NCEA Level 3 Mathematics and Statistics 91578 (3.6) — page 1 of 6

SAMPLE ASSESSMENT SCHEDULE

Mathematics and Statistics 91578 (3.6): Apply differentiation methods in solving problems

Assessment Criteria

Achievement / Achievement with Merit / Achievement with Excellence
Apply differentiation methods in solving problems involves:
  • selecting and using methods
  • demonstrating knowledge of concepts and terms
  • communicating using representations.
/ Relational thinking involves one or more of:
  • selecting and carrying out a logical sequence of steps
  • connecting different concepts or representations
  • demonstrating understanding of concepts
  • forming and using a modeland also relating findings to a context, or communicating thinking using appropriate mathematical statements.
/ Extended abstract thinking involves one or more of:
  • devising a strategy to investigate or solve a problem
  • identifying relevant concepts in context
  • developing a chain of logical reasoning, or proof
  • forming a generalisationand also using correct mathematical statements, or communicating mathematical insight.

Evidence Statement

One / Expected coverage / Achievement / Merit / Excellence
(a) / / Correct derivative.
(b) / / Correct solution with correct derivative shown, or equivalent.
Eg

(c) /
(Accept 0.2) / Correct . / Correct solution with correct derivative.
(d) / / Correct / At ,

Correct solution with correct derivative.
(e) /



/ Correct
and
Accept positive answer. / Correct expression for
Accept positive answer. / Correct solution.
Accept positive answer.
Not Achieved / NØ / No response, no relevant evidence.
N1 / Candidate answers ONE question demonstrating limited knowledge of differentiation techniques.
N2 / Candidate provides ONE correct derivative.
Achievement / A3 / Candidate provides TWO of the Achievement criteria.
A4 / Candidate provides THREE of the Achievement criteria.
Merit / M5 / Candidate provides ONE of the Merit criteria.
M6 / Candidate provides TWO of the Merit criteria.
Excellence / E7 / Candidate provides Excellence with minor errors ignored.
E8 / Candidate provides Excellence criteria correctly.

NCEA Level 3 Mathematics and Statistics 91578 (3.6) — page 1 of 6

Two / Expected coverage / Achievement / Merit / Excellence
(a) / / Correct derivative.
(b) /

(units not required) / Correct solution with correct derivative shown.
(c) / / Correct expression for derivative of numberator or denominator. / Correct derivative.
(d) / Let R = length of rope between pulley and car.
,


/ Correct expression for
Accept positive answer. / Correct solution with correct derivative.
Accept positive answer.
(e) /



/ Correct expression for / Correct solution with correct derivatives.
Not Achieved / NØ / No response, no relevant evidence.
N1 / Candidate answers ONE question demonstrating limited knowledge of differentiation techniques.
N2 / Candidate provides ONE correct derivative.
Achievement / A3 / Candidate provides TWO of the Achievement criteria.
A4 / Candidate provides THREE of the Achievement criteria.
Merit / M5 / Candidate provides ONE of the Merit criteria.
M6 / Candidate provides TWO of the Merit criteria.
Excellence / E7 / Candidate provides Excellence with minor errors ignored.
E8 / Candidate provides Excellence criteria correctly.
Three / Expected coverage / Achievement / Merit / Excellence
(a) / / Correct derivative.
(b) /
At x = 2

Or / Correct solution with correct derivative.
(c) /


Moving at 0.8ms-1 (accept –0.8) / Correct expression for / Correct solution with correct derivative.
(d) /
/ Correct derivative. / Correct solution with correct derivative.
(e) /



Max when


Maximum when cm / Correct expression for / Correct solution plus correct expression for
Not Achieved / NØ / No response, no relevant evidence.
N1 / Candidate answers ONE question demonstrating limited knowledge of differentiation techniques.
N2 / Candidate provides ONE correct derivative.
Achievement / A3 / Candidate provides TWO of the Achievement criteria.
A4 / Candidate provides THREE of the Achievement criteria.
Merit / M5 / Candidate provides ONE of the Merit criteria.
M6 / Candidate provides TWO of the Merit criteria.
Excellence / E7 / Candidate provides Excellence with minor errors ignored.
E8 / Candidate provides Excellence criteria correctly.