| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2005 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Composite & Inverse Functions |
| Type | Evaluate composite at point |
| Difficulty | Moderate -0.8 This is a straightforward question requiring basic function composition and understanding of quadratic range. Part (i) involves recognizing a negative quadratic has maximum value 10, and part (ii) is simple substitution: f(-1) = 6, then f(6) = -41. Both parts are routine with no problem-solving required, making it easier than average. |
| Spec | 1.02u Functions: definition and vocabulary (domain, range, mapping)1.02v Inverse and composite functions: graphs and conditions for existence |
| Answer | Marks | Guidance |
|---|---|---|
| (i) State \(f(x) \le 10\) | B1 | [Any equiv but must be or imply \(\le\)] |
| (ii) Attempt correct process for composition of functions | M1 | [whether algebraic or numerical] |
| Obtain 6 or correct expression for \(ff(x)\) | A1 | |
| Obtain \(-71\) | A1 | Total: 3 marks |
**(i)** State $f(x) \le 10$ | B1 | [Any equiv but must be or imply $\le$]
**(ii)** Attempt correct process for composition of functions | M1 | [whether algebraic or numerical]
Obtain 6 or correct expression for $ff(x)$ | A1 |
Obtain $-71$ | A1 | Total: 3 marks1 The function f is defined for all real values of $x$ by
$$f ( x ) = 10 - ( x + 3 ) ^ { 2 } .$$
(i) State the range of f .\\
(ii) Find the value of $\mathrm { ff } ( - 1 )$.
\hfill \mbox{\textit{OCR C3 2005 Q1 [4]}}