| Exam Board | CAIE |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2020 |
| Session | Specimen |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Function Transformations |
| Type | Algebraic to algebraic transformation description |
| Difficulty | Moderate -0.8 This is a straightforward question on function transformations requiring students to (a) apply a horizontal translation to a quadratic and simplify, and (b) describe the component transformations of y=f(-x). Both parts test standard recall and routine application of transformation rules with minimal problem-solving demand. |
| Spec | 1.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(y = (x-2)^2 + 3(x-2) + 4 = x^2 - x + 2\) | 2 M1A1 | In either order |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Reflection [in] \(y\) axis | 1 B1 | |
| Stretch factor 3 in \(y\) direction | 2 B1B1 | B1 for stretch, B1 for factor 3 in \(y\) direction |
| Total | 3 |
## Question 5(a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $y = (x-2)^2 + 3(x-2) + 4 = x^2 - x + 2$ | 2 M1A1 | In either order |
## Question 5(b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Reflection [in] $y$ axis | 1 B1 | |
| Stretch factor 3 in $y$ direction | 2 B1B1 | B1 for stretch, B1 for factor 3 in $y$ direction |
| **Total** | **3** | |5 (a) The curve $y = x ^ { 2 } + 3 x + 4$ is translated by $\binom { 2 } { 0 }$.\\
Find and simplify the equation of the translated curve.\\
(b) The graph of $y = \mathrm { f } ( x )$ is transformed to the graph of $y = 3 \mathrm { f } ( - x )$.
Describe fully the two single transformations which have been combined to give the resulting transformation.\\
\hfill \mbox{\textit{CAIE P1 2020 Q5 [5]}}