2.7 Expand (a + b)^n for positive integer n Quiz: AQA Further Maths, Unit 2

The 20 questions

1. Which row of Pascal's triangle gives the coefficients of (a + b)^4?

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

2. What is the coefficient of x^2 in (x + 1)^3?

   • 3
   • 6
   • 2
   • 1

3. How many terms are in the expansion of (a + b)^5?

   • 6
   • 5
   • 32
   • 4

4. What is the sum of the coefficients in the expansion of (x + y)^4?

   • 4
   • 8
   • 16
   • 12

5. How is each interior entry in Pascal's triangle calculated?

   • Product of two above
   • Mean of two above
   • Sum of two above
   • Difference of two above

6. What is the first term in the expansion of (a + b)^3?

   • a^2b
   • b^3
   • 3a^2
   • a^3

7. Expand (x + 2)^3.

   • x^3 + 6x^2 + 8x + 8
   • x^3 + 3x^2 + 6x + 8
   • x^3 + 6x^2 + 12x + 8
   • x^3 + 2x^2 + 4x + 8

8. Expand (2x + 1)^3.

   • 8x^3 + 12x^2 + 6x + 1
   • 8x^3 + 12x^2 + 3x + 1
   • 8x^3 + 6x^2 + 3x + 1
   • 2x^3 + 3x^2 + 3x + 1

9. What is the coefficient of x^2 in (1 + 3x)^4?

   • 108
   • 36
   • 18
   • 54

10. What is the coefficient of x in (x − 2)^4?

    • −32
    • 32
    • −8
    • 16

11. In the expansion of (x + y)^4, what is the coefficient of x^2y^2?

    • 6
    • 3
    • 12
    • 4

12. Expand (p − 1)^3.

    • p^3 − 3p^2 + 3p − 1
    • p^3 − p^2 + p − 1
    • p^3 + 3p^2 + 3p + 1
    • p^3 − 3p^2 − 3p − 1

13. What is C(6, 2), the third number from the left in row 6 of Pascal's triangle?

    • 12
    • 15
    • 30
    • 20

14. What is the coefficient of x^3 in (1 + x)^5?

    • 20
    • 10
    • 15
    • 5

15. Expand (2a − 3b)^2.

    • 2a^2 − 12ab + 9b^2
    • 4a^2 − 12ab + 9b^2
    • 4a^2 + 12ab + 9b^2
    • 4a^2 − 6ab + 9b^2

16. In the expansion of (x + 2)^5, what is the coefficient of x^3?

    • 80
    • 10
    • 40
    • 20

17. Expand (1 − 2x)^3.

    • 1 − 2x + 4x^2 − 8x^3
    • 1 − 6x − 12x^2 − 8x^3
    • 1 − 6x + 12x^2 − 8x^3
    • 1 + 6x + 12x^2 + 8x^3

18. Using the binomial expansion, what is 101^3?

    • 1003001
    • 1030030
    • 1000301
    • 1030301

19. What is the coefficient of x^2 in (x + 2)^4?

    • 12
    • 6
    • 48
    • 24

20. Simplify (x + y)^3 + (x − y)^3.

    • 2x^3 + 6xy^2
    • 2x^3 + 6x^2y
    • 2x^3 − 6xy^2
    • 6x^3 + 2xy^2

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