AQA C3 — Question 2

Exam BoardAQA
ModuleC3 (Core Mathematics 3)
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicNumerical integration
TypeSimpson's rule application
DifficultyModerate -0.3 This is a straightforward application of Simpson's rule with clearly specified parameters (5 ordinates, 4 strips). The function evaluation requires only calculator work with no algebraic manipulation. While Simpson's rule is a C3 topic, this is a routine textbook exercise requiring only formula recall and arithmetic, making it slightly easier than average.
Spec1.09f Trapezium rule: numerical integration
2 Use Simpson's rule with 5 ordinates ( 4 strips) to find an approximation to $$\int _ { 1 } ^ { 3 } \frac { 1 } { \sqrt { 1 + x ^ { 3 } } } \mathrm {~d} x$$ giving your answer to three significant figures.
Question 2:
(a)
AnswerMarks Guidance
Answer/WorkingMark Guidance
\(\frac{dy}{dx} = 4x^3 \tan 2x + 2x^4 \sec^2 2x\)M1A1A1 M1 product rule; A1 each correct term
(b)
AnswerMarks Guidance
Answer/WorkingMark Guidance
Quotient rule: \(\frac{dy}{dx} = \frac{2x(x-1) - x^2}{(x-1)^2}\)M1A1 M1 for correct quotient/product rule attempt
At \(x=3\): \(\frac{6(2)-9}{4} = \frac{3}{4}\)A1 
## Question 2:

**(a)**
| Answer/Working | Mark | Guidance |
|---|---|---|
| $\frac{dy}{dx} = 4x^3 \tan 2x + 2x^4 \sec^2 2x$ | M1A1A1 | M1 product rule; A1 each correct term |

**(b)**
| Answer/Working | Mark | Guidance |
|---|---|---|
| Quotient rule: $\frac{dy}{dx} = \frac{2x(x-1) - x^2}{(x-1)^2}$ | M1A1 | M1 for correct quotient/product rule attempt |
| At $x=3$: $\frac{6(2)-9}{4} = \frac{3}{4}$ | A1 | |

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2 Use Simpson's rule with 5 ordinates ( 4 strips) to find an approximation to

$$\int _ { 1 } ^ { 3 } \frac { 1 } { \sqrt { 1 + x ^ { 3 } } } \mathrm {~d} x$$

giving your answer to three significant figures.

\hfill \mbox{\textit{AQA C3  Q2}}
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