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150 multiple-choice questions and 165 flashcards, organised into 8 chapters, written to the Common Core HS Algebra 1 standards blueprint. Every question carries a full rationale.
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Common Core HS Algebra 1 standards (HSN, HSA, HSF, HSS domains) — typical Algebra 1 course covers: real numbers and algebraic expressions, linear equations/inequalities, linear functions and graphs, systems of linear equations, exponents and exponential functions, polynomials, factoring, quadratic equations and functions, sequences/series. MCQs reference public Common Core math standards.
CoStudy's High School Algebra 1 bank holds 315 items organised into 8 chapters that follow the published blueprint. Every multiple-choice question carries a written rationale explaining why the correct answer is correct and why each distractor is tempting but wrong.
Each chapter follows a domain of the published exam outline. Practise one on its own:
A sample of 12 multiple-choice questions from the bank, with the full rationale shown.
Solve: 3(x + 2) = 2x + 11.
Answer: D — x = 5 (distribute: 3x + 6 = 2x + 11; subtract 2x: x + 6 = 11; subtract 6: x = 5)
Multi-step linear: distribute, then move variables to one side and constants to other. 3x+6 = 2x+11 → x = 5. Standard solving procedure: simplify each side, combine, isolate variable.
Subtract: (3x² + 5x − 2) − (x² − 4x + 7).
Answer: B — 2x² + 9x − 9
B) Distribute the minus: 3x² + 5x − 2 − x² + 4x − 7 = 2x² + 9x − 9. A) only distributes negative to first term.
If a relation has the points (1, 2), (2, 3), (1, 4), it is:
Answer: D — Not a function — the input 1 maps to two outputs (2 and 4), violating uniqueness
D) Definition. A/B/C) Each contradicts.
Rewrite x² + 6x by completing the square.
Answer: C — (x + 3)² − 9
A) Sign error on the added/subtracted constant. B) Sign error on the linear term inside the binomial. C) Half of 6 is 3, square it: 9. Add and subtract 9: x² + 6x + 9 - 9 = (x+3)² - 9. D) Used 6 instead of half of 6.
Rationalize: 1/√5.
Answer: A — √5/5
A) Multiply numerator and denominator by √5: √5/5.
Use the quadratic formula to solve x² + 4x − 5 = 0.
Answer: B — x = −5 or x = 1
B) x = (−4 ± √(16 + 20))/2 = (−4 ± 6)/2 → x = 1 or x = −5.
Solve: x² = 49.
Answer: E — x = ±7 (both 7² = 49 and (-7)² = 49)
Square root property: x² = k → x = ±√k. Here x = ±7. Common mistake: forget negative solution. Always TWO solutions (unless one is zero).
f(x) = √x has domain:
Answer: B — x ≥ 0
B) Standard square-root domain (real-valued). A/C/D) Each is incorrect.
Simplify: 3(x + 4) - 2x.
Answer: C — x + 12 (distribute 3: 3x+12; combine: 3x-2x+12 = x+12)
Distribute 3 over (x+4): 3x + 12. Then combine like terms: 3x - 2x = x. Result: x + 12. Multi-step simplification: distribute → combine.
The function f(x) = |x − 2| has its vertex at:
Answer: B — (2, 0)
B) |x − 2| is min when x = 2. A/C/D) Each is incorrect.
Evaluate: 2³ · 2⁴.
Answer: D — 2⁷ = 128 (same base, add exponents: 2^(3+4) = 2⁷)
Product of powers with same base: add exponents. 2³ · 2⁴ = 2^(3+4) = 2⁷ = 128. Power rule. Don't multiply bases (that's a common error).
Solve the system: 2x + y = 11, x − y = 1.
Answer: C — (4, 3)
C) Add: 3x = 12 → x = 4. Then 4 − y = 1 → y = 3. B) miscomputes y from the second equation.
6 sample cards from the 165 in the bank.
When do you use a solid line in graphing inequalities?
For ≤ or ≥ (the line is included). Use dashed for < or >.
Solve by elimination: x + y = 10, x − y = 4.
Add: 2x = 14 → x = 7. Then y = 3.
What is the exponential growth formula?
y = a(1 + r)ᵗ, where a is initial amount, r is growth rate (decimal), t is time.
Expand: (x + 4)(x − 4).
x² − 16 (difference of squares).
Expand: (x − 5)².
x² − 10x + 25.
Worked Example: Simplify (2x³y²)² · (3x⁴y) using exponent rules.
Step 1: Apply the power rule to (2x³y²)². Raise EVERY factor inside to the 2nd power. (2x³y²)² = 2² · (x³)² · (y²)² = 4x⁶y⁴ Step 2: Now the expression is 4x⁶y⁴ · 3x⁴y. Step 3: Multiply the coefficients. 4 · 3 = 12 Step 4: Combine x-terms using the product rule (add exponents). x⁶ · x⁴ = x^(6+4) = x¹⁰ Step 5: Combine y-terms similarly. Remember y = y¹. y⁴ · y¹ = y^(4+1) = y⁵ Step 6: Put it all together. 12x¹⁰y⁵ Key idea: ALWAYS apply the outer exponent to each factor inside — including the coefficient. Missing the 2 in 2² is the #1 student error.
These samples are a small slice. The full bank runs flashcards, multiple choice and timed mock exams with per-chapter progress tracking, on the web and in the iOS app.
The High School Algebra 1 bank holds 315 items: 150 multiple-choice questions, 165 flashcards. 18 of them are on this page to read free, with no signup.
Yes. Every multiple-choice item carries a written rationale that states the controlling principle behind the correct answer and then addresses each wrong option in turn — why it tempts and precisely where it fails. Knowing why the plausible answer was wrong is worth more than knowing which letter was right.
It is organised into 8 chapters that follow the published exam blueprint: Foundations: Real Numbers, Expressions, and Properties; Solving Linear Equations and Inequalities; Linear Functions and the Coordinate Plane; Systems of Equations and Inequalities; Exponents and Exponential Functions; Polynomials and Factoring; Quadratic Functions and Equations; Radicals, Rational Expressions, and Sequences. The number of questions in each chapter is proportional to that domain's published weight, so working through the bank exposes you to roughly the mix the real exam uses.
Common Core HS Algebra 1 standards (HSN, HSA, HSF, HSS domains) — typical Algebra 1 course covers: real numbers and algebraic expressions, linear equations/inequalities, linear functions and graphs, systems of linear equations, exponents and exponential functions, polynomials, factoring, quadratic equations and functions, sequences/series. MCQs reference public Common Core math standards.
The samples on this page are free to read in full, rationales included, with no account. The complete 315-item bank, the timed mock exams and per-chapter progress tracking are part of CoStudy on the web and in the iOS app.
Last reviewed 2026-08-22. Banks are written against the certifying body's published exam outline and re-checked when that outline changes — exams get renumbered, retired and reweighted, and a bank written to a superseded outline teaches the wrong proportions. Figures that are re-indexed annually are deliberately not asserted as rules; the questions test the governing principle instead.