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, how does Kira get each inside number?

   Use the picture in question 4.

   • Double the number to its left
   • Multiply the two numbers above
   • Add the two numbers above it
7. 6.

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

   Use the picture in question 4.

   • 25
   • 31
   • 32
8. 7.

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

   • x² + y²
   • x² + xy + y²
   • x² + 2xy + y²
9. 8.

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

   • 1, 2, 2, 1
   • 1, 3, 3, 1
   • 1, 3, 1
10. 9.

    In Pia's expansion of (x + y)⁴, how do the powers of x change from term to term?

    • They stay at 4 throughout
    • They count down 4, 3, 2, 1, 0
    • They rise from 0 up to 4 in turn
11. 10.

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

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