CAIE P1 2023 June — Question 4 3 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2023
SessionJune
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicSolving quadratics and applications
TypeQuadratic in higher integer powers
DifficultyStandard +0.3 This is a disguised quadratic requiring the substitution u = x³, then solving 8u² + 215u - 27 = 0 using the quadratic formula, followed by cube roots. While it requires recognizing the substitution pattern and careful arithmetic, it's a standard technique taught explicitly in P1 with no novel problem-solving required, making it slightly easier than average.
Spec1.02f Solve quadratic equations: including in a function of unknown

Solve the equation \(8x^6 + 215x^3 - 27 = 0\). [3]

Question 4:
AnswerMarks
4Unless otherwise indicated, marks once gained cannot subsequently be lost, e.g. wrong working following a correct form of answer is ignored (isw).
4[8x6 215x3270] leading to  8x3 1  x3 27 0
OR
215 2152 4.8.27 215 47089
or
AnswerMarks Guidance
2.8 2.8M1 OE
If a substitution is used then the correct coefficients must
be retained. Condone substitution of x x3.
1
, 27
AnswerMarks Guidance
8A1 Both correct values seen.
1
SC: if M0 scored SC B1 is available for sight of and
8
27 OE
1
or 0.5 ,3
AnswerMarks Guidance
2A1 SC: if M0SCB1 scored then SCB1 is available for the
correct answers and no others. Do not ISW if answers
given as a range.
3
AnswerMarks Guidance
QuestionAnswer Marks
Question 4:
4 | Unless otherwise indicated, marks once gained cannot subsequently be lost, e.g. wrong working following a correct form of answer is ignored (isw).
4 | [8x6 215x3270] leading to  8x3 1  x3 27 0
OR
215 2152 4.8.27 215 47089
or
2.8 2.8 | M1 | OE
If a substitution is used then the correct coefficients must
be retained. Condone substitution of x x3.
1
, 27
8 | A1 | Both correct values seen.
1
SC: if M0 scored SC B1 is available for sight of and
8
27 OE
1
or 0.5 ,3
2 | A1 | SC: if M0SCB1 scored then SCB1 is available for the
correct answers and no others. Do not ISW if answers
given as a range.
3
Question | Answer | Marks | Guidance
Solve the equation $8x^6 + 215x^3 - 27 = 0$. [3]

\hfill \mbox{\textit{CAIE P1 2023 Q4 [3]}}