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SL 1.9—Binomial theorem where n is an integer - IB Questionbank | RevisionDojo

Practice SL 1.9—Binomial theorem where n is an integer with authentic IB Mathematics Analysis and Approaches (AA) exam questions for both SL and HL students. This question bank mirrors Paper 1, 2, 3 structure, covering key topics like functions and equations, calculus, complex numbers, sequences and series, and probability and statistics. Get instant solutions, detailed explanations, and build exam confidence with questions in the style of IB examiners.

Paper

Level

Question 1

SL & HLPaper 1

Find the non-zero values of $a$ and $b$ for which $(2x - a)^3 = 8x^3 - bx^2 + \frac{3}{2}bx - a^3$ .

[7]

Question 2

SL & HLPaper 1

Find the coefficient of $x^4$ in the expansion of $(1 + 3x)^7$ .

[3]

Question 3

SL & HLPaper 1

Find the term in $x^2$ in the expansion of $(1 - 3x^2)(1 + 4x)^5$ .

[4]

Question 4

SL & HLPaper 1

Find the first 4 terms, in ascending powers of $y$ , in the expansion of $(2 + y^2)^6$ .

[4]

Question 5

SL & HLPaper 1

Find the first $3$ terms in the expansion of $(y^3 - \frac{1}{y})^7$ in descending powers of $y$ .

[4]

Hence find the coefficient of $y^9$ in the expansion of $(y^4 - 2)(y^3 - \frac{1}{y})^7$ .

[5]

Question 6

SL & HLPaper 1

Given that the coefficient of $x^2$ in the expansion of $(1 + ax)^5(1 - 2x)^6$ is $10$ , find the possible values of $a$ .

[6]

Question 7

SL & HLPaper 1

Find the first 3 terms, in ascending powers of $x$ , in the expansion of $(1 - 4x)^7$ .

[3]

Question 8

SL & HLPaper 1

Given that the coefficient of $x^2$ in the expansion of $(2 + x)^4 + (1 - ax)^5$ is $64$ ,

Calculate the possible values of $a$ .

[6]

Question 9

SL & HLPaper 1

In the expansion of $(3 + 2x)^n$ , the coefficients of $x^2$ and $x^3$ are in the ratio $9 : 16$ .

Find the value of $n$ .

[6]

Question 10

SL & HLPaper 1

Expand and simplify $(3x + 1)^3$ .

[3]

SL 1.9—Binomial theorem where n is an integer Questionbank