OCR C1 2005 June — Question 3 5 marks

Exam BoardOCR
ModuleC1 (Core Mathematics 1)
Year2005
SessionJune
Marks5
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TopicCurve Sketching
TypeReflections
DifficultyEasy -1.2 This is a straightforward C1 question testing basic curve sketching and simple transformations. Part (i) requires sketching a standard cubic, (ii) asks for a reflection (a standard transformation), and (iii) involves a horizontal translation. All parts are routine recall and application of basic transformation rules with no problem-solving or novel insight required.
Spec1.02n Sketch curves: simple equations including polynomials1.02w Graph transformations: simple transformations of f(x)
3
  1. Sketch the curve \(y = x ^ { 3 }\).
  2. Describe a transformation that transforms the curve \(y = x ^ { 3 }\) to the curve \(y = - x ^ { 3 }\).
  3. The curve \(y = x ^ { 3 }\) is translated by \(p\) units, parallel to the \(x\)-axis. State the equation of the curve after it has been transformed.
Question 3(i):
AnswerMarks Guidance
Answer/WorkingMarks Guidance
Correct sketchB1 1 Correct sketch showing point of inflection at origin
Question 3(ii):
AnswerMarks Guidance
Answer/WorkingMarks Guidance
Reflection in \(x\)-axis or reflection in \(y\)-axisB1 Reflection
B1 2In \(x\)-axis or \(y=0\) or \(y\)-axis or \(x=0\)
Question 3(iii):
AnswerMarks Guidance
Answer/WorkingMarks Guidance
\(y = (x-p)^3\)M1 \(y = (x \pm p)^3\)
A1 2\(y = (x-p)^3\) 
## Question 3(i):

| Answer/Working | Marks | Guidance |
|---|---|---|
| Correct sketch | B1 **1** | Correct sketch showing point of inflection at origin |

## Question 3(ii):

| Answer/Working | Marks | Guidance |
|---|---|---|
| Reflection in $x$-axis or reflection in $y$-axis | B1 | Reflection |
| | B1 **2** | In $x$-axis or $y=0$ or $y$-axis or $x=0$ |

## Question 3(iii):

| Answer/Working | Marks | Guidance |
|---|---|---|
| $y = (x-p)^3$ | M1 | $y = (x \pm p)^3$ |
| | A1 **2** | $y = (x-p)^3$ |

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3 (i) Sketch the curve $y = x ^ { 3 }$.\\
(ii) Describe a transformation that transforms the curve $y = x ^ { 3 }$ to the curve $y = - x ^ { 3 }$.\\
(iii) The curve $y = x ^ { 3 }$ is translated by $p$ units, parallel to the $x$-axis. State the equation of the curve after it has been transformed.

\hfill \mbox{\textit{OCR C1 2005 Q3 [5]}}
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