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← Algebra I
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Practice deliberately

Work through Algebra I unit by unit, then test yourself under time.

Practice mode gives one hint and a worked explanation after every question. Test mode mixes all 7 units, holds the explanations until you submit, and then reports which units need another pass. The 8 questions printed further down this page are fixed, so you can read them and their worked answers without starting a set.

Algebra I coverage and review map

Connect every question to the exact skill it rehearses. Work through the units in order, then return to any topic that still needs a hint or a second attempt.

This page follows the Algebra I syllabus unit by unit. For shorter mixed retrieval outside the course sequence, use algebra i practice questions with answers.

01

Linear equations

Represent the constraints symbolically, choose an equivalence-preserving solution method, and verify the result in every original relationship.

Goal: recognise a linear equations problem from its wording, carry out the governing method, and check that the result is reasonable.

02

Inequalities

Define the central objects, connect at least two representations, solve direct and unfamiliar applications, and explain how the result can be checked.

Goal: recognise a inequalities problem from its wording, carry out the governing method, and check that the result is reasonable.

03

Functions and graphs

Connect formulas, tables, and graphs; identify domain and parameters; then interpret how changing an input or coefficient changes the output.

Goal: recognise a functions and graphs problem from its wording, carry out the governing method, and check that the result is reasonable.

04

Systems of equations

Represent the constraints symbolically, choose an equivalence-preserving solution method, and verify the result in every original relationship.

Goal: recognise a systems of equations problem from its wording, carry out the governing method, and check that the result is reasonable.

05

Exponents

Define the central objects, connect at least two representations, solve direct and unfamiliar applications, and explain how the result can be checked.

Goal: recognise a exponents problem from its wording, carry out the governing method, and check that the result is reasonable.

06

Polynomials

Define the central objects, connect at least two representations, solve direct and unfamiliar applications, and explain how the result can be checked.

Goal: recognise a polynomials problem from its wording, carry out the governing method, and check that the result is reasonable.

07

Quadratic functions

Connect formulas, tables, and graphs; identify domain and parameters; then interpret how changing an input or coefficient changes the output.

Goal: recognise a quadratic functions problem from its wording, carry out the governing method, and check that the result is reasonable.

Algebra I questions with worked answers

These 8 questions are printed in full on this page and are drawn across all 7 course units. Nothing here is generated on the fly. Cover the options, solve each one on paper, and only then open the worked answer to compare your method with the one shown.

Question 1: Solve 3(2x - 5) = 4x + 7.

Algebra I · Linear equations

  1. x = 11
  2. x = 1
  3. x = -11
  4. x = 6
Show the worked answer
  1. Multiply out the bracket first: 3(2x - 5) = 6x - 15.
  2. The equation is 6x - 15 = 4x + 7. Subtract 4x from both sides to get 2x - 15 = 7.
  3. Add 15 to both sides: 2x = 22.
  4. Divide by 2: x = 11. Check: 3(22 - 5) = 51 and 4(11) + 7 = 51.

Answer: x = 11

Question 2: Solve the inequality 5 - 2x is less than or equal to -9.

Algebra I · Inequalities

  1. x is greater than or equal to 7
  2. x is less than or equal to 7
  3. x is greater than or equal to -7
  4. x is less than or equal to -2
Show the worked answer
  1. Subtract 5 from both sides: -2x is less than or equal to -14.
  2. Divide both sides by -2.
  3. Dividing by a negative number flips the direction of the inequality.
  4. So x is greater than or equal to 7. Check x = 7: 5 - 14 = -9, which satisfies the statement.

Answer: x is greater than or equal to 7

Question 3: If f(x) = 3x^2 - 5x, what is f(-1) - f(2)?

Algebra I · Functions and graphs

  1. 6
  2. -6
  3. 10
  4. 2
Show the worked answer
  1. Find f(-1) first: 3(-1)^2 - 5(-1) = 3 + 5 = 8.
  2. Then f(2): 3(2)^2 - 5(2) = 12 - 10 = 2.
  3. Subtract in the order asked: f(-1) - f(2) = 8 - 2.
  4. 8 - 2 = 6.

Answer: 6

Question 4: Solve the system 2x + 3y = 12 and x - y = 1.

Algebra I · Systems of equations

  1. x = 3, y = 2
  2. x = 2, y = 3
  3. x = 4, y = 3
  4. x = 1, y = 0
Show the worked answer
  1. The second equation is easy to rearrange: x = y + 1.
  2. Substitute that into the first equation: 2(y + 1) + 3y = 12.
  3. That gives 2y + 2 + 3y = 12, so 5y = 10 and y = 2.
  4. Then x = 2 + 1 = 3. Check: 2(3) + 3(2) = 12.

Answer: x = 3, y = 2

Question 5: Simplify (2x^3)^4 / (4x^5).

Algebra I · Exponents

  1. 4x^7
  2. 4x^12
  3. 8x^7
  4. 2x^7
Show the worked answer
  1. Raise every factor inside the bracket to the fourth power: (2x^3)^4 = 2^4 x^12.
  2. 2^4 = 16, so the top is 16x^12.
  3. Divide the numbers: 16 / 4 = 4.
  4. Subtract the exponents when dividing powers: x^12 / x^5 = x^7. The answer is 4x^7.

Answer: 4x^7

Question 6: Expand (x + 5)(x - 3).

Algebra I · Polynomials

  1. x^2 + 2x - 15
  2. x^2 - 2x - 15
  3. x^2 + 8x - 15
  4. x^2 + 2x + 15
Show the worked answer
  1. Multiply each term in the first bracket by each term in the second.
  2. x times x = x^2, and x times -3 = -3x.
  3. 5 times x = 5x, and 5 times -3 = -15.
  4. Collect the middle terms: -3x + 5x = 2x, so the answer is x^2 + 2x - 15.

Answer: x^2 + 2x - 15

Question 7: Solve x^2 - 7x + 10 = 0.

Algebra I · Quadratic functions

  1. x = 2 or x = 5
  2. x = -2 or x = -5
  3. x = 1 or x = 10
  4. x = 3 or x = 4
Show the worked answer
  1. Look for two numbers that multiply to 10 and add to -7.
  2. -2 and -5 work, because (-2)(-5) = 10 and -2 + -5 = -7.
  3. So the equation factors as (x - 2)(x - 5) = 0.
  4. A product is zero when a factor is zero, so x = 2 or x = 5.

Answer: x = 2 or x = 5

Question 8: What is the vertex of the parabola y = x^2 - 6x + 5?

Algebra I · Quadratic functions

  1. (3, -4)
  2. (-3, 32)
  3. (3, 4)
  4. (6, 5)
Show the worked answer
  1. The x value of the vertex is -b / (2a), with a = 1 and b = -6.
  2. -(-6) / (2 x 1) = 6 / 2 = 3.
  3. Put x = 3 back into the equation: 9 - 18 + 5.
  4. 9 - 18 + 5 = -4, so the vertex is (3, -4).

Answer: (3, -4)

Which unit each printed question belongs to

Use this map after marking your work. If two misses share a unit, review that unit before starting a generated set.

The 8 printed Algebra I questions, the unit each one tests, and its answer.
QuestionUnitWhat it asksAnswer
1Linear equationsSolve 3(2x - 5) = 4x + 7.x = 11
2InequalitiesSolve the inequality 5 - 2x is less than or equal to -9.x is greater than or equal to 7
3Functions and graphsIf f(x) = 3x^2 - 5x, what is f(-1) - f(2)?6
4Systems of equationsSolve the system 2x + 3y = 12 and x - y = 1.x = 3, y = 2
5ExponentsSimplify (2x^3)^4 / (4x^5).4x^7
6PolynomialsExpand (x + 5)(x - 3).x^2 + 2x - 15
7Quadratic functionsSolve x^2 - 7x + 10 = 0.x = 2 or x = 5
8Quadratic functionsWhat is the vertex of the parabola y = x^2 - 6x + 5?(3, -4)

How the generated Algebra I sets are created

The 8 questions above are fixed and checked. The generator at the top of the page is different: it writes fresh questions with AI from the course and unit information shown here, then the application checks each one for a complete prompt, four choices, one keyed answer, and an explanation. Generated questions are original practice—not official or released exam questions—and AI can still make mathematical mistakes. Verify a disputed answer with the stated method, your course materials, or the MathGPT solver, and follow the site's academic-integrity guidance.

Questions about this Algebra I practice page

What does this page cover?

It covers all 7 Algebra I units listed above. Choose one unit for focused work, or mixed review to test method selection, and switch to test mode when you want all units mixed under time.

When can I see correct answers and explanations?

The 8 printed questions on this page keep their worked answers behind a toggle, so you can check any one of them straight away. In the generator above, practice mode explains each question as soon as you answer it, while test mode holds every explanation until you submit.

What should I do with a missed question?

Classify the miss as a definition, setup, calculation, interpretation, or timing error. Re-solve it from a blank page, then use the MathGPT tutor for a hint or method check.