Easy -1.3 This is a straightforward C1 integration question requiring only direct application of the power rule to two terms. Students need to recall that x^n integrates to x^(n+1)/(n+1) and rewrite 1/x² as x^(-2), then add the constant of integration. No problem-solving, substitution, or multi-step reasoning required—purely routine manipulation.
M1: \(x^n \to x^{n+1}\) for either term. A1: \(3\frac{x^3}{3}\) or \(-4\frac{x^{-1}}{-1}\) (one correct term, may be unsimplified). A1: both terms correct (may be unsimplified). Note M1A0A1 is not possible
Fully correct simplified answer with \(+c\) all appearing on the same line
## Question 3:
| Answer/Working | Mark | Guidance |
|---|---|---|
| $\int 3x^2 - \frac{4}{x^2}dx = 3\frac{x^3}{3} - 4\frac{x^{-1}}{-1}$ | M1, A1, A1 | M1: $x^n \to x^{n+1}$ for either term. A1: $3\frac{x^3}{3}$ **or** $-4\frac{x^{-1}}{-1}$ (one correct term, may be unsimplified). A1: both terms correct (may be unsimplified). Note M1A0A1 is not possible |
| $= x^3 + \frac{4}{x} + c$ or $x^3 + 4x^{-1} + c$ | A1 | Fully correct simplified answer with $+c$ all appearing on the same line |
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