10 questions🇬🇧English

🌀 Binomial Expansion – A-level

Maths · A-level — practises nCr, finding coefficients and expanding (1 + x)ⁿ, including validity ranges

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Questions

Which row of Pascal's triangle gives the coefficients in the expansion of (a + b)⁎?

1, 4, 6, 4, 1
1, 3, 3, 1
1, 5, 10, 10, 5, 1
1, 4, 4, 1
20s

What is the value of ⁵C₂?

20
10
60
5
20s

How many terms are there in the full expansion of (a + b)⁷?

8
7
14
6
20s

What is the coefficient of x² in the expansion of (1 + 2x)⁵?

20
40
10
80
30s

What is the coefficient of x³ in the expansion of (2 − x)⁶?

−20
160
−160
−120
30s

What is the term independent of x in the expansion of (x + 1/x)⁶?

15
30
20
6
30s

For which values of x is the binomial expansion of (1 − 3x)⁻¹ valid?

|x| > ⅓
|x| < 1
|x| < 3
|x| < ⅓
30s

What is the coefficient of x² in the expansion of (1 + x)^œ?

⅛
Œ
−Œ
−⅛
30s

Using the first three terms of the expansion of (1 + x)¹⁰ with x = 0.01, what is the approximate value of 1.01¹⁰?

1.1045
1.1
1.0145
1.145
60s

For which values of x is the binomial expansion of (4 + x)^(−œ) valid?

|x| < Œ
|x| < 4
|x| < 2
|x| < 1
30s