Question 6:
--- 6(a) ---
6(a) | Show a circle centre (4, 3)
Allow dashes for coordinates on axes | B1 | Note full circle is not required but must show centre and include
relevant arc.
Show a circle with radius 2.
Can be implied by at least two of the points (2, 3), (6, 3), (4, 1) and
(4, 5) being correct | B1FT | FT centre not at the origin.
Point representing (2, 1) | B1 | Half-line or ‘correct’ full line extending into the third quadrant
implies point (2, 1).
Show a half-line at their (2, 1) at an angle of 1,cutting top of
3
circle between x = 3 and x = 5 | B1FT | FT the point (±2, ±1) or (±1, ±2).
Shade the correct region
Needs correct half-line or “correct” full line extending into the third
quadrant AND correct circle | B1
5
--- 6(b) ---
6(b) | Carry out a correct method for finding the greatest value of arg z in
the correct region in (a) | M1 | E.g. sin−1(2/√(25)) + tan−1(3/4) or
sin−1(2/√(25)) + sin−1(3/5).
Or, e.g., substitute y = kx in circle equation, solve when
6 21
discriminant = 0, to get tan−1  .
 
6
 
Obtain answer 1.06, or 1.05 or 1.055 or 1.056 or 60.4° or 60.5° | A1 | The marks in (b) are available even if errors in (a).
No working seen scores 0/2 marks.
2
Question | Answer | Marks | Guidance