Pennsylvania · Algebra I end-of-course · From PDE’s test definition

Keystone Algebra 1 prep: the exam, module by module

The Keystone Algebra I is the end-of-course exam Pennsylvania students take when they finish Algebra I, often in grade 8 or 9. It is written to a published list: six assessment anchors, broken into eligible content statements (18 for Module 1 and 15 for Module 2), many with notes that say exactly how far a question can go. A trinomial to factor will have a leading coefficient of 1. A system will have two equations, never three. Knowing those limits changes how you prepare, because you can stop worrying about what is not on the test. This page reads PDE’s test definition and anchor document closely, then teaches both modules with problems of our own.

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In short

The Keystone Algebra I is Pennsylvania’s end-of-course Algebra I exam, set by the Pennsylvania Department of Education and taken online at or near the end of the course. It has two modules, each with 18 points of multiple-choice and technology-enhanced items and three 4-point constructed-response items, for 60 points in all, and no time limit. It is offered in winter, spring and summer. Modern Age Coders runs live online Keystone preparation, as a group batch or 1-on-1, built on the Algebra Foundations course.

Courses for the Keystone

Three courses for Pennsylvania Algebra I students

The first is the Keystone course itself; the other two sit either side of it.

Algebra Foundations course thumbnail

KEA / 01

Algebra I for the Keystone

All six anchors, both modules, with written constructed responses.

Open the syllabus →
Middle School Mathematics Mastery course thumbnail

KEA / 02

Before Algebra I

Integers, ratios and equations for students starting in grade 8.

Open the syllabus →
High School Mathematics course thumbnail

KEA / 03

After the Keystone

Geometry and Algebra II once Algebra I is banked.

Open the syllabus →

Two modules

How is the Keystone Algebra 1 exam structured?

In two modules of equal weight. Each module carries 18 points from multiple-choice and technology-enhanced items and 12 points from three constructed-response items, which makes 30 points per module.

Keystone Algebra I module design (PDE Keystone Exams Test Definition, Algebra I, read 31 October 2026)
Module 1: Operations and Linear Equations & InequalitiesModule 2: Linear Functions and Data Organization
Core MC/TE items18 points18 points
Core constructed response3 items, 4 points each, 12 points3 items, 4 points each, 12 points
Module total30 points30 points
Eligible content1815
Embedded field-test items5 MC/TE and 1 CR5 MC/TE and 1 CR
Testing time / administration time75 / 85 minutes75 / 85 minutes

Sixty points, forty percent written

PDE’s test definition sums it up: “a total of 60 points (Module 1 and Module 2 combined) with approximately 60% MC/TE items and 40% CR items.”

That 40 percent is unusually high for an end-of-course exam. Six constructed responses, each scored out of 4, decide a large share of the result, so writing out algebra clearly is not optional.

Field-test items

Each module also carries 5 field-test multiple-choice or technology-enhanced items and 1 field-test constructed response, which do not count. So a student sees 23 MC/TE items and 4 constructed responses in each module, and cannot tell which are field tests.

Treat every question as if it counts. That is the only sensible strategy when you cannot see the difference.

Source: Keystone Exams Test Definition, Algebra I, read on 31 October 2026. Modern Age Coders has no tie to the Pennsylvania Department of Education, to the company that delivers the Keystones, or to any school district.

Assessment anchors

What is on the Keystone Algebra 1 exam?

Six assessment anchors, three per module. PDE counts 18 pieces of eligible content in Module 1 and 15 in Module 2, and its anchor document lists every one, with notes that limit how hard a question can be.

Keystone Algebra I assessment anchors and selected eligible content limits (PDE Assessment Anchors and Eligible Content, Algebra I, April 2014 final, read 31 October 2026)
AnchorWhat it coversA limit PDE writes into the eligible content
A1.1.1 Operations with Real Numbers and ExpressionsComparing reals, square roots, GCF and LCM of monomials, exponents, estimation, polynomials, factoring, rational expressionsPolynomial products: “Nothing larger than a binomial multiplied by a trinomial.”
A1.1.2 Linear EquationsWriting and solving linear equations, justifying steps by properties, systemsSystems: “Limit systems to two linear equations.”
A1.1.3 Linear InequalitiesCompound inequalities on a number line, systems of inequalities by graphingCompound inequalities may include absolute value inequalities
A1.2.1 FunctionsPatterns, whether a relation is a function, domain and range, linear functions in tables, graphs and equationsRelations may be given as ordered pairs, a graph or a table
A1.2.2 Coordinate GeometryRate of change, slope, writing linear equations, trend linesSlope and intercept read from an equation or a graph
A1.2.3 Data AnalysisRange, quartiles and interquartile range, predictions from displays, compound probabilityProbabilities shown as a fraction, decimal or percent

The limits that save time

Factoring: trinomials are limited to the form ax² + bx + c where a equals 1 after factoring out all monomial factors, in PDE’s wording. So 2x² + 10x + 12 can appear (it becomes 2(x² + 5x + 6)), but a trinomial needing the “ac method” with a leading 3 cannot.

Exponents: PDE notes that exponents should be integers from -10 to 10. No fractional exponents, so radicals are handled as square roots, as in the anchor document’s own example, “Simplify square roots (e.g., √24 = 2√6).”

What surprises students

Module 2 is not all functions. Data Analysis is a full anchor: quartiles, box-and-whisker plots, stem-and-leaf plots, scatter plots and compound probability all live there.

And Module 1 asks students to identify the algebraic property that justifies a step in solving an equation. Knowing the names (distributive, additive property of equality) earns points here.

Source: Keystone Exams: Algebra I Assessment Anchors and Eligible Content, PDE.

Calculator and formula sheet

Is a calculator allowed on the Keystone Algebra 1, and what is on the formula sheet?

Students may use a calculator that meets PDE’s calculator policy, and they get the Algebra I formula sheet both on paper and inside the online test.

Calculator rules

PDE’s policy bans phones and other devices, wireless or computer algebra system (CAS) calculators, and sharing. A test administrator wipes the memory both before the session starts and once it ends.

Paper formula sheet

The 2026 to 2027 winter handbook says Algebra I students should receive a paper copy of the formula sheet, which is also available within the online test.

What the sheet holds

Slope, point-slope, slope-intercept and standard forms of a line, the arithmetic properties, and rectangle and prism formulas.

The sheet also says: “You may use calculator π or the number 3.14 as an approximation of π.” More usefully for Module 1, it lists the properties by name, the distributive, commutative, associative and identity properties and the additive and multiplicative properties of equality, so a student asked to justify a step can find the right word on the page in front of them. We teach with the real sheet from the first week.

Sources: Algebra I Formula Sheet and the 2026 to 2027 Winter Keystone Handbook for Assessment Coordinators, PDE.

2026 to 2027

When is the Keystone Algebra 1 exam in 2026 to 2027?

Four times: Winter Wave 1 from December 7 to 18, 2026; Winter Wave 2 from January 4 to 15, 2027; Spring from May 17 to 28, 2027; and Summer from July 26 to 30, 2027.

Keystone Exams testing windows (PDE Keystone Exams page, read 31 October 2026)
Window2026 to 20272027 to 2028
Winter Wave 1December 7 to 18, 2026December 6 to 17, 2027
Winter Wave 2January 4 to 15, 2027January 3 to 14, 2028
SpringMay 17 to 28, 2027May 15 to 26, 2028
SummerJuly 26 to 30, 2027July 24 to 28, 2028
Which wave fits which student (our planning guide, not PDE advice)
StudentLikely waveWhy
Block schedule, Algebra I in the fall semesterWinter Wave 1 or 2The exam sits at or near the end of the course
Full-year Algebra ISpring, May 17 to 28, 2027Right after the course ends
Retaking to reach proficiencyAny later wave, often winterTime to rebuild the weaker module first
Summer course or summer reviewSummer, July 26 to 30, 2027A short window, so plan early

The school decides when a student tests, so confirm the wave with the counselor. PDE’s parent FAQ also notes that districts can give the two modules on two days, or in the morning and afternoon of one day.

Constructed response, Module 1

How do you answer a Keystone Algebra 1 constructed-response question?

Every part answered, every step shown, and the answer interpreted in the situation. Here is a Module 1 problem we wrote around a compound inequality, eligible content A1.1.3.1.1 and A1.1.3.1.3.

  1. Our problem (not a Keystone item). A climbing gym charges a 30 sign-up fee plus 12 per visit. Maya wants to spend at least 150 and at most 240 this season. Part A: write a compound inequality for v, the number of visits. Part B: solve it and graph the solution on a number line. Part C: explain what the solution means for Maya, and say whether 19 visits is possible.
  2. Part A. The cost is 30 + 12v, so 150 ≤ 30 + 12v ≤ 240.
  3. Part B. Subtract 30 from all three parts: 120 ≤ 12v ≤ 210. Divide all three parts by 12: 10 ≤ v ≤ 17.5. On the number line, closed dots at 10 and 17.5 with the segment between them shaded.
  4. Part C. Visits must be whole numbers, so Maya can make 10, 11, 12 and so on up to 17 visits. 19 visits is not possible: 30 + 12 x 19 = 258, which is more than 240. Interpreting the solution in context, as A1.1.3.1.3 asks, is where the whole-number limit comes from.
  5. Where the four points come from, as we teach it. A correct inequality; correct solving with the operation done to all three parts; a correct graph; and an interpretation that rounds down to 17 and rejects 19 with a calculation. Spelling does not count; PDE’s FAQ says scores are based on content only.

The slip we see most

Subtracting 30 from the middle only, or from only one side. A compound inequality is three expressions at once, and every operation goes to all three.

The habit that fixes it

Write the three parts in columns and act on each column in turn. It looks slow and it is fast.

Module 2 in practice

What does a Keystone Module 2 question on data and trend lines look like?

Module 2 joins linear functions to data. Eligible content A1.2.2.2.1 asks students to write an equation for a line of best fit, and A1.2.3.2.3 to predict from it. Here is our example.

  1. Our data (invented). A plant’s height in centimeters over weeks: week 1, 4 cm; week 2, 7 cm; week 4, 12 cm; week 6, 18 cm. Part A: estimate a trend line. Part B: interpret the slope. Part C: predict the height at week 8.
  2. Part A. Use two points near the trend, say (2, 7) and (6, 18). Slope = (18 - 7) / (6 - 2) = 11/4 = 2.75. Point-slope form from the formula sheet: y - 7 = 2.75(x - 2), so y = 2.75x + 1.5.
  3. Part B. The slope 2.75 means the plant grows about 2.75 cm per week. The intercept 1.5 is the model’s height at week 0, which may not match reality, and saying so shows understanding.
  4. Part C. At x = 8: y = 2.75 x 8 + 1.5 = 23.5 cm. Prediction beyond the data assumes the trend continues, which a good answer mentions.

Different students may pick different points and get slightly different lines. That is expected with a trend line: what matters is a reasonable line, the formula used correctly, and a prediction read from it with the right units.

Graduation

Do you have to pass the Keystone Algebra 1 to graduate in Pennsylvania?

Proficiency on the Algebra I Keystone is one way to meet the statewide requirement, but not the only one. Since the class of 2023, Pennsylvania has offered five Pathways to Graduation.

What PDE says

PDE’s graduation page states: “Effective with the graduating class of 2023, Pennsylvania high school students have the option to demonstrate their postsecondary preparedness and meet statewide requirements through one of five Pathways to Graduation.”

Its parent FAQ adds that students should demonstrate proficiency on the Algebra I, Literature and Biology Keystones, or meet one of the other pathways, to graduate.

Banked, and retakeable

Keystone results are “banked until their junior year for accountability purposes and until their senior year for graduation purposes”, according to the FAQ. A grade 8 result can count years later.

The FAQ is equally clear that “All students who take a Keystone Exam may retake the exam.” A score below proficient is a reason to plan a later wave, not the end of the road.

Historically, PDE explains, the Keystones replaced the 11th-grade PSSA in math, reading and science in 2012 to 2013. Students still take the Algebra I Keystone for federal accountability whichever graduation pathway they use. Because pathways and local rules vary, ask the school counselor which route your teenager is on.

Sources: Statewide High School Graduation Requirements and the Keystone Exams parent FAQ (Spring 2026), PDE.

Practice

Twelve Keystone Algebra 1 practice questions, two per anchor

Written by us to the limits in PDE’s eligible content. They are not Keystone items or sampler questions.

Original practice by assessment anchor (ours), with answers
AnchorQuestionAnswer
A1.1.1Simplify the square root of 48.4 times the square root of 3
A1.1.1Factor x² - 3x - 28.(x - 7)(x + 4)
A1.1.2Solve 5(x - 2) = 3x + 6, and name the property used in the first step.x = 8; distributive property
A1.1.2Solve the system x + y = 10 and 2x - y = 5.(5, 5)
A1.1.3Solve and graph -3 < 2x + 1 ≤ 9.-2 < x ≤ 4
A1.1.3Solve |x - 4| < 3.1 < x < 7
A1.2.1Is {(2, 5), (3, 5), (4, 6)} a function? Give its domain.Yes; domain {2, 3, 4}
A1.2.1A table shows x = 0, 1, 2 and y = 3, 7, 11. Write the linear function.y = 4x + 3
A1.2.2Find the slope through (-1, 4) and (3, -4).-2
A1.2.2Write the equation of the line with slope 1/2 through (4, 1).y = (1/2)x - 1
A1.2.3Find the interquartile range of 3, 5, 6, 8, 10, 12, 15, 18.8 (Q1 = 5.5, Q3 = 13.5)
A1.2.3A bag has 4 red and 6 blue marbles. One is drawn, replaced, and another drawn. Find P(red then blue).24/100 = 0.24

Algebra I Item and Scoring Samplers are published on PDE’s Keystone Exams page. The page notes that because testing was cancelled in 2019 to 2020, the 2021 samplers are revised and enhanced versions of the 2017 ones. The Online Tools Training, PDE says, also lets students practise graphing functions and entering equations with the equation builder before test day. We use both in the final weeks.

A plan

An eight-week Keystone Algebra 1 study plan

Ours, counting back from the student’s wave: for the spring, from May 17, 2027.

  1. Week 1: a sampler, sorted by anchor. One module from PDE’s sampler, every miss tagged A1.1.1 to A1.2.3.
  2. Weeks 2 and 3: Module 1, anchors A1.1.1 and A1.1.2. Square roots, exponents, factoring within PDE’s limits, linear equations and two-equation systems.
  3. Week 4: anchor A1.1.3. Compound and absolute value inequalities, and systems of inequalities by graphing.
  4. Weeks 5 and 6: Module 2. Functions, slope and linear equations, then the full Data Analysis anchor: quartiles, displays, trend lines and compound probability.
  5. Week 7: constructed responses. Two four-point problems a lesson, one from each module, with the formula sheet beside them.
  6. Week 8: two modules, two sittings. A rehearsal in the format the school will use, then rest before the wave.

Starting points

Four kinds of Keystone student, and where each should start

Our experience of who arrives for Keystone help, and what to do first.

Starting points (ours)
StudentFirst focusThen
Grade 8, Algebra I a year earlyInteger and fraction fluency under algebraModule 1 anchors in order
Grade 9, solid course gradeConstructed-response writingThe Data Analysis anchor
Retaking after Below Basic or BasicThe weaker module from the score reportA later wave with time to rebuild
Strong student wanting AdvancedEligible content edge casesTimed full modules

For parents

Ask which wave your child is entered for. Block schedules often mean December or January, not May.

If the result is below proficient, ask about the next wave and the pathways. A retake is allowed.

For students

Learn the property names on the formula sheet. Module 1 can ask you to justify a step.

In every constructed response, finish with a sentence that answers the question in the situation’s own words.

The catalogue

Math courses around Keystone Algebra I

Before, during and after the Algebra I year.

I

Before Algebra I

Grades 6 to 8

KEA / P / 03

Math competitions

For grade 7 and 8 problem solvers.

Open the syllabus
II

The Keystone year

Algebra I
III

After the Keystone

High school

How lessons run

Algebra lessons on Eastern Time, around every wave

Weekdays or weekends, flexible: choose your batch, or for a very personalised plan choose 1-on-1 at your convenience, weekend mornings or weekdays.

After school ET

Weekly lessons through the Algebra I course.

Weekends

Module rehearsals before December, January and May.

1-on-1

Retake plans built from the score report.

Anchor-mapped

Every lesson tagged to PDE’s eligible content.

Written answers

A four-point response most weeks.

Formula sheet

PDE’s own sheet from week one.

Data anchor

Quartiles and probability, not skipped.

Samplers late

PDE’s released items to rehearse.

Group or solo

Fifteen to twenty, or one to one.

Student work

Built by our students

Some students turn their algebra into small programs. See student labs.

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Pennsylvania families ask

Keystone Algebra 1: common questions

When is the Keystone Algebra 1 exam in 2027?

PDE lists Winter Wave 2 from January 4 to 15, 2027, Spring from May 17 to 28, 2027 and Summer from July 26 to 30, 2027, after Winter Wave 1 in December 2026. The school decides which wave a student takes.

How many questions are on the Keystone Algebra 1?

Each module has 23 multiple-choice or technology-enhanced items and 4 constructed responses, including field-test items. The scored part is 18 MC/TE points and three 4-point constructed responses per module, 60 points in all.

How long is the Keystone Algebra 1 exam?

There is no time limit. PDE's parent FAQ says a typical student needs two to three hours, and each module about one to one and a half hours.

What is on Module 1 and Module 2 of the Algebra 1 Keystone?

Module 1 covers operations with real numbers and expressions, linear equations and linear inequalities. Module 2 covers functions, coordinate geometry and data analysis, including probability.

Is a calculator allowed on the Algebra 1 Keystone?

Yes, one that follows the state calculator policy. Phones, wireless calculators, computer algebra system calculators and shared calculators are not allowed, and the memory is cleared before and after each session.

Is there a formula sheet for the Algebra 1 Keystone?

Yes. Students receive a paper copy and can also open it in the online test. It includes the forms of a linear equation, slope and the arithmetic properties.

Do you need to pass the Keystone Algebra 1 to graduate?

Proficiency is one route, but since the class of 2023 Pennsylvania has offered five Pathways to Graduation. Check with the school counselor which pathway applies to your student.

Can you retake the Keystone Algebra 1?

Yes. PDE's parent FAQ says all students who take a Keystone Exam may retake it, and results are banked until senior year for graduation purposes.

Where can I find Keystone Algebra 1 practice tests?

PDE posts Item and Scoring Samplers on its Keystone Exams page, with the 2021 set revised from 2017. Our twelve questions here add two more for each anchor.

When are your classes?

Weekdays or weekends, flexible: choose your batch, or for a very personalised plan choose 1-on-1 at your convenience, weekend mornings or weekdays. Every Keystone lesson is set on Eastern Time.

Is Modern Age Coders part of the Keystone program?

No. We are a separate, independent online school. PDE writes and runs the Keystone Exams, and we have no link to it, to its testing vendor or to any district; we only cite and link the department's public documents.

Elsewhere on this site

Related pages

Next steps and Pennsylvania pages.

Eighth grade math tutoring

For early Algebra I students.

Middle school math placement

Getting into Algebra I in grade 8.

Precalculus tutoring

Two courses after the Keystone.

PSAT 8/9 math prep

The same algebra, a different test.

Pennsylvania coding and AI

Python and AI alongside Algebra I.

SAT math tutoring

Where Keystone algebra leads next.

Related pages in this guide

Part of the guide: US state math tests by state

High school end-of-course and graduation tests

State tests, grades 3 to 8

Standards behind the tests

More guides: US gifted and selective school tests · US math placement and college readiness tests · Homeschool and school math curricula guide · US math and coding competitions guide

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