CAIE P3 2024 June — Question 5 5 marks

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2024
SessionJune
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicPartial Fractions
TypeImproper fraction with linear factors – division then partial fractions
DifficultyModerate -0.8 This is a straightforward partial fractions question with a proper fraction (numerator degree less than denominator), linear distinct factors, and standard coefficients. It requires routine algebraic manipulation to find constants A and B, making it easier than average with no conceptual challenges or problem-solving required.
Spec1.02y Partial fractions: decompose rational functions
Express \(\frac{6x^2 - 2x + 2}{(x - 1)(2x + 1)}\) in partial fractions. [5]
Question 5:
AnswerMarks
5B C
State or imply the form A 
AnswerMarks Guidance
x1 2x1B1
Use a correct method for finding a constantM1 Correct appropriate method.
Obtain one of A = 3, B = 2 and C = –3A1
Obtain a second valueA1
Obtain a third valueA1
Alternative Method for Question 5
AnswerMarks Guidance
Divide numerator by denominator to reach A = 3(M1) axb
May be implied by 3 [+] with a and b not both 0.
x12x1
x5
Obtain 3 +
AnswerMarks
x12x1(A1)
D E
State or imply the form 
AnswerMarks
x1 2x1(B1)
Obtain one of D = 2 and E = − 3(A1)
Obtain a second value(A1)
5
AnswerMarks Guidance
QuestionAnswer Marks 
Question 5:
5 | B C
State or imply the form A 
x1 2x1 | B1
Use a correct method for finding a constant | M1 | Correct appropriate method.
Obtain one of A = 3, B = 2 and C = –3 | A1
Obtain a second value | A1
Obtain a third value | A1
Alternative Method for Question 5
Divide numerator by denominator to reach A = 3 | (M1) | axb
May be implied by 3 [+] with a and b not both 0.
x12x1
x5
Obtain 3 +
x12x1 | (A1)
D E
State or imply the form 
x1 2x1 | (B1)
Obtain one of D = 2 and E = − 3 | (A1)
Obtain a second value | (A1)
5
Question | Answer | Marks | Guidance
Express $\frac{6x^2 - 2x + 2}{(x - 1)(2x + 1)}$ in partial fractions. [5]

\hfill \mbox{\textit{CAIE P3 2024 Q5 [5]}}
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Q1 4 Q2 5 Q3 5 Q4 4 Q5 5 Q6 7 Q7 3 Q7 3 Q8 8 Q9 11 Q10 11 Q11 9