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IB
AHL 1.11—Partial fractions

IB Mathematics Analysis and Approaches AHL 1.11—partial Fractions Questionbank

IB Mathematics Analysis and Approaches Topic AHL… | RevisionDojo

SL 1.1—Using standard form

SL 1.2—Arithmetic sequences and series

SL 1.3—Geometric sequences and series

SL 1.4—Financial apps – compound interest, annual depreciation

SL 1.5—Intro to logs

SL 1.6—Simple proof

SL 1.7—Laws of exponents and logs

SL 1.8—Sum of infinite geo sequence

SL 1.9—Binomial theorem where n is an integer

AHL 1.10—Perms and combs, binomial with negative and fractional indices

AHL 1.11—Partial fractions

AHL 1.12—Complex numbers – Cartesian form and Argand diag

AHL 1.13—Polar and Euler form

AHL 1.14—Complex roots of polynomials, conjugate roots, De Moivre’s, powers & roots of complex numbers

AHL 1.15—Proof by induction, contradiction, counterexamples

AHL 1.16—Solution of systems of linear equations

Paper

Level

Question

HLPaper 1

Let $f(x) = \frac{5x+2}{(x+1)(x^2+4)}$ .

(a)

Express $f(x)$ in the form $\frac{A}{x+1} + \frac{Bx+C}{x^2+4}$ .

HLPaper 1

(a)

Express $\frac{7x-4}{(x-2)^2(2x+1)}$ in partial fractions.

HLPaper 1

(a)

Express $\frac{4x^2+5x+3}{(x+1)(x^2+2x+2)}$ in partial fractions.

HLPaper 1

Let $X_n=\displaystyle\sum_{k=1}^{n}\frac{k+2}{k(k+1)(k+2)}$ .

HLPaper 1

Let $Y_n=\displaystyle\sum_{k=1}^{n}\frac{1}{(k+1)(k+3)}$ .

IB Mathematics Analysis and Approaches (AA) Topic AHL 1.11—partial Fractions Questionbank

Practice IB Mathematics Analysis and Approaches (AA) Topic AHL 1.11—partial Fractions with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for AHL 1.11—partial Fractions and mirrors Paper 1, 2, 3 style where relevant.

Get instant solutions, detailed explanations, and build confidence with questions aligned to IB examiner expectations.

+

x2+4Bx+C

[4]

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2

(

2

x

+

1

)

7x−4

[5]

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)

(

x2

+

2

x

+

2

)

4x2+5x+3

[6]

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(b)

Hence, evaluate $\int_0^1 \frac{4x^2+5x+3}{(x+1)(x^2+2x+2)} \, dx$ .

[7]

k=1∑n

k(k+1)(k+2)k+2

(a)

Show $\displaystyle \frac{k+2}{k(k+1)(k+2)}=\frac{1}{k(k+1)}=\frac{1}{k}-\frac{1}{k+1}$ .

[2]

(b)

Hence show $X_n=1-\dfrac{1}{n+1}=\dfrac{n}{n+1}$ .

(c)

Show the equivalent form $X_n=\dfrac{1}{2}+\dfrac{n-1}{2(n+1)}$ .

(d)

Prove by induction that $X_n=\dfrac{n}{n+1}$ for all .

(e)

Evaluate $\displaystyle\sum_{k=12}^{50}\frac{k+2}{k(k+1)(k+2)}$ .

k=1∑n

(k+1)(k+3)1

(a)

Show $X_n=\dfrac{n}{n+1}$ .

[2]

(b)

Hence obtain a closed form for $Y_n$ .

[3]

(c)

Show the equivalent form $Y_n=\dfrac{n(n+5)}{4(n+2)(n+3)}+\dfrac{1}{6}$ .

(d)

Prove by induction that $Y_n=\dfrac{5}{12}-\dfrac{2n+5}{2(n+2)(n+3)}$ holds for all .

(e)

Evaluate $\displaystyle\sum_{k=8}^{30}\frac{1}{(k+1)(k+3)}$ exactly.

1

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Question 3

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Question 5

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1

=

n+1n

[3]

+

2(n+1)n−1

[2]

n\in\mathbb{Z}^+

n \in Z^{+}

[4]

+

1

)

(

k

+

2

)

k+2

[2]

1

)

2

)

(

n

+

3

)

n(n+5)

+

61

[2]

−

2(n+2)(n+3)2n+5

n\in\mathbb{Z}^+

[4]

1

)

(

k

+

3

)

1

[2]

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Sign up to write and grade your answer

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