Grade 11 · Math · Algebra 2

11th grade Pascal's triangle and the Binomial Theorem worksheet

6 printable versionsChallenge Me10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

When it’s done, scan the sheet with your phone and PencilGo marks it and picks the next one. Create a free account

Version

Pascal's triangle and the Binomial Theorem

Grade 11 Math Worksheet - Challenge Me

NameDate

Circle the best answer, or write your answer on the line.

Bo expands (2x + 1)^4. What is the coefficient of the x^3 term?
Esme expands (2x + 1)^5. What is the coefficient of the x^4 term?
3.
Jun wants only the x² term of (x + 3)⁴. Which is it?
- 18x²
- 54x²
- 6x²
4.
Kira wants the middle term of (x + y)⁸. Which is it?
- 8x⁴y⁴
- 70x⁴y⁴
- 56x⁴y⁴
5.
Luz wants the constant term of (2x + 3)³. What is it?
- 9
- 8
- 27
6.
Milo says (x + y)² = x² + y². Agree or disagree?
- Agree: it works for x = 0
- Disagree: it misses 2xy
- Agree: square each part
7.
Noah says (x + 2)³ = x³ + 8. Agree or disagree?
- Agree: cube each part
- Disagree: try x = 1
- Agree: 2³ is 8
8.
Pia says the coefficients of (x + y)⁷ add up to 14. Agree or disagree?
- Agree: there are 14 terms
- Agree: 7 + 7 = 14
- Disagree: they add to 128
9.
What do all the coefficients of (2x + 1)⁴ add up to, Ren?
- 32
- 16
- 81
10.
A row of Zee's triangle starts 1, 9, 36. Which row is it?
- Row 9
- Row 8
- Row 36

Pascal's triangle and the Binomial Theorem. Every version has 10 questions, and the answer key prints on the second page.

I can build and read Pascal's triangle, and say row n has n + 1 numbers that add to 2ⁿ.
I can expand (x + y)ⁿ and (ax + b)ⁿ fully, with alternating signs for a minus.
I can find one term or one coefficient without writing the whole expansion.
I can test an expansion by putting x = y = 1.

Standard: A-APR.C.5 (+)

Pascal's triangle: Rows of numbers where each inside number is the two above added

coefficient: The number in front of a term

binomial: A sum of two terms, like x + y

expand: Multiply out into separate terms

term: One part of a sum, like 6x²y²

Your child gave the power as the number of terms. (x + y)ⁿ has n + 1 terms, because the power of y runs from 0 up to n.

Your child multiplied n × (n − 1) but didn't divide by 2. Choosing 2 of n things counts each pair twice, so halve it.

Your child found the number part, 2 to a power, but left out how many ways the term appears. Multiply by the triangle number too.

What is the most common mistake with pascal's triangle and the binomial theorem?

Your child gave the power as the number of terms. (x + y)ⁿ has n + 1 terms, because the power of y runs from 0 up to n.

Are these 11th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

Every sheet you scan goes into your child’s record: dated, marked and ready for the year-end portfolio. Homeschool records