Grade 12 Advanced Functions Worksheets
Free printable advanced functions practice for Grade 12 students. Generate problems, solve them on screen or paper, and download as PDF.
What your child will practice
- Logarithmic FunctionsDefine logarithms as inverses of exponential functions and evaluate logarithmic expressions.
- Polynomial Function CharacteristicsIdentify degree, leading coefficient, and end behaviour of polynomial functions.
- Graphing Polynomial FunctionsGraph polynomial functions and identify zeros, turning points, and intervals of increase/decrease.
- Rational FunctionsIdentify key features of rational functions (asymptotes, intercepts, domain, range).
- Power RuleApply the power rule to differentiate polynomial functions.
Practice Worksheet
Advanced Functions Practice
Solve each problem. Show your work.
- 1.Evaluate the limit: lim (x->3) (x² - 9) / (x - 3)
- 2.Find the derivative of f(x) = 5x³ - 2x + 7 using the power rule.
- 3.Solve for x: log_2(x) + log_2(x-2) = 3
- 4.A company's profit P (in thousands of dollars) is modeled by the function P(x) = -x³ + 12x² - 36x, where x is the number of units sold (in thousands). Find the number of units sold that maximizes the profit.
- 5.Graph the rational function f(x) = (x + 1) / (x - 2). Identify the vertical asymptote, horizontal asymptote, and x-intercept.
- 6.A particle's position is given by the function s(t) = t³ - 6t² + 5, where s is in meters and t is in seconds. Calculate the instantaneous velocity of the particle at t = 4 seconds.
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Grade offline workFrequently Asked Questions
How often should my child practice advanced functions?
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.