| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2008 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Multiple transformation descriptions |
| Difficulty | Easy -1.2 This is a straightforward C1 question testing basic curve sketching and transformations. Parts (i) and (ii) require simple sketches of standard functions with minimal modifications (vertical translation and coefficient), while part (iii) asks for identification of a single transformation (vertical stretch factor 1.5). All components are routine recall and application with no problem-solving or novel insight required. |
| Spec | 1.02n Sketch curves: simple equations including polynomials1.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks |
|---|---|
| \(y = 2\) (horizontal asymptote); positive cubic | B1 |
| Curve passes through (0, 2) and approaches asymptote | B1 2 |
| Correct curve with correct curvature in +ve quadrant only | B1 |
| Completely correct curve | B1 2 |
| Answer | Marks |
|---|---|
| Stretch scale factor 1.5 parallel to y-axis | B1 |
| Answer | Marks |
|---|---|
| Stretch factor 1.5 parallel to y-axis (or in y-direction) | B1 B1 3/7 |
## 5(i)
$y = 2$ (horizontal asymptote); positive cubic | B1 |
Curve passes through (0, 2) and approaches asymptote | B1 2 |
Correct curve with correct curvature in +ve quadrant only | B1 |
Completely correct curve | B1 2 |
## 5(ii)
Stretch scale factor 1.5 parallel to y-axis | B1 |
## 5(iii)
Stretch factor 1.5 parallel to y-axis (or in y-direction) | B1 B1 3/7 |
---5 (i) Sketch the curve $y = x ^ { 3 } + 2$.\\
(ii) Sketch the curve $y = 2 \sqrt { x }$.\\
(iii) Describe a transformation that transforms the curve $y = 2 \sqrt { x }$ to the curve $y = 3 \sqrt { x }$.
\hfill \mbox{\textit{OCR C1 2008 Q5 [7]}}