A Level Mathematics Questionbanks



1. a) need values of 2x for 0( 2x(720

2x = 30 B1 cao

2x = 150, 390, 510 M1(150) M1(+360)

x = 15, 75, 195, 255 A2 (A1 at least 2;

-1 for extras)

[5]

b) need -30( x−30(330

x − 30 = 30 M1

x−30 = -30, 330

x =0, 60, 360 M1 ( 60o)

M1 A1 (0o or 360o)

A1 (both)

[5]

2. a) sinθ(sinθ + 1) =0 M1

sinθ = 0 or sinθ = -1 A1 (either)

θ = 0, π, 2π or θ = [pic] M1 (sin-1, 1 ans)

A2 (all correct)

[5]

b) (2cosθ + 1)(cosθ − 1) = 0 M1

cosθ = -[pic] or cosθ = 1 A1 (either)

θ ’ [pic], [pic] or 0 A2 (all) (A1 for 2)

[4]

3. a) cos2x = 1 − sin2x B1

3sin2x − (1 − sin2x) (4sin2x –1 M1 A1 cao

a = 4 b = -1 A1 ft

[4]

b) 4sin2x = 2 M1

sinx = [pic] A1 cao

x = (45o, (135o A3 (-1 eeoo)

[5]

4. sin x = [pic]( cos x = [pic] M1 A1

90 ................
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