1. State the remainder theorem
2. State the factor theorem
3. Solve the following simultaneous equations:
a. logx y = 2 and xy = 8
b. 2lg y = lg2 + lg x and 2^y = 4^x
4. Prove the following trig identities
a. sin θ + sin 2θ + sin 3θ ≡ sin 2θ(1 + 2cos θ)
b. 1 – cos 2t = 2cot2 t/sin2 t
c. (tan 2x)(1 + tan x)/tanx = 2/(1 – tan x)
5. Solve the following equations giving angles within the range 0° to 360°
a. sin 2x + cos x = 0
b. 5 cos x sin 2x + 4 sin^2 x = 4
2. State the factor theorem
3. Solve the following simultaneous equations:
a. logx y = 2 and xy = 8
b. 2lg y = lg2 + lg x and 2^y = 4^x
4. Prove the following trig identities
a. sin θ + sin 2θ + sin 3θ ≡ sin 2θ(1 + 2cos θ)
b. 1 – cos 2t = 2cot2 t/sin2 t
c. (tan 2x)(1 + tan x)/tanx = 2/(1 – tan x)
5. Solve the following equations giving angles within the range 0° to 360°
a. sin 2x + cos x = 0
b. 5 cos x sin 2x + 4 sin^2 x = 4