Exercises for Question Type 3: Doing quadratic factors and linear factors

Question 1

Skill question

Simplify and decompose into partial fractions: $\frac{x ^{2} - 4}{x ^{3} - x}$ .

[6]

Question 2

Skill question

Perform partial fraction decomposition on $\frac{2 x ^{3} + 5 x ^{2} + x + 3}{x ^{2} - 4}$ .

[6]

Question 3

Skill question

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

[5]

Question 4

Skill question

Decompose $\frac{3 x ^{2} - 3 x + 4}{( x ^{2} + 3 ) ( x - 1 )}$ into partial fractions.

[5]

Question 5

Skill question

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

[5]

Question 6

Skill question

Decompose into partial fractions: $\frac{x ^{2} + 2 x + 5}{x ^{3} + x ^{2} - x - 1}$ .

[7]

Question 7

Skill question

Find the partial fraction decomposition of $\frac{4 x + 7}{x ^{2} + 3 x + 2}$ .

[4]

Question 8

Skill question

Decompose the rational expression $\frac{2 x + 3}{x ^{2} - x - 2}$ into partial fractions.

[4]

Question 9

Skill question

Decompose $\frac{2 x ^{2} + 3 x + 4}{( x - 1 ) ( x ^{2} + 1 )}$ into partial fractions.

[6]

Question 10

Skill question

Decompose $\frac{4 x ^{2} + 2 x + 1}{( x - 3 ) ^{2} ( x + 2 )}$ into partial fractions.

[6]

IB Mathematics Analysis and Approaches Question Type 3: Doing Quadratic Factors and Linear Factors Exercises