CAIE P1 2019 March — Question 1 3 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2019
SessionMarch
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicBinomial Theorem (positive integer n)
TypeSingle coefficient given directly
DifficultyModerate -0.8 This is a straightforward application of the binomial theorem requiring students to identify the correct term, write out the binomial coefficient formula, set it equal to the given value, and solve a simple equation for p. It's more routine than average with minimal problem-solving required.
Spec1.04a Binomial expansion: (a+b)^n for positive integer n

The coefficient of \(x^3\) in the expansion of \((1 - px)^5\) is \(-2160\). Find the value of the constant \(p\). [3]

Question 1:
AnswerMarks
15C3( )( )3
− px soi
AnswerMarks Guidance
 B1 Can be part of expansion. Condone omission of ‒ sign
( −1 ) 10p3 =−2160 then ÷ and cube rootM1 Condone omission of ‒ sign.
p=6A1
3
AnswerMarks Guidance
QuestionAnswer Marks
Question 1:
1 | 5C3( )( )3
− px soi
  | B1 | Can be part of expansion. Condone omission of ‒ sign
( −1 ) 10p3 =−2160 then ÷ and cube root | M1 | Condone omission of ‒ sign.
p=6 | A1
3
Question | Answer | Marks | Guidance
The coefficient of $x^3$ in the expansion of $(1 - px)^5$ is $-2160$. Find the value of the constant $p$. [3]

\hfill \mbox{\textit{CAIE P1 2019 Q1 [3]}}