| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indices and Surds |
| Type | Solve equations with surds |
| Difficulty | Moderate -0.8 This is a straightforward application of Pythagoras' theorem followed by solving a quadratic equation. Part (i) requires simple algebraic manipulation, and part (ii) involves substituting and using the quadratic formula with surds—both are routine C1 skills with no problem-solving insight required. |
| Spec | 1.02b Surds: manipulation and rationalising denominators1.02f Solve quadratic equations: including in a function of unknown |
| Answer | Marks | Guidance |
|---|---|---|
| 2 | (i) | 9x2 = h2 + 4x2 + 4x + 1 and completion to |
| given answer , h2= 5x2 4x 1 | B1 |
| Answer | Marks |
|---|---|
| [2] | for a correct Pythagoras statement for this |
| Answer | Marks |
|---|---|
| may follow 3x2 = h2 + (2x + 1)2 oe for B0 B1 | condone another letter instead of h for |
Question 2:
2 | (i) | 9x2 = h2 + 4x2 + 4x + 1 and completion to
given answer , h2= 5x2 4x 1 | B1
B1
[2] | for a correct Pythagoras statement for this
triangle, in terms of x, with correct brackets
for correct expansion, with brackets or
correct signs; must complete to the given
answer with no errors in any interim working
may follow 3x2 = h2 + (2x + 1)2 oe for B0 B1 | condone another letter instead of h for
one mark but not both unless
recovered at some point
eg B1 for h2 = 9x2 (4x2 + 4x + 1) and
completion to correct answer
but
B0 for h2 = 9x2 4x2 + 4x + 1Fig. 8 shows a right-angled triangle with base $2x + 1$, height $h$ and hypotenuse $3x$.
\includegraphics{figure_1}
\begin{enumerate}[label=(\roman*)]
\item Show that $h^2 = 5x^2 - 4x - 1$. [2]
\item Given that $h = \sqrt{7}$, find the value of $x$, giving your answer in surd form. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C1 Q2 [5]}}