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Pennsylvania Keystone Exam · Algebra 1

Keystone Algebra 1 Practice: Free Practice Problems, Practice Exams and Worked Solutions

Prepare for the Pennsylvania Keystone Algebra 1 exam with practice problems written to every assessment anchor and eligible content skill, in the same multiple-choice and constructed-response format as the real test.

Try free Keystone Algebra 1 practiceSee Keystone practice exams

Keystone Algebra 1 exam format

The Keystone Algebra 1 exam is split into two modules. Each module has 18 multiple-choice questions and 3 constructed-response questions.

PartMultiple choiceConstructed responsePoints
Module 1 · Operations and Linear Equations & Inequalities18 (1 point each)3 (4 points each)30
Module 2 · Linear Functions and Data Organization18 (1 point each)3 (4 points each)30
Total36660

What's on the Keystone Algebra 1 exam: every assessment anchor and skill

Our Keystone Algebra 1 practice covers all six assessment anchors and 34 eligible content skills. Every practice problem is tagged to the skill it tests.

Module 1: Operations and Linear Equations & Inequalities

A1.1.1 · Operations with Real Numbers and Expressions

  • A1.1.1.1.1 Compare and order real numbers
  • A1.1.1.1.2 Simplify square roots
  • A1.1.1.2.1 GCF and LCM of monomials
  • A1.1.1.3.1 Exponents, roots and absolute value
  • A1.1.1.4.1 Estimation
  • A1.1.1.5.1 Add, subtract and multiply polynomials
  • A1.1.1.5.2 Factor algebraic expressions
  • A1.1.1.5.3 Simplify rational expressions

A1.1.2 · Linear Equations

  • A1.1.2.1.1 Write, solve and apply linear equations
  • A1.1.2.1.2 Properties that justify equation-solving steps
  • A1.1.2.1.3 Interpret solutions of linear equations
  • A1.1.2.2.1 Write and solve systems of linear equations
  • A1.1.2.2.2 Interpret solutions of systems in context

A1.1.3 · Linear Inequalities

  • A1.1.3.1.1 Compound and absolute-value inequalities
  • A1.1.3.1.2 Linear inequalities on a number line
  • A1.1.3.1.3 Interpret inequality solutions in context
  • A1.1.3.2.1 Graph systems of linear inequalities
  • A1.1.3.2.2 Interpret systems of inequalities in context

Module 2: Linear Functions and Data Organization

A1.2.1 · Functions

  • A1.2.1.1.1 Patterns and arithmetic sequences
  • A1.2.1.1.2 Decide whether a relation is a function
  • A1.2.1.1.3 Domain and range
  • A1.2.1.2.1 Use linear functions: equation, graph, table
  • A1.2.1.2.2 Translate between representations of a linear function

A1.2.2 · Coordinate Geometry

  • A1.2.2.1.1 Constant rates of change
  • A1.2.2.1.2 Apply rate of change (slope)
  • A1.2.2.1.3 Write or identify a linear equation
  • A1.2.2.1.4 Slope and y-intercept
  • A1.2.2.2.1 Line of best fit
  • A1.2.2.2.2 Predict from a line of best fit

A1.2.3 · Data Analysis

  • A1.2.3.1.1 Range, quartiles and interquartile range
  • A1.2.3.1.2 Mean, median and mode
  • A1.2.3.2.1 Estimate or predict from data
  • A1.2.3.2.2 Analyze box plots, stem-and-leaf plots and scatter plots
  • A1.2.3.3.1 Probability of compound events

Free Keystone Algebra 1 practice problems with answers

Try these sample Keystone Algebra 1 practice questions, one from each assessment anchor. Open each one to see the answer and a step-by-step worked solution.

Sample 1 · A1.1.1 · Operations with Real Numbers and Expressions

Simplify. Assume x ≥ 0.

√72x3
  1. A6x√2x
  2. B2x√6x
  3. C12x√2x
  4. D6x2√2x
Show the answer and worked solution

Answer: A. Split into perfect squares: 72x3 = 36 · x2 · 2x. The square root of 36x2 is 6x, so the result is 6x√2x.

Sample 2 · A1.1.2 · Linear Equations

A gym charges a $25 sign-up fee plus $15 per month. Dana has paid $130 in total. For how many months has Dana been a member?

  1. A7 months
  2. B8 months
  3. C5 months
  4. D10 months
Show the answer and worked solution

Answer: A. Write the equation 25 + 15m = 130. Subtract 25: 15m = 105, so m = 7 months.

Sample 3 · A1.1.3 · Linear Inequalities

Solve the inequality.

4x + 7 ≤ 2x − 5
  1. Ax ≤ −6
  2. Bx ≥ −6
  3. Cx ≤ −1
  4. Dx ≥ 6
Show the answer and worked solution

Answer: A. Subtract 2x from both sides: 2x + 7 ≤ −5. Subtract 7: 2x ≤ −12. Divide by 2 (positive, so the sign stays): x ≤ −6.

Sample 4 · A1.2.1 · Functions

The function f is defined below. What is the value of f(−2)?

f(x) = x2 − 3x + 1
  1. A−9
  2. B−1
  3. C3
  4. D11
Show the answer and worked solution

Answer: D. Substitute −2 for every x: (−2)2 − 3(−2) + 1 = 4 + 6 + 1 = 11. Squaring a negative gives a positive, and subtracting a negative adds.

Sample 5 · A1.2.2 · Coordinate Geometry

A line passes through (2, 5) and (6, −3). Which equation represents the line?

  1. Ay = 2x + 1
  2. By = −2x + 1
  3. Cy = −2x + 9
  4. Dy = −12x + 6
Show the answer and worked solution

Answer: C. Slope: −3 − 56 − 2 = −84 = −2. Use (2, 5): 5 = −2(2) + b, so b = 9. The line is y = −2x + 9.

Sample 6 · A1.2.3 · Data Analysis

A coin is flipped and a number cube is rolled. What is the probability of getting heads and a 6?

  1. A112
  2. B23
  3. C18
  4. D712
Show the answer and worked solution

Answer: A. The events are independent, so multiply: 12 · 16 = 112. Adding the two probabilities instead of multiplying them gives 23, a common mistake.

Practice more free Keystone Algebra 1 problems → Free practice includes 5 multiple-choice and 5 constructed-response problems for every skill.

Everything in Keystone Algebra 1 practice

  • 3,400 multiple-choice practice problems: 100 for every Keystone Algebra 1 skill.
  • 2,000 constructed-response practice problems in the Keystone format, with an equation editor, interactive number-line graphing and teacher scoring.
  • Full-length Keystone Algebra 1 practice exams: Module 1, Module 2 or the full 36 + 6 exam, scored like the real test.
  • A worked solution for every problem, right or wrong.
  • Teacher dashboards: class scores by assessment anchor, strongest and weakest topics, custom assignments and Google Classroom.

Frequently asked questions

What is on the Keystone Algebra 1 exam?

The Pennsylvania Keystone Algebra 1 exam has two modules. Module 1 covers operations with real numbers and expressions, linear equations, and linear inequalities. Module 2 covers functions, coordinate geometry, and data analysis. Each module has multiple-choice and constructed-response questions.

How many questions are on the Keystone Algebra 1 exam?

Each module has 18 multiple-choice questions worth 1 point each and 3 constructed-response questions worth 4 points each, for 36 multiple-choice and 6 constructed-response questions in all.

Is there free Keystone Algebra 1 practice?

Yes. Anyone can practice 5 multiple-choice and 5 constructed-response problems for every Keystone Algebra 1 skill on Advanced Insight Academy for free, with worked solutions, no account needed.

How should I study for the Keystone Algebra 1 exam?

Practice one assessment anchor at a time, read the worked solution for every problem you miss, and practice constructed-response questions where you show your work. Then take a full-length practice exam under test-like conditions.

What is a constructed-response question?

A constructed-response question has several parts. You write answers and show or explain your work instead of choosing from answer choices. On the Keystone Algebra 1 exam, each one is worth 4 points.

Start practicing for the Keystone Algebra 1 exam

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