CAIE P3 2018 June — Question 1 3 marks

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2018
SessionJune
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicCompleting the square and sketching
TypeComplete the square
DifficultyEasy -1.2 This is a straightforward completing the square exercise with a non-unit coefficient. It requires routine algebraic manipulation (factoring out 3, completing the square, simplifying) with no problem-solving or conceptual insight needed. Standard textbook question worth 3 marks, easier than average A-level content.
Spec1.02e Complete the square: quadratic polynomials and turning points

Express \(3x^2 - 12x + 7\) in the form \(a(x + b)^2 + c\), where \(a\), \(b\) and \(c\) are constants. [3]

Question 1:
AnswerMarks
1Obtain a correct unsimplified version of the x or x2 term of the expansion of
1
( )− 1  3  − 2
4−3x 2 or  1− x 
AnswerMarks
 4 M1
State correct first term 2B1
3 27
Obtain the next two terms x+ x2
AnswerMarks Guidance
4 64A1 + A1
Total:4
QuestionAnswer Marks
Question 1:
1 | Obtain a correct unsimplified version of the x or x2 term of the expansion of
1
( )− 1  3  − 2
4−3x 2 or  1− x 
 4  | M1
State correct first term 2 | B1
3 27
Obtain the next two terms x+ x2
4 64 | A1 + A1
Total: | 4
Question | Answer | Marks
Express $3x^2 - 12x + 7$ in the form $a(x + b)^2 + c$, where $a$, $b$ and $c$ are constants. [3]

\hfill \mbox{\textit{CAIE P3 2018 Q1 [3]}}