NCEA Level 3 Calculus (90635) 2012 — page 1 of 5

Assessment Schedule – 2012

Calculus: Differentiate functions and use derivatives to solve problems (90635)

Evidence Statement

Q / Evidence / Code / Judgement
ONE
(a)
(b)
(c)
(d)
(e)(i)
(ii)
(iii) /



3
(1) ,
(2) ,
(3)
/ a1
a1
a1
a1
m
m / One derivative with derivative symbol correct
Correct solution.
Accept  on right hand side of any inequality
3 correct solutions required
Q / Evidence / Code / Judgement
(f) /




Maximum when




r = 8.16
OR Alternative method
/ a1
e, m
e, m / Units not required.
Units not required.
Sufficiency for question ONE. A: 2a1, M: 2a1 +1m OR 1a1 + 2m, E: 2a1 + m + e OR 1a1 + 2m + e
Q / Evidence / Code / Judgement
TWO
(a)
(b)
(c) /


Acceleration = 0 when



At x = 2
Normal gradient = –2
At x = 2

or
Io = 8000


At x=5

= –555 Lux/m / a1
a2
a2
m, a2 / Accept t = 6
Units not required
Units not required
Q / Evidence / Code / Judgement
(d)
(e) /

at (–2,3)









When h = 10,


/ a1
m, a2
a1
m
e
a1
m
e / Units not required.
Units not required
Sufficiency for question TWO. A: 1a2, M: 1a2 +1m OR 2m, E: 1a2 + 1 m + e OR 2m + e

Judgement Statement

Achievement

/

Achievement with Merit

/

Achievement with Excellence

2 A / 2 M
with 3 m overall / 1 E + 1 M

Marking codes

Codes that may have been used in marking this examination paper have meaning as follows.

#Hash where a candidate obtains a correct answer but continues with further, unnecessary, material that is incorrect but does not show that the candidate shows a lack of understanding or a contradiction.

RAWWRight answer, wrong working where a candidate presents a correct answer but the working or reasoning leading to it is incorrect.

RRounding error where a candidate produces a correct sequence of calculations, but the answer does not agree to 2 significant figures with the answer given in the assessment schedule as a result of rounding a number in the sequence of calculations.

MEIMinor error ignoredwhere a candidate has made a minor error and this has been ignored.

Two ansTwo answers given where a candidate writes two answers, one correct and the other incorrect, and neither has been deleted (the correct answer is not accepted).