Edexcel C12 2016 January — Question 3 5 marks

Exam BoardEdexcel
ModuleC12 (Core Mathematics 1 & 2)
Year2016
SessionJanuary
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicIndefinite & Definite Integrals
TypePure definite integration
DifficultyEasy -1.2 This is a straightforward definite integration question requiring only basic integration rules (power rule for polynomials and x^{-1/2}) followed by substitution of limits. It's routine C2 material with no problem-solving element—purely procedural application of standard techniques, making it easier than average.
Spec1.08b Integrate x^n: where n != -1 and sums1.08d Evaluate definite integrals: between limits

3. Find, using calculus and showing each step of your working, $$\int _ { 1 } ^ { 4 } \left( 6 x - 3 - \frac { 2 } { \sqrt { x } } \right) \mathrm { d } x$$

Question 3:
AnswerMarks Guidance
WorkingMark Guidance
\(\int\!\left(6x-3-\frac{2}{\sqrt{x}}\right)dx = \frac{6x^2}{2}-3x-\frac{2x^{\frac{1}{2}}}{\frac{1}{2}}+(c)\)M1 A1 A1 M1: At least one power increased \(x^n\to x^{n+1}\). A1: Two of three terms correct un-simplified or simplified (constant not required). A1: All three terms correct un-simplified or simplified (constant not required)
\(\left[\frac{6x^2}{2}-3x-\frac{2x^{\frac{1}{2}}}{\frac{1}{2}}+(c)\right]_1^4=(28)-(-4)=32\)M1 A1 M1: Substitutes limits 4 and 1 and subtracts correct way round. A1: 32 cao (32 + c is A0). Question requires calculus so correct answer only scores no marks
## Question 3:
| Working | Mark | Guidance |
|---------|------|----------|
| $\int\!\left(6x-3-\frac{2}{\sqrt{x}}\right)dx = \frac{6x^2}{2}-3x-\frac{2x^{\frac{1}{2}}}{\frac{1}{2}}+(c)$ | M1 A1 A1 | M1: At least one power increased $x^n\to x^{n+1}$. A1: Two of three terms correct un-simplified or simplified (constant not required). A1: All three terms correct un-simplified or simplified (constant not required) |
| $\left[\frac{6x^2}{2}-3x-\frac{2x^{\frac{1}{2}}}{\frac{1}{2}}+(c)\right]_1^4=(28)-(-4)=32$ | M1 A1 | M1: Substitutes limits 4 and 1 and subtracts correct way round. A1: 32 cao (**32 + c is A0**). Question requires calculus so correct answer only scores no marks |

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3. Find, using calculus and showing each step of your working,

$$\int _ { 1 } ^ { 4 } \left( 6 x - 3 - \frac { 2 } { \sqrt { x } } \right) \mathrm { d } x$$

\hfill \mbox{\textit{Edexcel C12 2016 Q3 [5]}}