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Advanced Math Worksheet Generator

Limits, derivatives, integrals, and matrices with a symbolic library. No AI, no credits.

Grade 11 – Grade 12No account needed

Advanced math activities: limits, derivatives (power, product, quotient, chain; polynomial, rational, exponential, logarithmic, basic trigonometric), integrals (antiderivatives and definite), and matrices (operations, determinants, inverses, solving systems). Uses nerdamer (MIT license) for symbolic computation. The Course selector controls scope (AP Calculus AB versus BC, IB notation). Every answer is computed by code and verified by a second independent method. No AI, so it never uses a generation credit.

What students practice

  • Calculus
  • Matrices
  • Limits

Live sample sheet

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Advanced Math

1. Find d/dx [4x² - 3x + 1].
2. Find ∫ x² + 2x dx.
3. Find d/dx [2x³ - x].
4. Find ∫ 3x² + 1 dx.
5. Find d/dx [x³ + 2x²].
6. Find ∫ 4x³ dx.
7. Find d/dx [x² + 3x].
8. Find ∫ 3x² + 1 dx.
9. Find d/dx [4x² - 3x + 1].
10. Find ∫ 3x² + 1 dx.

Answer Key — Advanced Math

1. Find d/dx [4x² - 3x + 1].
d/dx [4x² - 3x + 1] = 8·x-3
Numerical check at x=1: f'(1) ≈ 5.0000
Symbolic at x=1: 5.0000
Answer: 8·x-3
2. Find ∫ x² + 2x dx.
∫ x² + 2x dx = ⅓x³ + x² + C
Numerical check: ∫₀² x² + 2x dx ≈ 6.6667
Symbolic: ⅓x³ + x² from 0 to 2 = 6.6667
Answer: 1/3·x^3+x^2 + C
3. Find d/dx [2x³ - x].
d/dx [2x³ - x] = 6·x^2-1
Numerical check at x=1: f'(1) ≈ 5.0000
Symbolic at x=1: 5.0000
Answer: 6·x^2-1
4. Find ∫ 3x² + 1 dx.
∫ 3x² + 1 dx = x³ + x + C
Numerical check: ∫₀² 3x² + 1 dx ≈ 10.0000
Symbolic: x³ + x from 0 to 2 = 10.0000
Answer: x^3+x + C
5. Find d/dx [x³ + 2x²].
d/dx [x³ + 2x²] = 3·x^2+4·x
Numerical check at x=1: f'(1) ≈ 7.0000
Symbolic at x=1: 7.0000
Answer: 3·x^2+4·x
6. Find ∫ 4x³ dx.
∫ 4x³ dx = x⁴ + C
Numerical check: ∫₀² 4x³ dx ≈ 16.0000
Symbolic: x⁴ from 0 to 2 = 16.0000
Answer: x^4 + C
7. Find d/dx [x² + 3x].
d/dx [x² + 3x] = 2·x+3
Numerical check at x=1: f'(1) ≈ 5.0000
Symbolic at x=1: 5.0000
Answer: 2·x+3
8. Find ∫ 3x² + 1 dx.
∫ 3x² + 1 dx = x³ + x + C
Numerical check: ∫₀² 3x² + 1 dx ≈ 10.0000
Symbolic: x³ + x from 0 to 2 = 10.0000
Answer: x^3+x + C
9. Find d/dx [4x² - 3x + 1].
d/dx [4x² - 3x + 1] = 8·x-3
Numerical check at x=1: f'(1) ≈ 5.0000
Symbolic at x=1: 5.0000
Answer: 8·x-3
10. Find ∫ 3x² + 1 dx.
∫ 3x² + 1 dx = x³ + x + C
Numerical check: ∫₀² 3x² + 1 dx ≈ 10.0000
Symbolic: x³ + x from 0 to 2 = 10.0000
Answer: x^3+x + C

Assumptions and Conventions

Assumptions:
  • Derivatives use the power, product, quotient, and chain rules.
  • Integrals are antiderivatives plus C (constant of integration).
  • Limits are computed by direct substitution when possible, and numerically otherwise.
Conventions:
  • Write derivatives in simplified form.
  • Include + C for indefinite integrals.
  • Matrix entries are written row by row.
  • Symbolic computation by nerdamer (MIT license).
Source: Symbolic computation: nerdamer (MIT license, https://nerdamer.com), retrieved 2026-10-11.

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No. Students never need an account. They open a shared link or join with a code.

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Yes. This tool computes answers by code, so you can generate, preview and print worksheet without an account. A free account adds saving and student links.

How are the answers computed?

Every answer is computed by code and verified by a second independent method. No AI is used.

What grades is the Advanced Math for?

This tool fits Grade 11 – Grade 12.

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Advanced Math

1. Find d/dx [4x² - 3x + 1].
2. Find ∫ x² + 2x dx.
3. Find d/dx [2x³ - x].
4. Find ∫ 3x² + 1 dx.
5. Find d/dx [x³ + 2x²].
6. Find ∫ 4x³ dx.
7. Find d/dx [x² + 3x].
8. Find ∫ 3x² + 1 dx.
9. Find d/dx [4x² - 3x + 1].
10. Find ∫ 3x² + 1 dx.

Answer Key — Advanced Math

1. Find d/dx [4x² - 3x + 1].
d/dx [4x² - 3x + 1] = 8·x-3
Numerical check at x=1: f'(1) ≈ 5.0000
Symbolic at x=1: 5.0000
Answer: 8·x-3
2. Find ∫ x² + 2x dx.
∫ x² + 2x dx = ⅓x³ + x² + C
Numerical check: ∫₀² x² + 2x dx ≈ 6.6667
Symbolic: ⅓x³ + x² from 0 to 2 = 6.6667
Answer: 1/3·x^3+x^2 + C
3. Find d/dx [2x³ - x].
d/dx [2x³ - x] = 6·x^2-1
Numerical check at x=1: f'(1) ≈ 5.0000
Symbolic at x=1: 5.0000
Answer: 6·x^2-1
4. Find ∫ 3x² + 1 dx.
∫ 3x² + 1 dx = x³ + x + C
Numerical check: ∫₀² 3x² + 1 dx ≈ 10.0000
Symbolic: x³ + x from 0 to 2 = 10.0000
Answer: x^3+x + C
5. Find d/dx [x³ + 2x²].
d/dx [x³ + 2x²] = 3·x^2+4·x
Numerical check at x=1: f'(1) ≈ 7.0000
Symbolic at x=1: 7.0000
Answer: 3·x^2+4·x
6. Find ∫ 4x³ dx.
∫ 4x³ dx = x⁴ + C
Numerical check: ∫₀² 4x³ dx ≈ 16.0000
Symbolic: x⁴ from 0 to 2 = 16.0000
Answer: x^4 + C
7. Find d/dx [x² + 3x].
d/dx [x² + 3x] = 2·x+3
Numerical check at x=1: f'(1) ≈ 5.0000
Symbolic at x=1: 5.0000
Answer: 2·x+3
8. Find ∫ 3x² + 1 dx.
∫ 3x² + 1 dx = x³ + x + C
Numerical check: ∫₀² 3x² + 1 dx ≈ 10.0000
Symbolic: x³ + x from 0 to 2 = 10.0000
Answer: x^3+x + C
9. Find d/dx [4x² - 3x + 1].
d/dx [4x² - 3x + 1] = 8·x-3
Numerical check at x=1: f'(1) ≈ 5.0000
Symbolic at x=1: 5.0000
Answer: 8·x-3
10. Find ∫ 3x² + 1 dx.
∫ 3x² + 1 dx = x³ + x + C
Numerical check: ∫₀² 3x² + 1 dx ≈ 10.0000
Symbolic: x³ + x from 0 to 2 = 10.0000
Answer: x^3+x + C

Assumptions and Conventions

Assumptions:
  • Derivatives use the power, product, quotient, and chain rules.
  • Integrals are antiderivatives plus C (constant of integration).
  • Limits are computed by direct substitution when possible, and numerically otherwise.
Conventions:
  • Write derivatives in simplified form.
  • Include + C for indefinite integrals.
  • Matrix entries are written row by row.
  • Symbolic computation by nerdamer (MIT license).
Source: Symbolic computation: nerdamer (MIT license, https://nerdamer.com), retrieved 2026-10-11.
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