Edexcel C1 2013 June — Question 3 5 marks

Exam BoardEdexcel
ModuleC1 (Core Mathematics 1)
Year2013
SessionJune
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicIndices and Surds
TypeSimplify algebraic expressions with indices
DifficultyEasy -1.3 This is a straightforward C1 indices question requiring only direct application of index laws with no problem-solving. Part (a) is routine evaluation of a fractional power, and part (b) is mechanical simplification using basic rules. Both parts are standard textbook exercises easier than the typical A-level question.
Spec1.02a Indices: laws of indices for rational exponents
3. (a) Find the value of \(8 ^ { \frac { 5 } { 3 } }\) (b) Simplify fully \(\frac { \left( 2 x ^ { \frac { 1 } { 2 } } \right) ^ { 3 } } { 4 x ^ { 2 } }\)
Question 3:
Part (a):
AnswerMarks Guidance
Answer/WorkingMarks Guidance
\(8^{\frac{1}{3}} = 2\) or \(8^5 = 32768\)M1 A correct attempt to deal with the \(\frac{1}{3}\) or the 5. \(8^{\frac{1}{3}} = \sqrt[3]{8}\) or \(8^5 = 8\times8\times8\times8\times8\)
\(8^{\frac{5}{3}} = 32\)A1 Cao
*A correct answer with no working scores full marks.*
*Alternative: \(8^{\frac{5}{3}} = 8 \times 8^{\frac{2}{3}} = 8 \times 2^2\) = M1 (Deals with the 1/3) \(= 32\) A1*
Total: (2)
Part (b):
AnswerMarks Guidance
Answer/WorkingMarks Guidance
\(\left(2x^{\frac{1}{2}}\right)^3 = 2^3 x^{\frac{3}{2}}\)M1 One correct power either \(2^3\) or \(x^{\frac{3}{2}}\). \(\left(2x^{\frac{1}{2}}\right)\times\left(2x^{\frac{1}{2}}\right)\times\left(2x^{\frac{1}{2}}\right)\) on its own is not sufficient for this mark.
\(\frac{8x^{\frac{3}{2}}}{4x^2} = 2x^{-\frac{1}{2}}\) or \(\frac{2}{\sqrt{x}}\)dM1A1 M1: Divides coefficients of \(x\) and subtracts their powers of \(x\). Dependent on the previous M1. A1: Correct answer
*Note: unless the power of \(x\) implies subtraction, evidence of subtraction e.g. \(\frac{8x^{\frac{3}{2}}}{4x^2} = 2x^{\frac{1}{2}}\) would score dM0 unless some evidence that \(3/2 - 2\) was intended.*
*Misconception: \(\frac{\left(2x^{\frac{1}{2}}\right)^3}{4x^2} = \left(\frac{2x^{\frac{1}{2}}}{4x^2}\right)^3\) scores 0/3*
Total: (3) [5]
## Question 3:

### Part (a):

| Answer/Working | Marks | Guidance |
|---|---|---|
| $8^{\frac{1}{3}} = 2$ or $8^5 = 32768$ | M1 | A correct attempt to deal with the $\frac{1}{3}$ or the 5. $8^{\frac{1}{3}} = \sqrt[3]{8}$ or $8^5 = 8\times8\times8\times8\times8$ |
| $8^{\frac{5}{3}} = 32$ | A1 | Cao |

*A correct answer with no working scores full marks.*

*Alternative: $8^{\frac{5}{3}} = 8 \times 8^{\frac{2}{3}} = 8 \times 2^2$ = M1 (Deals with the 1/3) $= 32$ A1*

**Total: (2)**

### Part (b):

| Answer/Working | Marks | Guidance |
|---|---|---|
| $\left(2x^{\frac{1}{2}}\right)^3 = 2^3 x^{\frac{3}{2}}$ | M1 | One correct power either $2^3$ or $x^{\frac{3}{2}}$. $\left(2x^{\frac{1}{2}}\right)\times\left(2x^{\frac{1}{2}}\right)\times\left(2x^{\frac{1}{2}}\right)$ on its own is not sufficient for this mark. |
| $\frac{8x^{\frac{3}{2}}}{4x^2} = 2x^{-\frac{1}{2}}$ or $\frac{2}{\sqrt{x}}$ | dM1A1 | M1: Divides coefficients of $x$ **and** subtracts their powers of $x$. **Dependent on the previous M1**. A1: Correct answer |

*Note: unless the power of $x$ implies subtraction, evidence of subtraction e.g. $\frac{8x^{\frac{3}{2}}}{4x^2} = 2x^{\frac{1}{2}}$ would score dM0 unless some evidence that $3/2 - 2$ was intended.*

*Misconception: $\frac{\left(2x^{\frac{1}{2}}\right)^3}{4x^2} = \left(\frac{2x^{\frac{1}{2}}}{4x^2}\right)^3$ scores 0/3*

**Total: (3) [5]**

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3. (a) Find the value of $8 ^ { \frac { 5 } { 3 } }$\\
(b) Simplify fully $\frac { \left( 2 x ^ { \frac { 1 } { 2 } } \right) ^ { 3 } } { 4 x ^ { 2 } }$\\

\hfill \mbox{\textit{Edexcel C1 2013 Q3 [5]}}
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