Question 1 - A-Level Maths

OCR C1 2007 June — Question 1 3 marks

Exam Board	OCR
Module	C1 (Core Mathematics 1)
Year	2007
Session	June
Marks	3
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Completing the square and sketching
Type	Complete the square
Difficulty	Easy -1.8 This is a straightforward algebraic expansion and simplification requiring only basic skills: expanding two brackets using $(a+b)^2$ and $(a-b)^2$ formulas, then collecting like terms. It's a routine C1 question with no problem-solving element, making it significantly easier than average A-level content.
Spec	1.02j Manipulate polynomials: expanding, factorising, division, factor theorem

1 Simplify $( 2 x + 5 ) ^ { 2 } - ( x - 3 ) ^ { 2 }$, giving your answer in the form $a x ^ { 2 } + b x + c$.

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Question 1:

Answer	Marks	Guidance
$(4x^2 + 20x + 25) - (x^2 - 6x + 9)$	M1	Square one bracket to give expression of form $ax^2 + bx + c$ where $a \neq 0, b \neq 0, c \neq 0$
$= 3x^2 + 26x + 16$	A1	One squared bracket fully correct
A1 (3)	All 3 terms of final answer correct

Alternative (difference of two squares):

Answer	Marks	Guidance
$(2x + 5 + (x-3))(2x + 5 - (x-3))$	M1	2 brackets with same terms but different signs
$= (3x+2)(x+8)$	A1	One bracket correctly simplified
$= 3x^2 + 26x + 16$	A1 (3)	All 3 terms of final answer correct

# Question 1:

$(4x^2 + 20x + 25) - (x^2 - 6x + 9)$ | M1 | Square one bracket to give expression of form $ax^2 + bx + c$ where $a \neq 0, b \neq 0, c \neq 0$
$= 3x^2 + 26x + 16$ | A1 | One squared bracket fully correct
| A1 (3) | All 3 terms of final answer correct

**Alternative (difference of two squares):**
$(2x + 5 + (x-3))(2x + 5 - (x-3))$ | M1 | 2 brackets with same terms but different signs
$= (3x+2)(x+8)$ | A1 | One bracket correctly simplified
$= 3x^2 + 26x + 16$ | A1 (3) | All 3 terms of final answer correct

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1 Simplify $( 2 x + 5 ) ^ { 2 } - ( x - 3 ) ^ { 2 }$, giving your answer in the form $a x ^ { 2 } + b x + c$.

\hfill \mbox{\textit{OCR C1 2007 Q1 [3]}}

This paper (10 questions)

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Q1 3 Q2 5 Q3 5 Q4 5 Q5 6 Q6 6 Q7 9 Q8 9 Q9 12 Q10 12

Answer	Marks	Guidance
\((4x^2 + 20x + 25) - (x^2 - 6x + 9)\)	M1	Square one bracket to give expression of form \(ax^2 + bx + c\) where \(a \neq 0, b \neq 0, c \neq 0\)
\(= 3x^2 + 26x + 16\)	A1	One squared bracket fully correct
A1 (3)	All 3 terms of final answer correct

Answer	Marks	Guidance
\((2x + 5 + (x-3))(2x + 5 - (x-3))\)	M1	2 brackets with same terms but different signs
\(= (3x+2)(x+8)\)	A1	One bracket correctly simplified
\(= 3x^2 + 26x + 16\)	A1 (3)	All 3 terms of final answer correct