Unit 1: Number and Algebra

Topic 1.9: The Binomial Theorem Questions

Practice 20 exam-style questions for IB Math AA SL Topic 1.9. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.

1Expand2 marks

2026

Expand

(1 + 2 x)^{3}

in ascending powers of

x

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2Show that1 mark

2026

Show that the expansion of

(1 + x)^{4}

has

6 x^{2}

as its middle term.

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3Write down1 mark

2026

Write down the number of terms in the expansion of (3x − 2)¹⁵.

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4Write down1 mark

2026

Write down the value of

(0 9) + (9 9)

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5Find2 marks

2026

Use Pascal's triangle to write down the coefficients in the expansion of

(a + b)^{6}

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6Write down2 marks

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Use Pascal's triangle to write down the coefficients in the expansion of (a + b)⁶.

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7Show that1 mark

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Show that

(2 7) = 21

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8Show that1 mark

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Show that 10C3 = 120.

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9Show that1 mark

2026

Show that 9C4 = 126.

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10Find1 mark

2026

Write down the number of terms in the expansion of

(3 x - 2)^{15}

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11Find2 marks

2026

Find the coefficient of x³ in the expansion of (2x − 1)⁵.

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12Expand3 marks

2026

Expand (x + 2)⁵.

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13Find2 marks

2026

The expansion of (x + h)⁵ begins x⁵ + ax⁴ + bx³ + … . Find a and b in terms of h.

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14Find3 marks

2026

In the expansion of (2x + k)⁵, the coefficient of x⁴ is 80. Find k.

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15Find3 marks

2026

In the expansion of (1 + x)ⁿ, the coefficient of x² is 36. Find n.

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16Find3 marks

2026

Find the coefficient of

x^{5}

in the expansion of

(3 + 2 x)^{7}

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17Find2 marks

2026

Find the term in x⁴ in the expansion of (x + 3)⁶.

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18Find3 marks

2026

In the expansion of

(1 + x)^{n}

, the coefficient of

x^{2}

is 36. Find n.

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19Find2 marks

2026

Find the coefficient of

x^{3}

in the expansion of

(2 x - 1)^{5}

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20Find3 marks

2026

In the expansion of (x − c)⁸, the coefficient of x⁶ is 112. Find the possible values of c.

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