Worksheets · Algebra 2

Determinants worksheet for Algebra 2

A 2x2 is one subtraction. A 3x3 expands along the top row into three 2x2s, with the middle one subtracted, which is the part people forget. Hard works backwards: the determinant is given and you solve for x.

Also taught in Precalculus, at its own level and with its own examples.

Select your difficulty

Pick more than one for a sheet that mixes them.

The preview can look cramped on a phone. The PDF and printed sheet come out normal.

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Determinants

Date Period

Evaluate each determinant, or find x.

  1. Evaluate 2×22 \times 2 determinants or solve for xx

    ∣ 1726 ∣
  2. ∣ −2424 ∣
  3. ∣ 3−577 ∣
  4. ∣ −1−514 ∣
  5. ∣ −72−1−6 ∣
  6. ∣ −3−73−5 ∣
  7. ∣ 132−7 ∣
  8. ∣ −147−6 ∣
  9. ∣ 75−56 ∣
  10. ∣ 6−31−1 ∣

  1. Evaluate 3×33 \times 3 determinants or solve for xx

    ∣ −9−5−4−2−1−7−2−48 ∣
  2. ∣ 9−7−3−3−72−18−9 ∣
  3. ∣ −3518−2−9−25−2 ∣
  4. ∣ −8−98−2−9−71−88 ∣
  5. ∣ −3−8−944−58−26 ∣
  6. ∣ −962−8−7−6−51−2 ∣
  7. ∣ 12−642−95−23 ∣
  8. ∣ −428−219−96−6 ∣
  9. ∣ 47−2454−77−1 ∣
  10. ∣ −9−4285−4592 ∣

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

DeterminantsAnswer keyVersion 1

Date Period

Evaluate each determinant, or find x.

  1. Evaluate 2×22 \times 2 determinants or solve for xx

    ∣ 1726 ∣−8
  2. ∣ −2424 ∣−16
  3. ∣ 3−577 ∣56
  4. ∣ −1−514 ∣1
  5. ∣ −72−1−6 ∣44
  6. ∣ −3−73−5 ∣36
  7. ∣ 132−7 ∣−13
  8. ∣ −147−6 ∣−22
  9. ∣ 75−56 ∣67
  10. ∣ 6−31−1 ∣−3

  1. Evaluate 3×33 \times 3 determinants or solve for xx

    ∣ −9−5−4−2−1−7−2−48 ∣150
  2. ∣ 9−7−3−3−72−18−9 ∣719
  3. ∣ −3518−2−9−25−2 ∣59
  4. ∣ −8−98−2−9−71−88 ∣1143
  5. ∣ −3−8−944−58−26 ∣830
  6. ∣ −962−8−7−6−51−2 ∣−182
  7. ∣ 12−642−95−23 ∣−18
  8. ∣ −428−219−96−6 ∣30
  9. ∣ 47−2454−77−1 ∣−426
  10. ∣ −9−4285−4592 ∣−176

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

∣ 3125 ∣

  1. Multiply the main diagonal: 3 times 5.
  2. Multiply the other diagonal: 1 times 2.
  3. Subtract.

The answer is 13.

Where students go wrong

Adding the diagonals instead of subtracting, and on a 3x3, forgetting that the middle term is subtracted. The signs across the top row alternate plus, minus, plus, whatever the numbers happen to be.

Also called finding the determinant, 2x2 determinants or 3x3 determinants.

What you can put on this worksheet

The determinant of a 2x2
∣ 41−4−7 ∣ → −24
The determinant of a 3x3
∣ 41−4−7−67−5−53 ∣ → 34
Sums of determinants, zero by structure, build one
Write a 2 by 2 matrix whose determinant is 28 (many answers) → [ 24−411 ]

Questions about these worksheets

Yes. Every determinants sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Algebra 2 is usually taken around 10th or 11th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the determinants questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are two levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 3: the determinant of a 2x2, the determinant of a 3x3 and sums of determinants, zero by structure, build one. Tick as many as you want and set how many of each, or let it spread them evenly.

Adding the diagonals instead of subtracting, and on a 3x3, forgetting that the middle term is subtracted. The signs across the top row alternate plus, minus, plus, whatever the numbers happen to be.