Demo - MCV4U

TEST FORMAT

REVIEW GUIDELINES

Part A: Knowledge & Understanding (15 marks)

Topics:

• Definition of derivative from first principles
• Power, product, quotient, and constant rules
• Domains of differentiability (e.g., square roots, absolute value)

Practice:

• Memorize the first principles definition:

\( f'(a) = \lim_{h \to 0} \frac{f(a+h) - f(a)}{h} \)

• Practice simple derivatives: \( x^n \), constants, and basic sums.
• Be able to determine where a function is not differentiable (e.g., at cusps, corners, or discontinuities).

Part B: Thinking & Inquiry (13 marks)

Topics:

• Use of first principles to find a derivative.
• Find horizontal tangents by solving \( f'(x) = 0 \).
• Justifying non-differentiability with one-sided limits.
• Interpreting velocity from position functions.

Practice:

• Fully work out at least 2-3 first-principles problems from scratch.
• Solve polynomial derivative problems and identify horizontal tangents.
• Review limit-based reasoning, especially with absolute value.

Part C: Communication (10 marks)

Topics:

• Explaining the difference between instantaneous and average rate of change.
• Relationship between continuity and differentiability.
• Clear explanation of finding a tangent line using steps.

Practice: 

• Be ready to clearly explain key concepts in your own words.
• Use examples from real life (e.g., driving speed vs. average speed).
• Review how to write equations of lines from points and slopes.

Part D: Application (12 marks)

Topics:

• Motion applications (velocity = derivative of position)
• Normal lines (perpendicular to tangents)
• Elasticity of demand from real-world examples

Practice: 

• Know how to:
• Differentiate position functions and intepret velocity
• Find and interpret the slope of a tangent or normal line
• Use \( E= \frac{p}{n(p)} \cdot n'(p) \) to discuss elasticity