IGCSE · Additional Mathematics 0606 · Series & counting

Binomial expansion: IGCSE Additional Mathematics questions with answers

Free Binomial expansion questions for IGCSE Additional Mathematics (0606), part of Series & counting. Each question has the answer and the marking points an examiner would look for.

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Binomial expansion practice questions

Question 1Structured · 3 marksA* challenge

Find the term independent of x in the expansion of (2x − 1x)6.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
-160
general term M1
r = 3 M1
-160 A1
3
Question 2Structured · 5 marks
(a)

Find the first three terms in the expansion of (2 − x)6 in ascending powers of x.

[3]
(b)

Hence find the coefficient of x2 in the expansion of (1 + x)(2 − x)6.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)64 − 192x + 240x2
64 B1
−192x B1
240x2 B1
3
(b)48
two products M1
48 A1
2
Question 3Structured · 3 marksA* challenge

Find the term independent of x in the expansion of (2x − 1x)8.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
1120
general term M1
r = 4 M1
1120 A1
3
Question 4Structured · 5 marks
(a)

Find the first three terms in the expansion of (2 − 2x)6 in ascending powers of x.

[3]
(b)

Hence find the coefficient of x2 in the expansion of (1 + x)(2 − 2x)6.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)64 − 384x + 960x2
64 B1
−384x B1
960x2 B1
3
(b)576
two products M1
576 A1
2
Question 5Structured · 5 marks
(a)

Find the first three terms in the expansion of (2 + 3x)6, in ascending powers of x.

[3]
(b)

Hence find the coefficient of x2 in the expansion of (1 + 2x)(2 + 3x)6.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)64 + 576x + 2160x2
64 B1
576x B1
2160x2 B1
3
(b)3312
2160 + (2)(576) M1
3312 A1
2
Question 6Structured · 5 marks
(a)

Find the first three terms in the expansion of (3 − x)5 in ascending powers of x.

[3]
(b)

Hence find the coefficient of x2 in the expansion of (1 + x)(3 − x)5.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)243 − 405x + 270x2
243 B1
−405x B1
270x2 B1
3
(b)-135
two products M1
-135 A1
2

More Series & counting questions

Permutations & combinationsArithmetic & geometric progressions

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Original Cambridge-style practice questions written for mentorriyaz.in. These are not Cambridge past paper questions, and this site is not affiliated with or endorsed by Cambridge University Press & Assessment. Updated 2026-11-04. Paper generator · mentorriyaz.in