Moderate -0.8 This is a straightforward algebraic manipulation followed by term-by-term integration. Students expand the numerator, divide each term by 4√x to get powers of x, then integrate using the standard power rule. It requires only routine algebraic skills and basic integration—no problem-solving insight needed, making it easier than average.
Attempts to write as sum of terms using correct index laws at least once; award for any term with correct index; cannot score for correct index from incorrect work
\(x^n \to x^{n+1}\)
dM1
Increases power of any term by 1; dependent on first M1
Any two terms correct unsimplified (indices processed) for first A1; all four terms correct, simplified, on one line with \(+C\) for second A1
# Question 4:
$\int \frac{3x^2 - 15x^{\frac{1}{2}} + 2x - 10}{4\sqrt{x}}\,dx = \int \frac{3}{4}x - \frac{15}{4} + \frac{1}{2}x^{\frac{1}{2}} - \frac{5}{2}x^{-\frac{1}{2}}\,dx$ | M1A1A1 | Attempts to write as sum of terms using correct index laws at least once; award for any term with correct index; cannot score for correct index from incorrect work
$x^n \to x^{n+1}$ | dM1 | Increases power of any term by 1; dependent on first M1
$\frac{3}{8}x^2 - \frac{15}{4}x + \frac{1}{3}x^{\frac{3}{2}} - 5x^{\frac{1}{2}} + C$ | A1A1 | Any two terms correct unsimplified (indices processed) for first A1; all four terms correct, simplified, on one line with $+C$ for second A1
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