| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/1 (Pre-U Mathematics Paper 1) |
| Year | 2013 |
| Session | June |
| Marks | 5 |
| Topic | Indefinite & Definite Integrals |
| Type | Pure definite integration |
| Difficulty | Easy -1.3 This is a straightforward application of basic integration rules (power rule) followed by direct substitution into limits. Part (i) requires only recall of standard integration formulas, and part (ii) is mechanical evaluation. No problem-solving, insight, or multi-step reasoning required—significantly easier than average A-level questions. |
| Spec | 1.08b Integrate x^n: where n != -1 and sums1.08d Evaluate definite integrals: between limits |
**(i)** Attempt integration — M1* [3]
Obtain at least $x^3 - 2x^2 + 8x$ — A1
Obtain $x^3 - 2x^2 + 8x + c$ — B1*
**(ii)** Attempt use of limits — M1 [2]
Obtain 26 — A1 **[5]**5 (i) Find $\int \left( 3 x ^ { 2 } - 4 x + 8 \right) \mathrm { d } x$.\\
(ii) Hence find $\int _ { 1 } ^ { 3 } \left( 3 x ^ { 2 } - 4 x + 8 \right) \mathrm { d } x$.
\hfill \mbox{\textit{Pre-U Pre-U 9794/1 2013 Q5 [5]}}