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Question 1
Algebra IFoundation

Algebra I practice question 1

Algebra I practice topics

Question sets mix direct skills with unfamiliar applications so method selection becomes part of the practice.

01

Linear equations and inequalities

Isolate a variable across several steps and remember to flip the inequality sign when you multiply or divide by a negative.

02

Functions and coordinate graphs

Evaluate function notation, find the slope between two points, and write a line in slope-intercept form.

03

Systems of equations

Solve pairs of equations by substitution or elimination, including word problems where you set the equations up yourself.

04

Exponents, polynomials, and quadratics

Apply the exponent rules, expand and factor polynomials, and solve quadratic equations by factoring.

Algebra I practice questions with worked answers

These 8 questions are printed in full on this page, with every step of the arithmetic written out. Cover the options, solve the question on paper first, and only then open the worked answer to compare your method with the one shown.

Question 1: Solve 5x - 7 = 3x + 9.

Foundation level · linear equations and inequalities

  1. x = 8
  2. x = 1
  3. x = 16
  4. x = -8
Show the worked answer
  1. Collect the x terms on one side: subtract 3x from both sides to get 2x - 7 = 9.
  2. Undo the subtraction: add 7 to both sides to get 2x = 16.
  3. Divide both sides by 2: x = 8.
  4. Check: 5(8) - 7 = 33 and 3(8) + 9 = 33, so both sides match.

Answer: x = 8

Question 2: Solve the inequality -3x + 4 > 19.

Exam level · linear equations and inequalities

  1. x < -5
  2. x > -5
  3. x < 5
  4. x > 5
Show the worked answer
  1. Subtract 4 from both sides: -3x > 15.
  2. Divide both sides by -3.
  3. Dividing by a negative number flips the inequality sign, so x < -5.
  4. Check with x = -6: -3(-6) + 4 = 22, and 22 > 19 is true.

Answer: x < -5

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

Foundation level · functions and coordinate graphs

  1. 15
  2. 3
  3. -1
  4. 11
Show the worked answer
  1. Replace every x with -2: f(-2) = 2(-2)^2 - 3(-2) + 1.
  2. Square first: (-2)^2 = 4, so the first term is 2 x 4 = 8.
  3. The middle term is -3 x -2 = +6.
  4. Add the pieces: 8 + 6 + 1 = 15.

Answer: 15

Question 4: A straight line passes through (2, 5) and (6, 17). What is its equation in slope-intercept form?

Exam level · functions and coordinate graphs

  1. y = 3x - 1
  2. y = 3x + 1
  3. y = 4x - 3
  4. y = 2x + 1
Show the worked answer
  1. Slope = change in y / change in x = (17 - 5) / (6 - 2) = 12 / 4 = 3.
  2. Put the slope into y = 3x + b and use the point (2, 5).
  3. 5 = 3(2) + b, so 5 = 6 + b and b = -1.
  4. The line is y = 3x - 1. Check (6, 17): 3(6) - 1 = 17.

Answer: y = 3x - 1

Question 5: Solve the system 3x + 2y = 18 and 5x - 2y = 14.

Exam level · systems of equations

  1. x = 4, y = 3
  2. x = 3, y = 4
  3. x = 4, y = -3
  4. x = 2, y = 6
Show the worked answer
  1. The y terms are +2y and -2y, so adding the equations removes y.
  2. (3x + 5x) + (2y - 2y) = 18 + 14, which gives 8x = 32.
  3. Divide by 8: x = 4.
  4. Put x = 4 into 3x + 2y = 18: 12 + 2y = 18, so 2y = 6 and y = 3.

Answer: x = 4, y = 3

Question 6: Two adult tickets and three child tickets cost $37. One adult ticket and four child tickets cost $31. What does one child ticket cost?

Challenge level · systems of equations

  1. $5
  2. $7
  3. $11
  4. $6
Show the worked answer
  1. Let a be the adult price and c the child price: 2a + 3c = 37 and a + 4c = 31.
  2. The second equation gives a = 31 - 4c.
  3. Substitute: 2(31 - 4c) + 3c = 37, so 62 - 8c + 3c = 37 and 62 - 5c = 37.
  4. 5c = 25, so c = 5. A child ticket costs $5, and a = 31 - 20 = $11.

Answer: $5

Question 7: Simplify (3x^3)(4x^5).

Foundation level · exponents, polynomials, and quadratics

  1. 12x^8
  2. 12x^15
  3. 7x^8
  4. 12x^2
Show the worked answer
  1. Multiply the number parts: 3 x 4 = 12.
  2. When powers of the same base are multiplied, the exponents add.
  3. x^3 x x^5 = x^(3+5) = x^8.
  4. Putting the parts together gives 12x^8.

Answer: 12x^8

Question 8: Solve x^2 - 5x - 24 = 0.

Challenge level · exponents, polynomials, and quadratics

  1. x = 8 or x = -3
  2. x = -8 or x = 3
  3. x = 6 or x = -4
  4. x = 12 or x = -2
Show the worked answer
  1. Look for two numbers that multiply to -24 and add to -5.
  2. Try -8 and 3: (-8) x 3 = -24 and (-8) + 3 = -5, so that pair works.
  3. So x^2 - 5x - 24 factors as (x - 8)(x + 3) = 0.
  4. Each bracket can be zero: x = 8 or x = -3. Check x = 8: 64 - 40 - 24 = 0.

Answer: x = 8 or x = -3

How the three Algebra I difficulty levels differ

The difficulty buttons above change what a question asks of you, not just the size of the numbers. Each example below is taken from the question set on this page.

Difficulty levels for Algebra I practice, with an example question from this page.
LevelWhat it testsExample questionTime target
FoundationOne skill at a time, with the numbers kept small enough to check in your head.Solve 5x - 7 = 3x + 9.About 1 minute
ExamThe wording of a real test paper: pick the method first, then carry out two or three steps.Solve the inequality -3x + 4 > 19.2 to 3 minutes
ChallengeTwo ideas combined, or a result you have to interpret after the calculation ends.Two adult tickets and three child tickets cost $37. One adult ticket and four child tickets cost $31. What does one child ticket cost?4 to 5 minutes

How to practice Algebra I effectively

Begin without notes and explain your choice before checking. For every miss, identify whether the cause was a definition, setup, calculation, interpretation, or time decision. Re-solve the question from a blank page, then return to the same skill in a mixed set tomorrow.

What your Algebra I answer review should show

A useful review shows more than the correct option. Compare the method with your first attempt, locate the earliest incorrect decision, and write one rule that would prevent the same error in a new Algebra I problem.

Move from mixed Algebra I questions to a complete course

This page targets flexible Algebra I question practice. When you need a syllabus-aligned sequence with unit selection, use Algebra I practice by unit and return here later for mixed retrieval.

Questions about Algebra I practice

When should I change the difficulty?

Move up after you can solve several questions accurately without hints and explain the method. Move down for one short set when errors show that a definition or setup is still uncertain.

How often should I practice?

Short sessions on several days usually build stronger recall than one long session. Revisit missed Algebra I skills the next day, then mix them with older topics later in the week.

Where can I review the lessons in order?

Use Algebra I practice by unit for a syllabus-aligned sequence with unit selection, practice, and a complete answer review.

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