Evidence Achievement (u) Merit (r) Excellence (t) Question ONE Apply the algebra Apply the algebra of Apply the algebra of of complex numbers complex numbers, complex numbers, in solving using relational using extended problems. thinking, in solving abstract thinking, in problems. solving problems. f(1) = 0 1a Correct so 3c 4c 8c +18 = 0 – – expression. 18 = 9c 2 = c u = 1 + i = 2 ½ cis(450) 1b Correct solution. u8 = 24cis3600 Degrees or rads 1c Award u if minor 4x 8 = x2 4x + 4 – – error Award r only for 0 = x2 8x + 12 – ( or no check Correct solution 0 = (x 2)(x 6) – – done) with check. x = 2 or 6 check if x = 2 check if x = 6 lhs = 0, rhs = 0 lhs = 4 rhs = 4 so x = 2 is valid so x = 4 is valid z5 = 32ni Let z rcisθ 1d Award u if changed correctly Correct solution into polar form: either using degrees r5cis = or radians. 5θ = 32ncis(90 + 360n) r5cis 5θ 32ncis(90 + 360n) either using r5 = 32n =90 + 360n 5θ degrees or 2n0.2 r = = 18 + 72n θ radians. z1 = 2n0.2 cis 180 z2 = 2n0.2 cis 900 z3 = 2n0.2 cis 1620 z4 = 2n0.2cis2340 z4 = 2n0.2cis3060
Question ONE Evidence Achievement (u) Merit (r) Excellence (t) Apply the algebra of complex numbers in solving problems. Apply the algebra of complex numbers, using relational thinking, in solving problems. Apply the algebra of complex numbers, using extended abstract thinking, in solving problems. 1a f(1) = 0 so 3c – 4c – 8c +18 = 0 18 = 9c 2 = c Correct expression. 1b u = 1 + i = 2 ½ cis(450) u8 = 24cis3600 Correct solution. Degrees or rads 1c 4x – 8 = x2 – 4x + 4 0 = x2 – 8x + 12 0 = (x – 2)(x – 6) x = 2 or 6 check if x = 2 check if x = 6 lhs = 0, rhs = 0 lhs = 4 rhs = 4 so x = 2 is valid so x = 4 is valid Award u if minor error ( or no check done) Award r only for Correct solution with check. 1d Let z rcisθ z5 = 32ni r5cis 5θ = 32ncis(90 + 360n) r5 = 32n 5θ =90 + 360n r = 2n0.2 θ = 18 + 72n z1 = 2n0.2 cis 180 z2 = 2n0.2 cis 900 z3 = 2n0.2 cis 1620 z4 = 2n0.2cis2340 z4 = 2n0.2cis3060 Award u if changed correctly into polar form: r5cis 5θ = 32ncis(90 + 360n) either using degrees or radians. Correct solution either using degrees or radians.
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