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150 multiple-choice questions and 165 flashcards, organised into 9 chapters, written to the Common Core HS Algebra 2 standards blueprint. Every question carries a full rationale.
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Common Core HS Algebra 2 standards — typical course covers: functions and inverses, quadratic functions (vertex/standard/factored forms), polynomial functions (higher degree, end behavior, zeros), rational functions, radical functions, exponential and logarithmic functions, sequences and series, complex numbers, conic sections (introduction), probability and statistics introduction. MCQs reference public Common Core standards.
CoStudy's High School Algebra 2 bank holds 315 items organised into 9 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 the exponential equation: 2ˣ = 16.
Answer: D — x = 4 (16 = 2⁴, so x = 4; or take log₂: x = log₂(16) = 4)
16 = 2⁴, so 2ˣ = 2⁴ → x = 4 (equal bases means equal exponents). Alternative: take log₂ of both sides. Foundation of exponential equation solving.
If f(x) = x² + 1 and g(x) = 2x, then (f ∘ g)(3) =
Answer: D — 37
D) g(3) = 6, f(6) = 37. A/B/C) Each is incorrect.
The polynomial p(x) = (x − 2)²(x + 1) has end behavior:
Answer: A — Down on left, up on right
Leading term x³ (positive coefficient, odd degree). Odd degree + positive leading: down-left, up-right. B/C) Even-degree behavior. D) Negative leading coefficient.
Sin(30°) =
Answer: A — 1/2 (special angle: sin 30° = 1/2; equilateral triangle bisected)
Special angles: sin 30° = 1/2, cos 30° = √3/2; sin 45° = cos 45° = √2/2; sin 60° = √3/2, cos 60° = 1/2; sin 90° = 1, cos 90° = 0. Algebra 2 covers basic trig.
Compute (2 − 3i)².
Answer: D — −5 − 12i
A) Computed (a² + b²) = 13 + (-12i), which mishandles the i² term. B) Treated i² as +1 instead of −1; gave 4 − 12i + 9 = 13 − 12i... actually 4 − 12i + 9. The intended trap: handling i² as +1. C) Cross-term sign error. D) Expand (2 − 3i)² = 4 − 12i + 9i² = 4 − 12i − 9 = −5 − 12i. The i² = −1 step is critical.
Probability mass function value: P(X = k) for binomial X ~ Bin(n=4, p=0.5) at k=2:
Answer: D — 6/16 = 3/8 (C(4,2)·(0.5)²·(0.5)² = 6·1/16 = 3/8)
Binomial probability: P(X=k) = C(n,k) p^k (1-p)^(n-k). C(4,2) = 6. p^2 = 0.25, (1-p)^2 = 0.25. Product: 6 · 0.0625 = 0.375 = 3/8. Algebra 2/AP Stats overlap.
The geometric sequence 3, 6, 12, 24, ... has nth term:
Answer: C — aₙ = 3 · 2^(n − 1)
C) Standard geometric formula. A/B) Arithmetic. D) Wrong base.
Solve: x² + 1 = 0.
Answer: C — x = ±i
C) Complex solutions. A/B/D) Each is incorrect.
P(A or B) = P(A) + P(B) − P(A and B) is the:
Answer: B — Inclusion-exclusion (addition) rule
B) Standard. A/C/D) Each is a different rule.
Domain of f(x) = √(x − 4):
Answer: D — x ≥ 4
D) Radicand must be ≥ 0. A/B/C) Each is incorrect.
What is the discriminant of x² - 4x + 4 = 0?
Answer: A — 0 (b²-4ac = 16-16 = 0; one repeated real root)
Discriminant b²-4ac. Here 16 - 16 = 0. Zero discriminant: one repeated real root. Positive: two distinct real roots. Negative: two complex conjugate roots. Indicates nature of solutions.
Evaluate: ln(e³).
Answer: C — 3 (ln(eˣ) = x, so ln(e³) = 3)
ln = natural log (base e). ln(eˣ) = x. ln(e³) = 3. Inverse function property. ln(1) = 0, ln(e) = 1. Algebra 2 logarithm foundations.
6 sample cards from the 165 in the bank.
Worked Example: Simplify the complex expression (3 + 2i)(4 − 5i).
Step 1: Apply FOIL (distribute). (3 + 2i)(4 − 5i) = 3·4 + 3·(−5i) + 2i·4 + 2i·(−5i) = 12 − 15i + 8i − 10i² Step 2: Substitute i² = −1. −10i² = −10·(−1) = 10 Expression becomes 12 − 15i + 8i + 10 Step 3: Combine real parts and imaginary parts separately. Real: 12 + 10 = 22 Imaginary: −15i + 8i = −7i Step 4: Write in standard form a + bi. 22 − 7i Final answer: 22 − 7i
Standard equation of a circle centered at (h, k) with radius r?
(x − h)² + (y − k)² = r².
Simplify √50.
5√2. (√(25 × 2) = 5√2.)
Worked Example: Convert y = 2x² − 12x + 23 to vertex form by completing the square.
Step 1: Factor the leading coefficient out of the x-terms. y = 2(x² − 6x) + 23 Step 2: Take half of the linear coefficient (−6), square it, and add/subtract inside the parentheses. Half of −6 = −3; (−3)² = 9 y = 2(x² − 6x + 9 − 9) + 23 Step 3: Group the perfect-square trinomial. y = 2[(x − 3)² − 9] + 23 Step 4: Distribute the 2 to the −9 and combine constants. y = 2(x − 3)² − 18 + 23 y = 2(x − 3)² + 5 Step 5: Identify the vertex. Vertex form y = a(x − h)² + k → vertex (h, k) = (3, 5). Final answer: y = 2(x − 3)² + 5; vertex (3, 5).
Multiply: (x − 3)(x + 3).
x² − 9. (Difference of squares.)
What's the 'vertex form' of a quadratic?
y = a(x − h)² + k. The vertex is (h, k).
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 2 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 9 chapters that follow the published exam blueprint: Linear Functions and Systems Review; Quadratic Functions and Complex Numbers; Polynomial Functions; Rational Expressions and Functions; Radical Functions and Rational Exponents; Exponential and Logarithmic Functions; Sequences and Series; Trigonometric Functions (Introduction); Statistics and Probability. 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 2 standards — typical course covers: functions and inverses, quadratic functions (vertex/standard/factored forms), polynomial functions (higher degree, end behavior, zeros), rational functions, radical functions, exponential and logarithmic functions, sequences and series, complex numbers, conic sections (introduction), probability and statistics introduction. MCQs reference public Common Core 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.