Moderate -0.8 This is a straightforward application of trigonometric identities requiring students to find cos θ using the Pythagorean identity sin²θ + cos²θ = 1, then calculate tan θ = sin θ/cos θ. It's a routine 3-mark question with a clear method and no problem-solving required, making it easier than average but not trivial since it requires exact value manipulation with surds.
Question 4:
4 | 1/√15 i.s.w. not +/− | 3 | M2 for √15 seen
M1 for rt angled triangle with side 1 and
hyp 4, or cos2 θ = 1 − 1/4 2. | 3
(ii)) sketch of correct sh
correct period and amplitude
period halved for y = cos 2x;
amplitude unchanged
(iiii)) 30, 150, 210, | G1
G1
G1
B2 | Not ruled lines
need 1 and −1 indicated; nos. on horiz
axis not needed if one period shown
B1 for 2 of these, ignore extras outside
range. | 5