Edexcel P1 2018 Specimen — Question 2 5 marks

Exam BoardEdexcel
ModuleP1 (Pure Mathematics 1)
Year2018
SessionSpecimen
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicIndices and Surds
TypeSimplify algebraic expressions with indices
DifficultyEasy -1.2 This is a straightforward indices and surds question testing basic manipulation skills. Part (a) requires converting a negative fractional power to surd form using standard rules, and part (b) involves routine simplification of algebraic expressions with fractional powers. Both parts are mechanical applications of index laws with no problem-solving or insight required, making this easier than average for A-level.
Spec1.02a Indices: laws of indices for rational exponents1.02b Surds: manipulation and rationalising denominators
  1. Given that \(3^{-1.5} = a\sqrt{3}\) find the exact value of \(a\) [2]
  2. Simplify fully \(\frac{(2x^{\frac{1}{2}})^3}{4x^2}\) [3]
Question 2:
AnswerMarks
2(a)1 (cid:167)(cid:117) 3(cid:183)
3−1(cid:17)5 = (cid:168) (cid:184)
(cid:168) (cid:184)
AnswerMarks
3 3 (cid:169)(cid:117) 3(cid:185)M1
3 1
(cid:32) so a(cid:32)
AnswerMarks
9 9A1
(2)
Alternative
3(cid:16)1.5
3(cid:16)1.5 (cid:32)a 3(cid:159)a(cid:32) (cid:32)3(cid:16)1.5(cid:16)0.5
AnswerMarks
30.5M1
1
(cid:159)a(cid:32)3(cid:16)2 (cid:32)
AnswerMarks
9A1
(b)3
(cid:167) 1 (cid:183) 3
2x2 (cid:32)23x2
(cid:168) (cid:184)
AnswerMarks Guidance
(cid:169) (cid:185)One correct power either23 or x 3 2. M1
3
8x2 2
(cid:32)2x(cid:16)1
2 or
AnswerMarks
4x2 xdM1
A1
(3)
(5 marks)
Notes:
(a)
M1: Scored for a full attempt to write 3(cid:16)1.5 in the form a 3 or, as an alternative, makes a the
subject and attempts to combine the powers of 3
1
A1: For a(cid:32) Note: A correct answer with no working scores full marks
9
(b)
3
(cid:167) 1 (cid:183)
M1: For an attempt to expand (cid:168) 2x2 (cid:184) Scored for one correct power either 23 or x 3 2.
(cid:169) (cid:185)
(cid:167) 1 (cid:183) (cid:167) 1 (cid:183) (cid:167) 1 (cid:183)
(cid:168)2x2 (cid:184)(cid:117)(cid:168)2x2 (cid:184)(cid:117)(cid:168)2x2 on its own is not sufficient for this mark.
(cid:184)
(cid:169) (cid:185) (cid:169) (cid:185) (cid:169) (cid:185)
dM1: For dividing their coefficients of x and subtracting their powers of x. Dependent upon the previous
M1
2
2x(cid:16)1
A1: Correct answer 2 or
x
AnswerMarks Guidance
QuestionScheme Marks 
Question 2:
--- 2(a) ---
2(a) | 1 (cid:167)(cid:117) 3(cid:183)
3−1(cid:17)5 = (cid:168) (cid:184)
(cid:168) (cid:184)
3 3 (cid:169)(cid:117) 3(cid:185) | M1
3 1
(cid:32) so a(cid:32)
9 9 | A1
(2)
Alternative
3(cid:16)1.5
3(cid:16)1.5 (cid:32)a 3(cid:159)a(cid:32) (cid:32)3(cid:16)1.5(cid:16)0.5
30.5 | M1
1
(cid:159)a(cid:32)3(cid:16)2 (cid:32)
9 | A1
(b) | 3
(cid:167) 1 (cid:183) 3
2x2 (cid:32)23x2
(cid:168) (cid:184)
(cid:169) (cid:185) | One correct power either23 or x 3 2. | M1
3
8x2 2
(cid:32)2x(cid:16)1
2 or
4x2 x | dM1
A1
(3)
(5 marks)
Notes:
(a)
M1: Scored for a full attempt to write 3(cid:16)1.5 in the form a 3 or, as an alternative, makes a the
subject and attempts to combine the powers of 3
1
A1: For a(cid:32) Note: A correct answer with no working scores full marks
9
(b)
3
(cid:167) 1 (cid:183)
M1: For an attempt to expand (cid:168) 2x2 (cid:184) Scored for one correct power either 23 or x 3 2.
(cid:169) (cid:185)
(cid:167) 1 (cid:183) (cid:167) 1 (cid:183) (cid:167) 1 (cid:183)
(cid:168)2x2 (cid:184)(cid:117)(cid:168)2x2 (cid:184)(cid:117)(cid:168)2x2 on its own is not sufficient for this mark.
(cid:184)
(cid:169) (cid:185) (cid:169) (cid:185) (cid:169) (cid:185)
dM1: For dividing their coefficients of x and subtracting their powers of x. Dependent upon the previous
M1
2
2x(cid:16)1
A1: Correct answer 2 or
x
Question | Scheme | Marks
\begin{enumerate}[label=(\alph*)]
\item Given that $3^{-1.5} = a\sqrt{3}$ find the exact value of $a$ [2]
\item Simplify fully $\frac{(2x^{\frac{1}{2}})^3}{4x^2}$ [3]
\end{enumerate}

\hfill \mbox{\textit{Edexcel P1 2018 Q2 [5]}}
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