Moderate -0.5 This is a straightforward algebraic verification question requiring careful arithmetic with surds. Students must add fractions and multiply expressions containing √17, then show both sides are equal. While it requires attention to detail with surds and fractions, it's purely computational with no problem-solving or insight needed—the path is completely prescribed by 'show that'.
Question 1:
1 | showing a + b + c = 6 o.e
92 −17
bc=
16
=64/16 o.e. correctly obtained
completion showing abc = 6 o.e. | 1
M1
A1
A1 | simple equiv fraction eg 192/32 or 24/4
correct expansion of numerator; may be
unsimplified 4 term expansion; M0 if get
( )2
no further than 17 ; M0 if no
evidence before 64/16 o.e.
may be implicit in use of factors in
completion | 4
You are given that $a = \frac{3}{2}$, $b = \frac{9 - \sqrt{17}}{4}$ and $c = \frac{9 + \sqrt{17}}{4}$. Show that $a + b + c = abc$. [4]
\hfill \mbox{\textit{OCR MEI C1 Q1 [4]}}