Solve the equation tan²2x-4 tan2x = 0 for 0° ≤ x ≤ 180°.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.

1. [M1] (a) [tan2x = 0 →] Any two of 2x = 0, 180, 360
2. [A1] (a) [x = ] 0, 90, 180 nfww and no extras from tan 2x = 0 in range 0 ≤ x ≤180
3. [M1] (a) [tan 2x = 4 →] 2x = 75.96... or 255.96...
4. [A1] (a) 38 [.0] or 37.98[18...] isw
5. [A1] (a) 128 [.0] or 127.98[18...] isw and no extras from tan 2x = 4 in range 0 ≤ x ≤180
6. [B1] (b) sin(y+1.2) = 1/4
7. [M2] (b) Two correct values for y + 1.2 soi
8. [M1] (b) for any one correct value for y + 1.2
9. [A3] (b) -0.947 or -0.9473[19...] isw
10. [A2] (b) for two correct angles, ignoring extras in range
11. [A1] (b) for one correct angle, ignoring extras in range
12. [A3] (b) 1.69 or 1.688[91...] isw
13. [A3] (b) -4.59 or -4.594[27...] isw
14. [A3] (b) and no others in range –5 < y < 2