| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/1 (Pre-U Mathematics Paper 1) |
| Session | Specimen |
| Marks | 4 |
| Topic | Indefinite & Definite Integrals |
| Type | Integration with given constant |
| Difficulty | Moderate -0.8 This is a straightforward definite integration question requiring only basic polynomial integration and solving a simple quadratic equation. The integrand is linear, the technique is standard, and finding k involves elementary algebra with no conceptual challenges beyond routine A-level integration. |
| Spec | 1.08d Evaluate definite integrals: between limits1.08e Area between curve and x-axis: using definite integrals |
Obtain $\left[x^2 - x\right]_1^k$ [B1]
Substitute both limits in their expression and equate to RHS [M1]
$k^2 - k = 6$ [A1]
Obtain $k = 3$ only [A1] **4 marks**2 Find the value of the positive constant $k$ for which $\int _ { 1 } ^ { k } ( 2 x - 1 ) \mathrm { d } x = 6$.
\hfill \mbox{\textit{Pre-U Pre-U 9794/1 Q2 [4]}}