OCR MEI Paper 3 2019 June — Question 4 3 marks

Exam BoardOCR MEI
ModulePaper 3 (Paper 3)
Year2019
SessionJune
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicProof
TypeAlgebraic inequality proof
DifficultyStandard +0.3 This is a straightforward algebraic proof requiring rationalizing denominators by multiplying by conjugates, then recognizing the telescoping sum pattern. While it requires careful algebraic manipulation and the insight to rationalize each term, the technique is standard A-level material and the telescoping pattern becomes clear once rationalization is performed. Slightly easier than average due to being a direct verification rather than requiring novel problem-solving.
Spec1.01a Proof: structure of mathematical proof and logical steps1.02b Surds: manipulation and rationalising denominators
4 In this question you must show detailed reasoning.
Show that \(\frac { 1 } { \sqrt { 10 } + \sqrt { 11 } } + \frac { 1 } { \sqrt { 11 } + \sqrt { 12 } } + \frac { 1 } { \sqrt { 12 } + \sqrt { 13 } } = \frac { 3 } { \sqrt { 10 } + \sqrt { 13 } }\).
Question 4:
AnswerMarks Guidance
AnswerMarks Guidance
DR: \(\frac{\sqrt{11}-\sqrt{10}}{11-10} + \frac{\sqrt{12}-\sqrt{11}}{12-11} + \frac{\sqrt{13}-\sqrt{12}}{13-12}\)M1 Rationalising denominators, allow one error
\(\sqrt{13} - \sqrt{10}\)A1
\(\frac{3}{\sqrt{10}+\sqrt{13}} = \frac{3(\sqrt{13}-\sqrt{10})}{13-10} = \sqrt{13}-\sqrt{10}\) [hence the two expressions are equal]E1 Convincing completion
[3] 
## Question 4:
| Answer | Marks | Guidance |
|--------|-------|----------|
| DR: $\frac{\sqrt{11}-\sqrt{10}}{11-10} + \frac{\sqrt{12}-\sqrt{11}}{12-11} + \frac{\sqrt{13}-\sqrt{12}}{13-12}$ | M1 | Rationalising denominators, allow one error |
| $\sqrt{13} - \sqrt{10}$ | A1 | |
| $\frac{3}{\sqrt{10}+\sqrt{13}} = \frac{3(\sqrt{13}-\sqrt{10})}{13-10} = \sqrt{13}-\sqrt{10}$ [hence the two expressions are equal] | E1 | Convincing completion |
| **[3]** | | |

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4 In this question you must show detailed reasoning.\\
Show that $\frac { 1 } { \sqrt { 10 } + \sqrt { 11 } } + \frac { 1 } { \sqrt { 11 } + \sqrt { 12 } } + \frac { 1 } { \sqrt { 12 } + \sqrt { 13 } } = \frac { 3 } { \sqrt { 10 } + \sqrt { 13 } }$.

\hfill \mbox{\textit{OCR MEI Paper 3 2019 Q4 [3]}}
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Q1 6 Q2 5 Q3 6 Q4 3 Q5 3 Q6 7 Q7 4 Q8 10 Q9 6 Q10 4 Q11 6 Q12 2 Q13 6 Q14 4 Q15 3