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.
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2026• Aimnova practice — 1.9.1
Use Pascal's triangle to write down the coefficients in the expansion of (a + b)⁶.
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2026• Aimnova practice — 1.9.1
Write down the number of terms in the expansion of (3x − 2)¹⁵.
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2026• Aimnova practice — 1.9.3
Find the coefficient of x³ in the expansion of (2x − 1)⁵.
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2026• Aimnova practice — 1.9.3
Find the coefficient of x⁵ in the expansion of (3 + 2x)⁷.
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2026• Aimnova practice — 1.9.3
Find the term in x⁴ in the expansion of (x + 3)⁶.
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2026• Aimnova practice — 1.9.2
The expansion of (x + h)⁵ begins x⁵ + ax⁴ + bx³ + … . Find a and b in terms of h.
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2026• Aimnova practice — 1.9.3
In the expansion of (x + a)⁶, the coefficient of x⁴ is 60. Find the possible values of a.
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2026• Aimnova practice — 1.9.3
In the expansion of (2x + k)⁵, the coefficient of x⁴ is 80. Find k.
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2026• Aimnova practice — 1.9.3
In the expansion of (1 + ax)⁴, the coefficient of x² is 54. Find the possible values of a.
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2026• Aimnova practice — 1.9.3
In the expansion of (1 + x)ⁿ, the coefficient of x² is 36. Find n.
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2026• Aimnova practice — 1.9.3
In the expansion of (1 + x)ⁿ, the coefficient of x² is 66. Find n.
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2026• Aimnova practice — 1.9.3
In the expansion of (x − c)⁸, the coefficient of x⁶ is 112. Find the possible values of c.
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2026• Aimnova practice — 1.9.3
Find the term in x² in the expansion of (2 + x)⁵.
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2026• Aimnova practice — 1.9.1
Find the value of ⁸C₃, without a calculator.
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2026• Aimnova practice — 1.9.1
Show that the coefficient of x⁴ in the expansion of (x + 1)⁶ is 15.
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2026• Aimnova practice — 1.9.2
Expand (3 − x)⁴.
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2026• Aimnova practice — 1.9.2
Expand (x + 2)⁵.
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2026• Aimnova practice — 1.9.2
Find the first three terms, in ascending powers of x, of (1 + 2x)⁸.
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2026• Aimnova practice — 1.9.3
Find the constant term in the expansion of (x + 3/x)⁴.
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2026• Aimnova practice — 1.9.3
Find the term independent of x in the expansion of (2x² − 1/x)⁶.
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