6: the equation y = mx + b for a line intercepting the vertical axis at b
  • Which equation describes the line drawn on the grid? (Picture: A coordinate grid from −5 to 5 with one straight line that falls from left to right. It passes through the grid points (−2, 4), (0, 2) and (2, 0).) Answer: y = −x + 2. Source: Common Core State Standards for Mathematics, 8.EE.B.6: the equation y = mx + b for a line intercepting the vertical axis at b
  • Which equation is the line through (0, 4) and (2, 10)? Answer: y = 3x + 4. Source: Common Core State Standards for Mathematics, 8.F.B.4: determine the rate of change and initial value of a linear function
  • Which equation is the line through (2, 5) with slope −1? Answer: y = −x + 7. Source: Common Core State Standards for Mathematics, 8.F.B.4: determine the rate of change and initial value of a linear function
  • Which equation is the line with slope 3 that crosses the y-axis at −2? Answer: y = 3x − 2. Source: Common Core State Standards for Mathematics, 8.EE.B.6: the equation y = mx + b for a line intercepting the vertical axis at b
  • Which point lies on the line y = 3x − 4? Answer: (2, 2). Source: Common Core State Standards for Mathematics, HSA.REI.D.10: the graph of an equation in two variables is the set of all its solutions

Level 4: exponents, polynomials and factoring 24

  • A rectangle is x + 4 long and x − 1 wide. Which expression is its area? Answer: x² + 3x − 4. Source: Common Core State Standards for Mathematics, HSA.APR.A.1: add, subtract and multiply polynomials
  • Add (3x² + 2x − 5) + (x² − 6x + 9). Answer: 4x² − 4x + 4. Source: Common Core State Standards for Mathematics, HSA.APR.A.1: add, subtract and multiply polynomials
  • Evaluate 2⁻³. Answer: 1/8. Source: Common Core State Standards for Mathematics, 8.EE.A.1: know and apply the properties of integer exponents
  • Evaluate 27^(1/3). Answer: 3. Source: Common Core State Standards for Mathematics, HSN.RN.A.2: rewrite expressions involving radicals and rational exponents using the properties of exponents
  • Evaluate √81 − √16. Answer: 5. Source: Common Core State Standards for Mathematics, 8.EE.A.2: square roots of small perfect squares and cube roots of small perfect cubes
  • Expand (x − 6)². Answer: x² − 12x + 36. Source: Common Core State Standards for Mathematics, HSA.APR.A.1: add, subtract and multiply polynomials
  • Factor 2x² + 5x + 3. Answer: (2x + 3)(x + 1). Source: Common Core State Standards for Mathematics, HSA.SSE.A.2: use the structure of an expression to identify ways to rewrite it
  • Factor 3x² − 12 completely. Answer: 3(x − 2)(x + 2). Source: Common Core State Standards for Mathematics, HSA.SSE.A.2: use the structure of an expression to identify ways to rewrite it
  • Factor the greatest common factor out of 4x³ + 8x². Answer: 4x²(x + 2). Source: Common Core State Standards for Mathematics, HSA.SSE.A.2: use the structure of an expression to identify ways to rewrite it
  • Factor x² + 7x + 12. Answer: (x + 3)(x + 4). Source: Common Core State Standards for Mathematics, HSA.SSE.A.2: use the structure of an expression to identify ways to rewrite it
  • Factor x² − 2x − 15. Answer: (x − 5)(x + 3). Source: Common Core State Standards for Mathematics, HSA.SSE.A.2: use the structure of an expression to identify ways to rewrite it
  • Factor x² − 64. Answer: (x − 8)(x + 8). Source: Common Core State Standards for Mathematics, HSA.SSE.A.2: use the structure of an expression to identify ways to rewrite it
  • Multiply (2x − 1)(x + 4). Answer: 2x² + 7x − 4. Source: Common Core State Standards for Mathematics, HSA.APR.A.1: add, subtract and multiply polynomials
  • Multiply (3 × 10⁴)(2 × 10⁵). Answer: 6 × 10⁹. Source: Common Core State Standards for Mathematics, 8.EE.A.4: perform operations with numbers expressed in scientific notation
  • Multiply (x + 3)(x + 5). Answer: x² + 8x + 15. Source: Common Core State Standards for Mathematics, HSA.APR.A.1: add, subtract and multiply polynomials
  • Multiply (x + 7)(x − 7). Answer: x² − 49. Source: Common Core State Standards for Mathematics, HSA.APR.A.1: add, subtract and multiply polynomials
  • Multiply 3x(2x − 5). Answer: 6x² − 15x. Source: Common Core State Standards for Mathematics, HSA.APR.A.1: add, subtract and multiply polynomials
  • Simplify (2x³y)². Answer: 4x⁶y². Source: Common Core State Standards for Mathematics, 8.EE.A.1: know and apply the properties of integer exponents
  • Simplify (6x⁵) ÷ (2x²). Answer: 3x³. Source: Common Core State Standards for Mathematics, 8.EE.A.1: know and apply the properties of integer exponents
  • Simplify (x⁴)³. Answer: x¹². Source: Common Core State Standards for Mathematics, 8.EE.A.1: know and apply the properties of integer exponents
  • Simplify x³ · x⁵. Answer: x⁸. Source: Common Core State Standards for Mathematics, 8.EE.A.1: know and apply the properties of integer exponents
  • Simplify x⁹ ÷ x³. Answer: x⁶. Source: Common Core State Standards for Mathematics, 8.EE.A.1: know and apply the properties of integer exponents
  • Simplify √50. Answer: 5√2. Source: Common Core State Standards for Mathematics, HSN.RN.A.2: rewrite expressions involving radicals and rational exponents using the properties of exponents
  • Subtract (5x² − 3x + 2) − (2x² + 4x − 7). Answer: 3x² − 7x + 9. Source: Common Core State Standards for Mathematics, HSA.APR.A.1: add, subtract and multiply polynomials

Level 5: quadratics and functions 24

  • A ball's height in feet t seconds after it is thrown is h = −16t² + 64t. After how many seconds does it land? Answer: 4 seconds. Source: Common Core State Standards for Mathematics, HSA.SSE.B.3.a: factor a quadratic expression to reveal the zeros of the function it defines
  • The height in meters of a fountain jet t seconds after it leaves the nozzle is h = −5t² + 20t. What is its greatest height? Answer: 20 meters. Source: Common Core State Standards for Mathematics, HSF.IF.C.8.a: use factoring and completing the square in a quadratic function to show zeros, extreme values and symmetry of the graph
  • How many real solutions does x² + 4x + 5 = 0 have? Answer: No real solutions. Source: Common Core State Standards for Mathematics, HSA.REI.B.4.b: solve quadratic equations by inspection, taking square roots, completing the square, the quadratic formula and factoring
  • How many real solutions does x² − 6x + 9 = 0 have? Answer: Exactly one. Source: Common Core State Standards for Mathematics, HSA.REI.B.4.b: solve quadratic equations by inspection, taking square roots, completing the square, the quadratic formula and factoring
  • If f(x) = 3x − 5, what is f(4)? Answer: 7. Source: Common Core State Standards for Mathematics, HSF.IF.A.2: use function notation and evaluate functions for inputs in their domains
  • If f(x) = x² + 2x, what is f(−3)? Answer: 3. Source: Common Core State Standards for Mathematics, HSF.IF.A.2: use function notation and evaluate functions for inputs in their domains
  • If g(x) = 2x + 1, for which x is g(x) = 15? Answer: x = 7. Source: Common Core State Standards for Mathematics, HSF.IF.A.2: use function notation and evaluate functions for inputs in their domains
  • Solve (x − 3)² = 16. Answer: x = 7 or x = −1. Source: Common Core State Standards for Mathematics, HSA.REI.B.4.b: solve quadratic equations by inspection, taking square roots, completing the square, the quadratic formula and factoring
  • Solve (x − 4)(x + 1) = 0. Answer: x = 4 or x = −1. Source: Common Core State Standards for Mathematics, HSA.SSE.B.3.a: factor a quadratic expression to reveal the zeros of the function it defines
  • Solve 2x² − 8 = 0. Answer: x = 2 or x = −2. Source: Common Core State Standards for Mathematics, HSA.REI.B.4.b: solve quadratic equations by inspection, taking square roots, completing the square, the quadratic formula and factoring
  • Solve x² + 3x − 10 = 0. Answer: x = 2 or x = −5. Source: Common Core State Standards for Mathematics, HSA.REI.B.4.b: solve quadratic equations by inspection, taking square roots, completing the square, the quadratic formula and factoring
  • Solve x² = 121. Answer: x = 11 or x = −11. Source: Common Core State Standards for Mathematics, HSA.REI.B.4.b: solve quadratic equations by inspection, taking square roots, completing the square, the quadratic formula and factoring
  • Solve x² − 7x + 10 = 0. Answer: x = 2 or x = 5. Source: Common Core State Standards for Mathematics, HSA.REI.B.4.b: solve quadratic equations by inspection, taking square roots, completing the square, the quadratic formula and factoring
  • Solve x² − 9x = 0. Answer: x = 0 or x = 9. Source: Common Core State Standards for Mathematics, HSA.REI.B.4.b: solve quadratic equations by inspection, taking square roots, completing the square, the quadratic formula and factoring
  • Use the quadratic formula to solve x² + 2x − 4 = 0. Answer: x = −1 ± √5. Source: Common Core State Standards for Mathematics, HSA.REI.B.4.b: solve quadratic equations by inspection, taking square roots, completing the square, the quadratic formula and factoring
  • What are the zeros of f(x) = x² − x − 12? Answer: x = 4 or x = −3. Source: Common Core State Standards for Mathematics, HSA.SSE.B.3.a: factor a quadratic expression to reveal the zeros of the function it defines
  • What are the zeros of the quadratic function in the graph? (Picture: A coordinate grid from −5 to 5 with a U-shaped curve that opens upward. Its lowest point is at the grid point (1, −4) and it crosses the y-axis at −3.) Answer: x = −1 or x = 3. Source: Common Core State Standards for Mathematics, HSF.IF.C.7.a: graph linear and quadratic functions and show intercepts, maxima and minima
  • What is the average rate of change of f(x) = x² from x = 1 to x = 4? Answer: 5. Source: Common Core State Standards for Mathematics, HSF.IF.B.6: calculate the average rate of change of a function over a specified interval
  • What is the axis of symmetry of the parabola y = x² + 8x + 1? Answer: x = −4. Source: Common Core State Standards for Mathematics, HSF.IF.C.8.a: use factoring and completing the square in a quadratic function to show zeros, extreme values and symmetry of the graph
  • What is the vertex of the parabola y = (x − 2)² + 3? Answer: (2, 3). Source: Common Core State Standards for Mathematics, HSF.IF.C.7.a: graph linear and quadratic functions and show intercepts, maxima and minima
  • What is the vertex of the parabola y = x² − 6x + 5? Answer: (3, −4). Source: Common Core State Standards for Mathematics, HSF.IF.C.8.a: use factoring and completing the square in a quadratic function to show zeros, extreme values and symmetry of the graph
  • Where does the parabola y = 2x² − 3x + 7 cross the y-axis? Answer: (0, 7). Source: Common Core State Standards for Mathematics, HSF.IF.C.7.a: graph linear and quadratic functions and show intercepts, maxima and minima
  • Which number c makes x² + 10x + c a perfect square? Answer: 25. Source: Common Core State Standards for Mathematics, HSA.SSE.B.3.b: complete the square in a quadratic expression
  • Which of these sets of ordered pairs is a function of the first number? Answer: {(1, 2), (2, 2), (3, 5)}. Source: Common Core State Standards for Mathematics, HSF.IF.A.1: a function assigns to each element of the domain exactly one element of the range

How this list was compiled: Our own questions. The five levels follow the Common Core State Standards for Mathematics from grade 5 through the high school Algebra and Functions standards (https://www.thecorestandards.org/Math/, read 2026-10-09). Each question names the standard it practices and links to that standard's page. Every answer is arithmetic or algebra on what the question prints, worked out a second time on 2026-10-09. Licence: Own work. Questions, answer choices, explanations and graphs were written and drawn for this site. Nothing is copied or reworded from a state test, a placement test, a released form, a textbook or another practice test.

How it works

This free algebra practice test has 120 questions of our own in five levels, from order of operations to quadratics, each with its working. Answer on screen or print it. Unofficial: not a state test or any school's placement test.

Read the full guide

The five levels

Level 1 is expressions and order of operations. Level 2 is linear equations and inequalities. Level 3 is slope, lines and systems. Level 4 is exponents, polynomials and factoring. Level 5 is quadratics and functions. Each has 24 questions and follows the Common Core State Standards for Mathematics, read October 9, 2026.

A test of 25

Exam mode draws 25 algebra test questions and scores each level, so it works as an algebra diagnostic test or as algebra exam practice: the result names the level where you missed most. The 25 is our number, not any exam's.

How the math is written

Powers are written x² or x⁻³, √ is a square root, a fraction uses a slash and a dot means multiply.

  • Check a solved equation by putting your answer back into the line you started from.
  • Multiplying or dividing an inequality by a negative number reverses its sign.

Questions and answers

Is there an algebra test PDF to print?

Yes. Print the question sheet opens 25 questions, five from each level in rising order, with the answer key if you tick it. Choose Save as PDF in the print window to keep it as an algebra test PDF.

Is this a practice algebra test with answers?

Yes. Every question shows the right answer and its working as soon as you answer it. In exam mode the answers wait until the end, where each missed question is listed with its working.

Is this an elementary algebra practice test?

As general practice, yes. Elementary, or beginning, algebra is a first algebra course, and each school sets what its own covers. The five levels run from expressions and linear equations to factoring and quadratics, so pick the levels your course includes.

Can I use this to practice for an algebra placement test?

Only as general practice. A school or college writes its own placement test, and this page copies none. The school's testing page says what its own test covers.

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