Pascal's triangle and the Binomial Theorem

Answer Key - Grade 11 Math Worksheet - Building Confidence

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

1. 1.

   Ari's robot expands (x + y)^5 and prints one term per line. How many terms will there be?

   6 terms
2. 2.

   Bo writes out (x + y)^8 on a long strip of paper (a very long strip). How many terms will there be?

   9 terms
3. 3.

   In math club, Esme plans to expand (x + y)^11. How many terms will there be?

   12 terms
5. 4.

   Using the triangle, which numbers does Jun read in row 4?

   • 1, 3, 3, 1
   • 1, 4, 4, 1
   • 1, 4, 6, 4, 1
6. 5.

   Using the triangle, what does row 5 add up to, Luz?

   Use the picture in question 4.

   • 31
   • 25
   • 32
7. 6.

   Milo expands (x + y)². Which is right?

   • x² + xy + y²
   • x² + 2xy + y²
   • x² + y²
8. 7.

   Noah expands (x + y)³. Which coefficients appear in order?

   • 1, 2, 2, 1
   • 1, 3, 3, 1
   • 1, 3, 1
9. 8.

   Ren draws (x + y)² as a square split into parts. Which parts appear?

   • x² and y², with nothing between
   • x², xy and y²
   • x², xy, xy and y²
10. 9.

    In Tala's area model of (x + y)², why is the middle term 2xy?

    • x and y are both doubled
    • 2 is the power
    • Two equal xy rectangles
11. 10.

    Zee looks at one term of (x + y)⁵. What do its powers of x and y add up to?

    • 6
    • 5
    • 10