Mathematical Methods 2019 v1.2

IA 2: Sample Assessment Instrument

Examination Overview (15%)

• Created by QCAA to aid teachers in assessment planning.
• Includes student's name, number, teacher, and exam date.

Marking Summary

• Total Marks Allocated: 15
• Criteria: Foundational knowledge and problem-solving

Examination Conditions

• Technique: Examination
• Unit: Unit 3: Further Calculus
• Topics:
  • Topic 1: The logarithmic function
  • Topic 2: Further differentiation and applications
  • Topic 3: Integrals
• Duration: 2 hours + 5 minutes perusal
• Questions: Unseen
• Materials: Only QCAA formula sheet provided, notes not permitted
• Technology: Required, schools specify technology used

Instructions

• Show all working in provided space
• Use a black or blue pen
• Non-CAS graphics calculator allowed for technology-active paper

Examination Papers

Paper 1 (Technology-Free)

Question 1 (7 marks)

• Solve given logarithmic and exponential equations.

Question 2 (13 marks)

• Determine derivatives of complex functions.

Question 3 (7 marks)

• Calculate exact values of definite integrals.

Question 4 (6 marks)

• Determine times when a particle is at rest using its position-time function.

Question 5 (6 marks)

• Find coordinates of stationary point of a logarithmic function.

Question 6 (5 marks)

• Evaluate the rate of flu spread in a school based on given model.

Paper 2 (Technology-Active)

Question 7 (9 marks)

• Sketch and analyze logarithmic and trigonometric functions.
• Determine when functions have equal gradients.

Question 8 (8 marks)

• Analyze rabbit population model to determine initial population and future population estimates.
• Calculate when population increase rate hits a specific value.

Question 9 (4 marks)

• Calculate the area between intersecting exponential functions.

Question 10 (8 marks)

• Find the line that divides an area under a curve into equal parts.
• Justify and evaluate the solution.

Question 11 (7 marks)

• Calculate volume of snow on a ski run using height model and given conditions.

Examination Marks Summary

Paper 1 (Technology-Free)

• Simple Familiar (SF): 27
• Complex Familiar (CF): 17
• Complex Unfamiliar (CU): 0

Paper 2 (Technology-Active)

• Simple Familiar (SF): 21
• Complex Familiar (CF): 0
• Complex Unfamiliar (CU): 15

Overall

• Total Simple Familiar (SF): 48
• Total Complex Familiar (CF): 17
• Total Complex Unfamiliar (CU): 15

Instrument-Specific Marking Guide

Assessment Objectives

1. Select, recall, and use facts, rules, definitions, and procedures.
2. Comprehend mathematical concepts and techniques.
3. Communicate using mathematical language and conventions.
4. Evaluate reasonableness of solutions.
5. Justify procedures using reasoning.
6. Solve problems using mathematical concepts.

Cut-off Marks

• 15 Marks (93%): Consistent correct use and application.
• 14 Marks (87%): Correct selection and application.
• 13 Marks (80%) and below: Decreases in thoroughness and accuracy.

Additional Information

• Licensed under Creative Commons BY 4.0
• Full terms and conditions available on the QCAA website.