OCR C1 2010 January — Question 4 7 marks

Exam BoardOCR
ModuleC1 (Core Mathematics 1)
Year2010
SessionJanuary
Marks7
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicIndices and Surds
TypeSolve exponential equations
DifficultyEasy -1.3 This is a straightforward C1 question testing basic index laws and exponential equations with simple integer solutions. Part (i) requires recognizing 81 = 3^4, part (ii) applies the power of 1/2 to get 6p^2 = 24, and part (iii) uses the multiplication rule to get 5^(2n+4) = 5^2. All three parts are routine recall and manipulation with no problem-solving required, making this easier than average.
Spec1.02a Indices: laws of indices for rational exponents

4 Solve the equations
  1. \(3 ^ { m } = 81\),
  2. \(\left( 36 p ^ { 4 } \right) ^ { \frac { 1 } { 2 } } = 24\),
  3. \(5 ^ { n } \times 5 ^ { n + 4 } = 25\).

4 Solve the equations\\
(i) $3 ^ { m } = 81$,\\
(ii) $\left( 36 p ^ { 4 } \right) ^ { \frac { 1 } { 2 } } = 24$,\\
(iii) $5 ^ { n } \times 5 ^ { n + 4 } = 25$.

\hfill \mbox{\textit{OCR C1 2010 Q4 [7]}}