| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2012 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Function Transformations |
| Type | Identify transformation from equations |
| Difficulty | Moderate -0.8 This is a straightforward C1 question testing basic function transformation knowledge: sketching a standard curve, identifying a horizontal translation, and applying a horizontal stretch. All parts require direct recall of transformation rules with no problem-solving or multi-step reasoning required. |
| Spec | 1.02m Graphs of functions: difference between plotting and sketching1.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| [Correct shaped graph in Q1] | M1 | Correct shape of graph in Q1. Ignore reflection in the \(x\) axis. Ignore "feathering". Finite "plot" scores M0. Need not meet origin for M mark. Allow slight curve downwards for M mark but not for A |
| [Graph in Q1 only] | A1 [2] | Correct graph in Q1 only. Allow tending to horizontal |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Translate(d) or Translation | B1 | Do not accept "shift", "move" etc. without the word translation/translate(d) |
| Parallel to \(x\)-axis, \((+)4\) units | B1 [2] | For "parallel to the \(x\) axis" allow "horizontally", "across", "to the right", "in the (positive) \(x\) direction". Do not accept "in/on/across/up/along/to/towards the \(x\) axis". Allow e.g. "4 units across in the positive \(x\) direction parallel to the \(x\) axis" but do not award second B1 if statements are contradictory. "Factor 4" not acceptable |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(y = \sqrt{\left(\frac{x}{5}\right)}\) | M1 | \(\sqrt{5x}\) or \(\sqrt{\frac{x}{5}}\) seen. SC If doubt over whether use of square root/solidus is totally correct B1 (Must still have "\(y =\)") |
| A1 [2] | Must have "\(y =\)" to earn A mark (do not allow "\(f(x) =\)"). Allow \(\sqrt{5}y = \sqrt{x}\) or equivalent |
## Question 5(i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| [Correct shaped graph in Q1] | M1 | Correct shape of graph in Q1. Ignore reflection in the $x$ axis. Ignore "feathering". Finite "plot" scores **M0**. Need not meet origin for **M** mark. Allow slight curve downwards for **M** mark but not for **A** |
| [Graph in Q1 only] | A1 [2] | Correct graph in Q1 only. Allow tending to horizontal |
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## Question 5(ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Translate(d) or Translation | B1 | **Do not accept** "shift", "move" etc. without the word translation/translate(d) |
| Parallel to $x$-axis, $(+)4$ units | B1 [2] | For "parallel to the $x$ axis" allow "horizontally", "across", "to the right", "in the (positive) $x$ direction". **Do not accept** "in/on/across/up/along/to/towards the $x$ axis". Allow e.g. "4 units across in the positive $x$ direction parallel to the $x$ axis" but do not award second B1 if statements are contradictory. "Factor 4" not acceptable |
---
## Question 5(iii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $y = \sqrt{\left(\frac{x}{5}\right)}$ | M1 | $\sqrt{5x}$ or $\sqrt{\frac{x}{5}}$ seen. SC If doubt over whether use of square root/solidus is totally correct **B1** (Must still have "$y =$") |
| | A1 [2] | **Must have** "$y =$" to earn A mark (do not allow "$f(x) =$"). Allow $\sqrt{5}y = \sqrt{x}$ or equivalent |
---5 (i) Sketch the curve $y = \sqrt { x }$.\\
(ii) Describe the transformation that transforms the curve $y = \sqrt { x }$ to the curve $y = \sqrt { x - 4 }$.\\
(iii) The curve $y = \sqrt { x }$ is stretched by a scale factor of 5 parallel to the $x$-axis. State the equation of the transformed curve.
\hfill \mbox{\textit{OCR C1 2012 Q5 [6]}}