MATH1021 Class Test 2 Preparation Notes

Learning Outcomes Tested

  • Ability to solve mathematical problems using trigonometric, logarithmic, and exponential functions

  • Communicate mathematical ideas using standard practices

Performance Criteria for Class Test 2

Understanding of Key Concepts and Techniques

  • High Distinction: Articulate and apply all key concepts clearly and concisely.

  • Distinction: Apply all key concepts correctly, but not all articulated clearly.

  • Credit: Apply most key concepts correctly.

  • Pass: Apply only the simplest key concepts correctly.

  • Unsatisfactory: Most key concepts absent or applied incorrectly.

Mathematical Manipulations and Computations

  • High Distinction: Successful and complete all required algebraic manipulations and calculations.

  • Distinction: Successful and complete essential calculations.

  • Credit: Successful calculations with minor flaws.

  • Pass: Accurate but incomplete calculations or minor flaws present.

  • Unsatisfactory: Mostly incorrect or absent calculations.

Communication
Use of Mathematical Terminology and Notation

  • High Distinction: Use terminology and notation rigorously.

  • Distinction: Generally accurate usage with some exceptions.

  • Credit: Somewhat careless terminology and notation.

  • Pass: Mostly careless and inaccurate usage.

  • Unsatisfactory: Poor usage of terminology and notation.

Test Format and Instructions

  • MATH1021 Mathematics for Engineers Preliminary

  • Total Marks: 28

  • Time Allowed: 45 minutes

  • Permitted Aids: Scientific Calculator

    • Write name and student ID.

    • Show all working to gain full marks.

    • Marks deducted for poorly arranged work.

    • Solution presentation is important for clear communication of knowledge.

Questions Overview

Question 1 (6 Marks)

  • Given a function ( f(x) = 2x^2 / (x - 3) )

    • Tasks: Evaluate ( f(0), f(2a), f(a+b) )

    • Understanding Key Concepts: Recognizing function notation (2 marks)

    • Mathematical Manipulations: Correct substitution and arithmetic calculations (2 marks)

    • Use of Terminology: Properly setting out solutions (2 marks)

Question 2 (6 Marks)

  • Task: Sketch ( y = x^2 - 3x - 28 )

    • Identify minimum/maximum values using the quadratic formula:

    • Calculate ( b^2 - 4ac )

    • Determine critical points and sketch the parabola.

Question 3 (6 Marks)

  • Task: Express ( \frac{x}{x^2 + x - 2} ) in partial fraction form.

    • Manipulate and solve equations to achieve partial fractions.

Question 4 (6 Marks)

  • Task: Find the inverse of ( f(x) = 2x - 3 )

    • Steps include:

    • Interchanging x and y.

    • Making y the subject.

Question 5 (4 Marks)

  • Task: Analyze air pressure decrease with height using the equation ( P = P_0 e^{-0.00012h} )

    • Estimate air pressure at 12,000 meters as a percentage of sea level value.