The Pennsylvania Keystone Algebra 1 Exam is an end-of-course assessment designed to measure student proficiency in Algebra 1 content. Unlike the PSSA, which all students take in grades 3–8, the Keystone Exam is taken when a student has completed an Algebra 1 course — typically in high school, though some students take it in eighth grade. Reaching the “Proficient” level on the Keystone Algebra 1 exam is one pathway toward satisfying Pennsylvania’s graduation requirements.
This guide covers exactly what is on the Keystone Algebra 1 exam, the official performance levels and score scale, sample problems with solutions, and a structured prep plan.
ViewMath is not affiliated with or endorsed by the Pennsylvania Department of Education. For official Keystone Exam information, visit pa.gov/agencies/education.
Keystone Algebra 1 Exam: Quick Facts
According to the Pennsylvania Department of Education, the Keystone Algebra 1 Exam:
- Is an end-of-course assessment in Algebra 1
- Is scored on a scale of 1200–1800
- Has four performance levels: Below Basic (1200–1438), Basic (1439–1499), Proficient (1500–1545), and Advanced (1546–1800)
- Covers two Assessment Anchor modules: Operations and Linear Equations & Inequalities; and Linear Functions and Data Organizations
- Includes multiple-choice and constructed-response questions
Pennsylvania has established Pathways to Graduation that provide alternative options for students who do not reach Proficient on the Keystone Exam. Check with your school counselor or the Pennsylvania Department of Education for the most current graduation requirements.
Keystone Algebra 1: Topic Areas
Module 1: Operations and Linear Equations & Inequalities
This module covers the algebraic skills central to a first-year algebra course:
Operations with Real Numbers
- Properties of real numbers: commutative, associative, distributive, identity, and inverse
- Simplifying numerical and algebraic expressions
- Operations with integers, fractions, and decimals
- Absolute value
- Square roots of perfect squares; approximating irrational square roots
Linear Equations in One and Two Variables
- Solving one-step and multi-step linear equations
- Solving equations with variables on both sides
- Writing and solving equations to model real-world problems
- Understanding equations that have one solution, infinitely many solutions, or no solution
Linear Inequalities
- Solving and graphing linear inequalities in one variable on a number line
- Solving compound inequalities (and/or)
- Interpreting inequality solutions in context
Systems of Linear Equations
- Solving systems by graphing, substitution, and elimination
- Interpreting solutions: one solution (consistent independent), no solution (inconsistent), infinitely many solutions (dependent)
- Solving word problems using systems of equations
Module 2: Linear Functions and Data Organizations
Properties of Linear Functions
- Identifying functions from tables, graphs, and mappings
- Slope as rate of change; calculating slope from two points or from a graph
- Writing equations in slope-intercept form (y = mx + b) and point-slope form
- Interpreting slope and y-intercept in context
- Graphing linear equations on the coordinate plane
- Parallel and perpendicular lines: relationships between slopes
Polynomials and Factoring
- Adding, subtracting, and multiplying polynomials
- Factoring: GCF, trinomials, and difference of squares
- Using factoring to solve quadratic equations
Data Analysis
- Reading and interpreting scatter plots
- Identifying linear, nonlinear, positive, and negative associations
- Drawing and using trend lines to make predictions
- Two-way frequency tables: interpreting joint and marginal frequencies
Sample Keystone Algebra 1 Problems
Linear Equations
Solve: 3(x − 4) = 2x + 7.
Solution: 3x − 12 = 2x + 7. 3x − 2x = 7 + 12. x = 19. Answer: x = 19.
Systems of Equations
Two students collect cans for a food drive. Together they collect 52 cans. One student collects 8 more cans than the other. How many cans does each student collect?
Solution: Let x = first student, y = second student. x + y = 52 and x = y + 8. Substituting: (y + 8) + y = 52. 2y + 8 = 52. 2y = 44. y = 22. x = 30. Answer: 30 cans and 22 cans.
Slope-Intercept Form
Write an equation in slope-intercept form for a line that passes through (0, −3) and (4, 5).
Solution: Slope = (5 − (−3))/(4 − 0) = 8/4 = 2. y-intercept = −3 (given by the point (0, −3)). Equation: y = 2x − 3. Answer: y = 2x − 3.
Factoring
Factor completely: x² − 9x + 18.
Solution: Find two numbers that multiply to 18 and add to −9: those are −3 and −6. Factored form: (x − 3)(x − 6). Answer: (x − 3)(x − 6).
Common Keystone Algebra 1 Mistakes
- Sign errors when solving equations: The most common error on Keystone Algebra 1 is dropping or reversing a negative sign when moving terms across the equals sign. Always check by substituting the solution back into the original equation.
- Slope formula: confusing rise and run: Slope = rise/run = (y₂ − y₁)/(x₂ − x₁). A common error is computing (x₂ − x₁)/(y₂ − y₁). Label each coordinate pair before substituting.
- Systems: substituting into the derived equation instead of the original: After solving for one variable, always substitute back into one of the original equations — not the equation you derived. This is a source of verification errors.
- Factoring sign errors: In x² − bx + c, both factors have negative signs. In x² + bx − c, one factor is positive and one is negative. Drawing a sign chart before guessing factor pairs saves time.
Keystone Algebra 1 Study Plan
Weeks 1–2: Module 1 — Operations and Linear Equations
Review real number properties and simplifying expressions. Practice solving multi-step linear equations (including those with variables on both sides, fractions, and distributive property). Cover linear inequalities — solving, graphing, and writing. Cover systems of equations by all three methods (graphing, substitution, elimination), emphasizing word problem setup.
Weeks 3–4: Module 2 — Linear Functions and Data
Cover slope, slope-intercept form, and point-slope form. Practice writing equations from two points, from a slope and y-intercept, and from contextual scenarios. Cover polynomial operations and factoring. Finish with scatter plots, trend lines, and two-way frequency tables. End with a full mixed practice test covering both modules.
Pennsylvania Algebra 1 Resources
ViewMath offers Algebra 1 practice test books, study guides, and workbooks aligned to the skills assessed on the Pennsylvania Keystone Algebra 1 Exam. Browse the full Algebra 1 collection in the sidebar below.
ViewMath is an independent publisher. Our materials are not official Keystone Exam materials and are not affiliated with the Pennsylvania Department of Education.
