100+ Free Keystone Algebra I Practice Questions

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Key Facts: Keystone Algebra I Exam

2 Modules

Exam structure

Pennsylvania Department of Education

1500

Proficient cut score

PDE Assessment Standards

Untimed

Time limit

PDE INSIGHT Testing Guide

The Pennsylvania Keystone Algebra I exam measures proficiency across two modules covering real numbers, polynomials, linear equations and inequalities, functions, linear graphing, data analysis, and probability. Passing (Proficient or Advanced) is a high school graduation pathway requirement in Pennsylvania.

Sample Keystone Algebra I Practice Questions

Try these sample questions to test your Keystone Algebra I exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Simplify the radical expression completely: \(\sqrt{72}\).

A.\(6\sqrt{2}\)

B.\(2\sqrt{6}\)

C.\(36\sqrt{2}\)

D.\(12\sqrt{2}\)

Explanation: To simplify \(\sqrt{72}\), factor 72 into its largest perfect square factor: \(72 = 36 \times 2\). Then, \(\sqrt{72} = \sqrt{36} \times \sqrt{2} = 6\sqrt{2}\).

2Simplify the monomial product: \((3x^4)(4x^5)\).

A.\(12x^{20}\)

B.\(7x^9\)

C.\(12x^9\)

D.\(7x^{20}\)

Explanation: Multiply the numerical coefficients: \(3 \times 4 = 12\). Apply the product rule for exponents \(x^a \cdot x^b = x^{a+b}\): \(x^4 \cdot x^5 = x^{4+5} = x^9\). Combining gives \(12x^9\).

3Simplify the expression using exponent rules: \((2x^3)^4\).

A.\(8x^{12}\)

B.\(16x^{12}\)

C.\(16x^7\)

D.\(8x^7\)

Explanation: Apply the power of a product rule: \((2x^3)^4 = 2^4 \cdot (x^3)^4\). Compute \(2^4 = 16\) and use the power rule for exponents \((x^a)^b = x^{a \cdot b}\) to get \((x^3)^4 = x^{12}\). Thus, the answer is \(16x^{12}\).

4Express the number \(0.00045\) in standard scientific notation.

A.\(4.5 \times 10^{-4}\)

B.\(4.5 \times 10^{-5}\)

C.\(45 \times 10^{-5}\)

D.\(4.5 \times 10^4\)

Explanation: Move the decimal point 4 places to the right to place it after the first non-zero digit (4), obtaining 4.5. Since the original number is less than 1, the exponent on 10 is \(-4\), yielding \(4.5 \times 10^{-4}\).

5Which of the following numbers is an irrational number?

A.\(\sqrt{16}\)

B.\(0.\overline{3}\)

C.\(\sqrt{20}\)

D.\(-\frac{7}{4}\)

Explanation: An irrational number cannot be expressed as a ratio of two integers. \(\sqrt{20} = 2\sqrt{5}\) is non-repeating and non-terminating, making it irrational. \(\sqrt{16} = 4\), \(0.\overline{3} = 1/3\), and \(-7/4\) are all rational numbers.

6Simplify the algebraic expression with negative exponents: \(\frac{24a^6b^{-2}}{4a^{-2}b^3}\).

A.\(\frac{6a^8}{b^5}\)

B.\(\frac{6a^4}{b^5}\)

C.\(6a^8b\)

D.\(\frac{6a^4}{b}\)

Explanation: Divide numerical coefficients: \(24 / 4 = 6\). For variable \(a\): \(a^{6 - (-2)} = a^{6+2} = a^8\). For variable \(b\): \(b^{-2 - 3} = b^{-5} = 1/b^5\). Combining gives \(\frac{6a^8}{b^5}\).

7Simplify the expression by combining like radical terms: \(3\sqrt{20} - 2\sqrt{45} + \sqrt{80}\).

A.\(4\sqrt{5}\)

B.\(2\sqrt{5}\)

C.\(5\sqrt{5}\)

D.\(6\sqrt{5}\)

Explanation: Simplify each radical: \(3\sqrt{20} = 3(2\sqrt{5}) = 6\sqrt{5}\); \(-2\sqrt{45} = -2(3\sqrt{5}) = -6\sqrt{5}\); \(\sqrt{80} = 4\sqrt{5}\). Combine like radicals: \(6\sqrt{5} - 6\sqrt{5} + 4\sqrt{5} = 4\sqrt{5}\).

8Estimate the value of \(\sqrt{130}\) to the nearest tenth.

A.\(11.1\)

B.\(11.4\)

C.\(11.7\)

D.\(12.1\)

Explanation: Identify surrounding perfect squares: \(121 < 130 < 144\), so \(11 < \sqrt{130} < 12\). Since 130 is 9 away from 121 and 14 away from 144, \(\sqrt{130} \approx 11.4017\). Rounded to the nearest tenth, this is 11.4.

9Evaluate \((4 \times 10^5) \times (3 \times 10^{-8})\) and express the result in standard scientific notation.

A.\(1.2 \times 10^{-2}\)

B.\(1.2 \times 10^{-3}\)

C.\(12 \times 10^{-3}\)

D.\(1.2 \times 10^{-13}\)

Explanation: Multiply numbers: \(4 \times 3 = 12\). Combine powers of 10: \(10^5 \times 10^{-8} = 10^{5 + (-8)} = 10^{-3}\). This yields \(12 \times 10^{-3}\). Adjust to scientific notation: \(12 = 1.2 \times 10^1\), so \((1.2 \times 10^1) \times 10^{-3} = 1.2 \times 10^{-2}\).

10Simplify the expression with rational exponents: \(\left(\frac{8x^9}{27y^6}\right)^{\frac{2}{3}}\).

A.\(\frac{4x^6}{9y^4}\)

B.\(\frac{2x^3}{3y^2}\)

C.\(\frac{4x^3}{9y^2}\)

D.\(\frac{16x^6}{81y^4}\)

Explanation: Apply power \(2/3\) to each factor: \(8^{2/3} = (\sqrt[3]{8})^2 = 2^2 = 4\); \(27^{2/3} = (\sqrt[3]{27})^2 = 3^2 = 9\); \((x^9)^{2/3} = x^{9 \cdot \frac{2}{3}} = x^6\); \((y^6)^{2/3} = y^{6 \cdot \frac{2}{3}} = y^4\). Combining gives \(\frac{4x^6}{9y^4}\).

About the Keystone Algebra I Exam

The Pennsylvania Keystone Exam in Algebra I is an end-of-course assessment designed to assess student proficiency in Pennsylvania Core Standards for Algebra I. It covers Module 1 (Operations and Linear Equations & Inequalities) and Module 2 (Linear Functions and Data Organizations).

Assessment

Two modules: Module 1 (Operations and Linear Equations & Inequalities) and Module 2 (Linear Functions and Data Organizations), each with multiple-choice and constructed-response items aligned to the Algebra I Assessment Anchors and Eligible Content.

Time Limit

Untimed; PDE estimates about 75 minutes of testing per module (85-90 minutes per module including administration). Delivered online only beginning with the Spring 2026 administration.

Passing Score

1500 cut score for Proficient (1500-1545); 1546-1800 is Advanced on the 1200-1800 scale

Exam Fee

Free (administered by PA public school districts) (Pennsylvania Department of Education (PDE) & Data Recognition Corp (DRC))

Keystone Algebra I Exam Content Outline

15%

Real Numbers and Exponents

Simplify square roots, evaluate rational exponent expressions, convert scientific notation, and estimate irrational values.

15%

Polynomials and Factoring

Perform operations on polynomials and factor algebraic expressions using GCF, difference of squares, and trinomial methods.

10%

Linear Equations

Solve multi-step, absolute value, and literal linear equations in real-world contexts.

10%

Linear Inequalities and Systems

Solve single-variable compound inequalities and two-variable linear systems algebraically and graphically.

15%

Functions and Rate of Change

Analyze functional relationships, evaluate function expressions, identify domain/range, and compute rates of change.

15%

Linear Graphs and Forms

Write and convert linear equations in slope-intercept, point-slope, and standard forms; determine slope of parallel and perpendicular lines.

10%

Data Analysis and Scatter Plots

Model data with lines of best fit, analyze scatter plot trends, interpret box plots and stem-and-leaf diagrams.

10%

Probability and Statistics

Determine simple and compound theoretical/experimental probabilities and analyze statistical measures of center and spread.

How to Pass the Keystone Algebra I Exam

What You Need to Know

Passing score: 1500 cut score for Proficient (1500-1545); 1546-1800 is Advanced on the 1200-1800 scale
Assessment: Two modules: Module 1 (Operations and Linear Equations & Inequalities) and Module 2 (Linear Functions and Data Organizations), each with multiple-choice and constructed-response items aligned to the Algebra I Assessment Anchors and Eligible Content.
Time limit: Untimed; PDE estimates about 75 minutes of testing per module (85-90 minutes per module including administration). Delivered online only beginning with the Spring 2026 administration.
Exam fee: Free (administered by PA public school districts)

Keys to Passing

Work through all 100 available questions
Review every answer and explanation
Track weak areas and revisit them
Use our AI tutor for tough concepts

Keystone Algebra I Study Tips from Top Performers

1Master linear equation solving steps: distribution, combining like terms, isolating variables, and checking solution validity.

2Practice factoring techniques thoroughly, especially factoring out the GCF before attempting trinomial or difference-of-squares factoring.

3Understand the connection between linear functions, slope (m), y-intercept (b), and their contextual meanings in real-world problems.

4Review statistical graphs (box-and-whisker plots, scatter plots) and line-of-best-fit equation interpretations.

Frequently Asked Questions

What is the Pennsylvania Keystone Exam in Algebra I?

The Keystone Exam in Algebra I is a Pennsylvania state-mandated end-of-course assessment evaluating student mastery of algebraic concepts defined in the PA Assessment Anchors.

How is the Keystone Algebra I exam structured?

The exam is divided into two modules: Module 1 covers Operations and Linear Equations & Inequalities (50%), while Module 2 covers Linear Functions and Data Organizations (50%).

Is the Keystone Algebra I exam required for high school graduation in PA?

Yes, under Pennsylvania Act 158, achieving a Proficient or Advanced score on the Keystone Exams (or fulfilling an approved alternative pathway) is a state graduation requirement.

What scale score is needed to pass Keystone Algebra I?

Scores range from 1200 to 1800. A score of 1500–1545 earns a 'Proficient' rating, and 1546 or above earns an 'Advanced' rating.