How is the general term written?

The term with r + 1 in (a + b)ⁿ is n choose r times a to the n minus r times b to the r.

How do I find a constant term?

Set the power of x in the general term to zero and solve for r.

S6 Maths: Binomial Theorem, Paper 2 — general term and specific terms

2026-11-02

Tutor Prep Guide · Primary English

The general term turns which term and which power into one expression that you solve for r.

Focus　Write the general term, set the power of x to the target, solve for r and substitute back.

01　Paper details (check answers afterwards)

Item	Detail
Questions	10
Suggested time	25
Difficulty mix	Foundation 4 · Intermediate 3 · Challenge 2 · Error redo 1
Chapter	Chapter: S6 Maths: Binomial Theorem
Level	S6

02　Questions (10 items)

FoundationExpand (2 + x)³.
FoundationFind the coefficient of x² in (1 + 2x)⁶.
FoundationWrite down the coefficients in the expansion of (a + b)⁵.
FoundationFind the coefficient of x³ in (3 + x)⁴.
IntermediateFind the coefficient of x² in (1 − x)⁷.
IntermediateFind the constant term in (x + 1/x)⁶.
IntermediateThe coefficient of x³ in (1 + x)ⁿ is 56. Find n.
ChallengeFind the constant term in (2x − 1/x²)⁶.
ChallengeFind the coefficient of x² in (1 + x)⁴(1 + 2x)³.
Error redoError: a student expands (1 + x)⁴ as 1 + 4x + 4x² + 4x³ + x⁴. What is correct?

03　Answers and one-line notes

#	Answer	One-line note
1	8 + 12x + 6x² + x³	The coefficients run 1, 3, 3 and 1, with powers of 2 falling from 8.
2	60	Six choose two is 15 and 2 squared is 4, so the coefficient is 60.
3	1, 5, 10, 10, 5, 1	The fifth row of the triangle is symmetric with 5 and 10 in the middle.
4	12	Four choose three is 4 and the remaining factor is 3, giving 12.
5	21	Seven choose two is 21 and the minus sign disappears because the power is even.
6	20	The power of x in the general term is 6 minus 2r, so r is 3 and the term is six choose three.
7	n = 8	Eight choose three is 56, so n is 8.
8	240	The general term has x to the power 6 minus 3r, so r is 2 and the term is 15 times 16.
9	42	Add the three ways of making x squared: 1 times 12, 4 times 6 and 6 times 1.
10	1 + 4x + 6x² + 4x³ + x⁴	The middle coefficients are 4, 6 and 4 rather than all 4, because they come from the triangle.

04　What to do after marking

After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
Repeat the same item two days later; move to the next paper only when both attempts are correct.
Parents only need the answer and note columns; there is no need to explain every item.

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