Assessment FOR Learning — Diagnostic (probes prerequisites)
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Purpose: Identifies gaps in MHF4U prerequisites (algebra, function notation, factoring, simplification) before the unit. Honest answers help your teacher tailor instruction.
Question 1 Knowledge — Prereq
[3 marks]
Evaluate \( f(2) \) and \( f(2+h) \) for \( f(x)=x^2-3x+5 \). Simplify \( f(2+h) \) fully.
Question 2 Knowledge — Prereq
[3 marks]
Factor completely: a) \( x^2-9 \); b) \( x^3-8 \); c) \( 2x^2+5x-3 \).
Question 3 Knowledge — Prereq
[2 marks]
Rationalize the numerator: \( \displaystyle \frac{\sqrt{x+5}-\sqrt{5}}{x} \).
Question 4 Thinking
[3 marks]
A graph shows \(f(x)\) with a hole at \(x=2\) and \(f(2)\) defined separately at a different y-value. Sketch (in words) and state whether \(\lim_{x\to 2}f(x)\) exists, and whether \(f\) is continuous at 2. Justify.
Question 5 Communication
[3 marks]
In your own words, explain the difference between average rate of change over an interval and instantaneous rate of change at a point. Use the words "secant" and "tangent."
Question 6 Thinking
[3 marks]
Set up (do NOT evaluate) the difference quotient \(\frac{f(x+h)-f(x)}{h}\) for \(f(x)=\frac{1}{x}\). Show the algebra needed to remove the \(h\) from the denominator.
Question 7 Reflection
[2 marks]
Which prerequisite skill (factoring, function notation, rationalizing, simplification) do you feel least confident with? What specific step trips you up?
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