CAIE P3 2018 June — Question 2 3 marks

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2018
SessionJune
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicBinomial Theorem (positive integer n)
TypeBinomial with negative or fractional powers of x
DifficultyEasy -1.2 This is a straightforward application of the binomial theorem requiring identification of the term where powers of x cancel to give x^(-1). It's a standard textbook exercise with a single technique and minimal steps, making it easier than average but not trivial since students must correctly handle negative powers.
Spec1.04a Binomial expansion: (a+b)^n for positive integer n

Find the coefficient of \(\frac{1}{x}\) in the expansion of \(\left(x - \frac{2}{x}\right)^5\). [3]

Question 2:
AnswerMarks Guidance
2State or imply u2 =u+5, or equivalent in 5x B1
Solve for u, or 5xM1
1
Obtain root (1+ 21), or decimal in [2.79, 2.80]
AnswerMarks Guidance
2A1
Use correct method for finding x from a positive rootM1
Obtain answer x = 0.638 and no other answerA1
Total:5
QuestionAnswer Marks
Question 2:
2 | State or imply u2 =u+5, or equivalent in 5x | B1
Solve for u, or 5x | M1
1
Obtain root (1+ 21), or decimal in [2.79, 2.80]
2 | A1
Use correct method for finding x from a positive root | M1
Obtain answer x = 0.638 and no other answer | A1
Total: | 5
Question | Answer | Marks
Find the coefficient of $\frac{1}{x}$ in the expansion of $\left(x - \frac{2}{x}\right)^5$. [3]

\hfill \mbox{\textit{CAIE P3 2018 Q2 [3]}}