IB Mathematics AA HL  Popular Quizzes
The Binomial Theorem
Paper
Difficulty
View
Question 1
[Maximum mark: 5]
The third term in the expansion of $(x+p)^8$ is $252x^6$. Find the possible values of $p$.
Formula Booklet
Mark Scheme
Video
Revisit
Check with RV Newton
Formula Booklet
Mark Scheme
Solutions
Revisit
Ask Newton
Question 2
[Maximum mark: 5]
Consider the expansion of $\left(\dfrac{x^2}{2} + \dfrac{a}{x}\right)^6$. The constant term is $960$.
Find the possible values of $a$.
Formula Booklet
Mark Scheme
Video
Revisit
Check with RV Newton
Formula Booklet
Mark Scheme
Solutions
Revisit
Ask Newton
Question 3
[Maximum mark: 6]
In the expansion of $px^2(5 + px)^8$, the coefficient of the term in $x^6$ is $3402$. Find the value of $p$.
Formula Booklet
Mark Scheme
Video
Revisit
Check with RV Newton
Formula Booklet
Mark Scheme
Solutions
Revisit
Ask Newton
Question 4
[Maximum mark: 5]
In the expansion of $(2x + 1)^n$, the coefficient of the term in $x^2$ is $40n$, where $n \in \mathbb{Z}^+$. Find $n$.
Formula Booklet
Mark Scheme
Video
Revisit
Check with RV Newton
Formula Booklet
Mark Scheme
Solutions
Revisit
Ask Newton
Question 5
[Maximum mark: 5]
In the expansion of $x(2x + 1)^n$, the coefficient of the term in $x^3$ is $20n$, where $n \in \mathbb{Z}^+$. Find $n$.
Formula Booklet
Mark Scheme
Video
Revisit
Check with RV Newton
Formula Booklet
Mark Scheme
Solutions
Revisit
Ask Newton
Question 6
[Maximum mark: 8]
Use the extension of the binomial theorem for $n \in \mathbb{Q}$ to show that $\sqrt{\dfrac{1+x}{1x}} \approx 1 + x + \dfrac{x^2}{2}$, $x < 1$.
Formula Booklet
Mark Scheme
Video
Revisit
Check with RV Newton
Formula Booklet
Mark Scheme
Solutions
Revisit
Ask Newton
Question 7
[Maximum mark: 7]

Write down the quadratic expression $3x^2 + 5x  2$ in the form $(axb)(x+c)$.[2]

Hence, or otherwise, find the coefficient of the term in $x^9$ in the expansion
of $(3x^2+5x2)^5$. [5]
Formula Booklet
Mark Scheme
Video (a)
Video (b)
Revisit
Check with RV Newton
Formula Booklet
Mark Scheme
Solutions
Revisit
Ask Newton
Thank you Revision Village Members
#1 IB Math Resource
Revision Village is ranked the #1 IB Math Resources by IB Students & Teachers.
34% Grade Increase
Revision Village students scored 34% greater than the IB Global Average in their exams (2021).
80% of IB Students
More and more IB students are using Revision Village to prepare for their IB Math Exams.