Grade 12 Calculus Worksheets
Free printable calculus practice for Grade 12 students. Generate problems, solve them on screen or paper, and download as PDF.
Practice Worksheet
Grade 12 Calculus Practice
Solve each problem. Show your work.
- 1.Differentiate f(x) = 5x^3: f'(x) = _____
- 2.Evaluate lim(x→2) (x² - 4)/(x - 2): _____
- 3.Find the slope of the tangent to f(x) = x³ - 2x at x = 1: _____
- 4.Differentiate f(x) = 3x^2: f'(x) = _____
- 5.Evaluate lim(x→3) (x² - 9)/(x - 3): _____
- 6.Find the slope of the tangent to f(x) = x³ - 2x at x = 2: _____
Show answer key
- Question 1: 15x^2
- Question 2: 4
- Question 3: 1
- Question 4: 6x
- Question 5: 6
- Question 6: 10
Free Practice Worksheets
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Build confidence with approachable problems
Solve each problem. Take your time.
- 1.Evaluate the limit: lim(x -> 3) (x² - 9) / (x - 3)
- 2.Find the derivative of f(x) = 4x³ - 5x² + 2x using the power rule.
- 3.Calculate the derivative of f(x) = (x² + 1)(x - 3) using the product rule.
- 4.Find the derivative of f(x) = (2x + 1)^4 using the chain rule.
- 5.Find the derivative of f(x) = (3x) / (x + 2) using the quotient rule.
- 6.A particle's position is given by s(t) = t³ - 3t. Find the velocity function v(t).
A selection of topic skills
Solve each problem. Show your work.
- 1.Evaluate the limit: lim(x -> 3) of (x² - 9) / (x - 3).
- 2.Find the derivative of f(x) = (x² + 1) * e^x using the product rule.
- 3.A spherical balloon is being inflated such that its volume increases at a constant rate of 20 cm³/s. How fast is the radius increasing when the radius is 5 cm? (Volume of a sphere V = (4/3) * pi * r³)
- 4.Find the absolute maximum and minimum values of f(x) = 2x³ - 3x² - 12x + 1 on the closed interval [-2, 3].
- 5.A farmer has 100 meters of fencing and wants to enclose a rectangular area against a long, straight wall (no fence needed along the wall). What dimensions will produce the maximum area?
- 6.Given the function f(x) = x^4 - 4x³, determine the intervals where the graph is concave up and find the coordinates of any inflection points.
Practise specific Calculus skills
Skill map
How calculus skills connect
Shore up what feeds in, work through the core skills in order, then move on to what they unlock. A means the skill has an instant answer checker.
What Your Child Will Learn
The calculus portion of this course introduces the derivative as the foundational tool for understanding rates of change, building from an intuitive treatment of limits and continuity toward the formal definition of the derivative from first principles. Students then move quickly to derivative shortcut rules — the power rule, product rule, quotient rule, and chain rule — applying them to polynomial, rational, and composite functions.
Applications form the heart of the unit: students use derivatives to find velocity and acceleration from position functions, sketch curves by identifying intervals of increase/decrease and concavity, and solve optimization problems that ask for a maximum or minimum value subject to a constraint (such as the dimensions that minimize material for a given volume). Related rates problems — where two changing quantities are linked by an equation and students must find how fast one changes given the rate of the other — are typically the most conceptually demanding topic in the course.
Throughout, students are expected to connect the algebraic derivative back to its graphical meaning (the slope of a tangent line) and its real-world meaning (an instantaneous rate of change), tying together the function fluency built in Grade 11 and Advanced Functions.
Skills Covered
- Finding derivatives from first principles using limits
- Applying the power, product, quotient, and chain rules
- Determining velocity and acceleration from position functions
- Sketching curves using increasing/decreasing intervals and concavity
- Solving optimization problems with a constraint
- Solving related rates problems
Curriculum Aligned: Calculus half of Calculus & Vectors (MCV4U in Ontario), typically taken after or alongside Advanced Functions as preparation for university-level STEM programs.
Parent Tip: This is genuinely advanced material, and it's completely reasonable for parents to step back from checking the math itself. The more valuable role at this stage is logistical: making sure your teen has access to a reliable answer key, a study group, or an online tool like Wolfram Alpha to verify derivatives, and simply asking whether they're keeping up with the pace of new rules each week.
What your child will practice
- LimitsDetermine limits of functions algebraically and interpret their meaning graphically.
- Definition of DerivativeDetermine the derivative of a function using first principles (limit definition).
- Product and Quotient RulesApply the product rule and quotient rule to differentiate functions.
- Chain RuleApply the chain rule to differentiate composite functions.
- Derivatives of Trigonometric FunctionsDetermine the derivatives of sine, cosine, and tangent functions.
- Derivatives of Exponential and Logarithmic FunctionsDetermine the derivatives of exponential and logarithmic functions.
- Velocity and AccelerationDetermine velocity and acceleration from a position function using derivatives.
- Optimization ProblemsSolve optimization problems using derivatives to find maximum and minimum values.
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Check my workFrequently Asked Questions
How often should my child practice calculus?
Short daily practice sessions of 10-15 minutes are more effective than long weekly sessions. Consistency builds lasting understanding.
How do I know if my child is at the right level for these worksheets?
If your child can complete about 70% of the problems correctly, the level is appropriate. If it's too easy or too hard, try an adjacent grade level.
Can I use these worksheets for homeschool?
Yes. The worksheets align with standard curriculum expectations and can supplement any math program. Generate multiple worksheets to create a full practice set.