Grade 11 · Math · Algebra 2

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

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Pascal's triangle and the Binomial Theorem

Grade 11 Math Worksheet

NameDate

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

Bo expands (x + y)^8. What is the coefficient of the x^6y² term?
Esme expands (x + y)^10. What is the coefficient of the x^8y² term?
3.
Jun expands (x + 1)⁴. Which is right?
- x⁴ + 1
- x⁴ + 4x³ + 6x² + 4x + 1
- x⁴ + 4x³ + 4x² + 4x + 1
4.
Kira expands (x − y)³. Which is right?
- x³ − 3x²y − 3xy² − y³
- x³ − 3x²y + 3xy² − y³
- x³ + 3x²y + 3xy² − y³
5.
Luz expands (2x + 1)³. Which is right?
- 8x³ + 12x² + 6x + 1
- 2x³ + 6x² + 6x + 1
- 8x³ + 6x² + 3x + 1
6.
Which row of the triangle does Milo need for (x + y)⁶?
- Row 5: 1, 5, 10, 10, 5, 1
- Row 7, the seventh row from the top
- Row 6: 1, 6, 15, 20, 15, 6, 1
7.
In (x + y)⁶, what coefficient does Noah find for x³y³?
- 6
- 20
- 15
8.
Why does each row of Pia's triangle read the same from both ends?
- Picking k is like leaving n − k
- x and y are equal numbers
- Each row adds up to the same total
9.
Ren expands (x − 2)³ = x³ − 6x² + 12x − 8. What pattern do the signs make?
- +, −, +, −
- −, −, −, −
- +, +, +, −
10.
What is the constant term of (x − 2)³ in Tala's expansion?
- −8
- 8
- −6

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.

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