Answer Key — Fourier and Laplace transforms

Fourier analysis & transforms

Do not share with students before practice tests.

Worksheets — Sets 1–10

| Set | Guidance | | --- | --- | | Set 1 | Fourier and Laplace transforms — verify written work and accept reasonable drawings. | | Set 2 | Fourier and Laplace transforms — verify written work and accept reasonable drawings. | | Set 3 | Fourier and Laplace transforms — verify written work and accept reasonable drawings. | | Set 4 | Fourier and Laplace transforms — verify written work and accept reasonable drawings. | | Set 5 | Fourier and Laplace transforms — verify written work and accept reasonable drawings. | | Set 6 | Fourier and Laplace transforms — verify written work and accept reasonable drawings. | | Set 7 | Fourier and Laplace transforms — verify written work and accept reasonable drawings. | | Set 8 | Fourier and Laplace transforms — verify written work and accept reasonable drawings. | | Set 9 | Fourier and Laplace transforms — verify written work and accept reasonable drawings. | | Set 10 | Fourier and Laplace transforms — verify written work and accept reasonable drawings. |

Worksheets — Sets 11–20

| Set | Guidance | | --- | --- | | Set 11 | Fourier and Laplace transforms — verify written work and accept reasonable drawings. | | Set 12 | Fourier and Laplace transforms — verify written work and accept reasonable drawings. | | Set 13 | Fourier and Laplace transforms — verify written work and accept reasonable drawings. | | Set 14 | Fourier and Laplace transforms — verify written work and accept reasonable drawings. | | Set 15 | Fourier and Laplace transforms — verify written work and accept reasonable drawings. | | Set 16 | Fourier and Laplace transforms — verify written work and accept reasonable drawings. | | Set 17 | Fourier and Laplace transforms — verify written work and accept reasonable drawings. | | Set 18 | Fourier and Laplace transforms — verify written work and accept reasonable drawings. | | Set 19 | Fourier and Laplace transforms — verify written work and accept reasonable drawings. | | Set 20 | Fourier and Laplace transforms — verify written work and accept reasonable drawings. |

Review tiers 1–10

• Checklists are parent-judged.
• Written items: verify against practice set patterns.
• Standard text: Definition and properties of the Fourier transform Convolution theorem and filtering Discrete Fourier transform (DFT) and sampling Laplace transform review and connection to frequency domain Inverse transforms and transform pairs (table methods)

Practice test scoring

| Tier | Pass guidance | | --- | --- | | 1–3 | Most oral tasks smooth; majority of written correct | | 4–6 | 7/10+ total with clear understanding | | 7–8 | 9/12+ with explanations | | 9–10 | Near-perfect; ready to move on |

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