4.1.1 Binomial expansion Quiz: Pearson Edexcel Maths, Unit 4

The 20 questions

1. What is the number of terms in the binomial expansion of (1 + x)^n for a positive integer n?

   • n - 1
   • 2n
   • n
   • n + 1

2. Which notation represents the binomial coefficient n choose r?

   • nPr
   • n! / r
   • n^Cr
   • nCr

3. What is the value of 5C0 in a binomial expansion?

   • 25
   • 5
   • 1
   • 0

4. What is the coefficient of x in the expansion of (1 + 2x)^5?

   • 2
   • 5
   • 32
   • 10

5. For what range of x values is the expansion of (1 + x)^n valid when n is not a positive integer?

   • x > 1
   • x < 1
   • |x| < 1
   • all real x

6. What is the general formula for the rth term in the expansion of (a + b)^n?

   • nCr a^n b^r
   • nCr a^r b^(n-r)
   • nCr a^(n-r) b^r
   • nPr a^(n-r) b^r

7. What is the value of 4C2?

   • 4
   • 8
   • 12
   • 6

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

   • 1
   • 2
   • 4
   • 16

9. Find the first term in the ascending powers expansion of (1 - 3x)^-1.

   • -1
   • -3x
   • 1 + 3x
   • 1

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

    • 27
    • 6
    • 9
    • 3

11. Which method must be used to expand (1 - x)^(-1/2) up to the x^2 term?

    • Binomial series
    • Pascal triangle
    • Integration by parts
    • Synthetic division

12. What is the fourth term in the expansion of (1 + x)^5?

    • 20x^3
    • 10x^3
    • 10x^4
    • 5x^3

13. What is the sum of all coefficients in the expansion of (1 + 2x)^4?

    • 243
    • 16
    • 32
    • 81

14. What is the coefficient of x in the expansion of (4 - x)^(1/2)?

    • -1/2
    • 1/4
    • -1/4
    • 1/2

15. Which property of Pascal triangle rows relates directly to binomial coefficients?

    • Arithmetic mean
    • Geometric ratio
    • Combinations
    • Prime factors

16. What is the constant term in the expansion of (x + 2/x)^4?

    • 16
    • 32
    • 24
    • 8

17. What is the expansion of (1 + x)^-2 up to the x^2 term?

    • 1 - 2x + 3x^2
    • 1 - x + x^2
    • 1 - 2x - 3x^2
    • 1 + 2x + 3x^2

18. How many non-zero terms are in the exact expansion of (x + y)^7?

    • 9
    • 8
    • 7
    • 14

19. What does nCr equal in terms of factorials?

    • n! / (r!(n-r)!)
    • n! / (n-r)!
    • n! / r!
    • (n-r)! / n!

20. In the expansion of (ax + b)^n, what determines the highest power of x?

    • The sum a + b
    • The value of b
    • The value of a
    • The index n

Related quizzes

• Sequences given by a formula for the nth term Quiz · 4.2.1 · 20 questions
• Sigma notation for sums of series Quiz · 4.3.1 · 20 questions
• Arithmetic sequences and series Quiz · 4.4.1 · 20 questions
• Geometric sequences and series Quiz · 4.5.1 · 20 questions
• Sequences and series in modelling Quiz · 4.6.1 · 20 questions
• Structure of mathematical proof and methods of proof Quiz · 1.1.1 · 20 questions
• Vectors in two and three dimensions Quiz · 10.1.1 · 20 questions
• Laws of indices for all rational exponents Quiz · 2.1.1 · 20 questions
• Straight lines and their equations Quiz · 3.1.1 · 20 questions
• Sine, cosine and tangent for all angles Quiz · 5.1.1 · 20 questions