Calculus I · 2A · diagnostic

Derivative Prerequisite Diagnostic

Check the prerequisite skills needed for Derivative Foundations and Techniques and follow targeted review links before beginning the unit.

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Section overview

Orientation and prerequisites

What this section is building

Check the prerequisite skills needed for Derivative Foundations and Techniques and follow targeted review links before beginning the unit.

Notice

A function reports an amount; its derivative reports how that amount responds to a small input change.

Decide

Check prerequisites, identify the input and output, and attach units before calculating.

Avoid

Reading derivative notation as an ordinary fraction or skipping the limit meaning.

Prerequisite Diagnostic

Complete without a calculator unless your course normally permits one.

Exercise

Expand $(x+h)^2$ .

Exercise

Factor $x^2-9$ .

Exercise

Simplify $(x^2-4)/(x-2)$ for $x\ne2$ .

Exercise

Rewrite $1/x^3$ with a negative exponent.

Exercise

Rewrite $\sqrt[3]{x^2}$ with a rational exponent.

Exercise

Simplify $\frac{1/(x+h)-1/x}{h}$ .

Exercise

Solve $3x^2-12x+9=0$ .

Exercise

State the slope formula through $(x_1,y_1)$ and $(x_2,y_2)$ .

Exercise

Write the point-slope equation for slope $4$ through $(2,-1)$ .

Exercise

Evaluate $\lim_{h\to0}[(2+h)^2-4]/h$ .

Exercise

State $\lim_{u\to0}\sin u/u$ .

Exercise

For $f(x)=x^2$ , calculate $f(a+h)-f(a)$ .

Answer reveal

Worked solution

Your setup or answer

Write a real attempt before opening the supplied answer.

Method

How to use the result

Missing zero to two items: begin the unit. Missing three to five: review the attached algebra topics while starting the first conceptual lessons. Missing six or more: repair factoring, exponents, rational expressions, and limits first. This is not gatekeeping; it is the shortest route through the material.

Source & rights

Original instruction with traceable references.

BetterGrades-original composition declared by source handoff; owner provenance review required before public release

Reference textbooks remain rights-separated and are not published as application assets. Any direct adaptation requires separate identification and attribution.

Prerequisite Diagnostic

Complete without a calculator unless your course normally permits one.

Exercise

Expand $(x+h)^2$ .

Exercise

Factor $x^2-9$ .

Exercise

Simplify $(x^2-4)/(x-2)$ for $x\ne2$ .

Exercise

Rewrite $1/x^3$ with a negative exponent.

Exercise

Rewrite $\sqrt[3]{x^2}$ with a rational exponent.

Exercise

Simplify $\frac{1/(x+h)-1/x}{h}$ .

Exercise

Solve $3x^2-12x+9=0$ .

Exercise

State the slope formula through $(x_1,y_1)$ and $(x_2,y_2)$ .

Exercise

Write the point-slope equation for slope $4$ through $(2,-1)$ .

Exercise

Evaluate $\lim_{h\to0}[(2+h)^2-4]/h$ .

Exercise

State $\lim_{u\to0}\sin u/u$ .

Exercise

For $f(x)=x^2$ , calculate $f(a+h)-f(a)$ .

Answer reveal

Worked solution

Your setup or answer

Write a real attempt before opening the supplied answer.

Method

How to use the result

Source & rights

Original instruction with traceable references.

BetterGrades-original composition declared by source handoff; owner provenance review required before public release

Reference textbooks remain rights-separated and are not published as application assets. Any direct adaptation requires separate identification and attribution.