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.
Practice Worksheet
Grade 12 Advanced Functions Practice
Solve each problem. Show your work.
- 1.Evaluate log base 3 of 27: _____
- 2.Find the remainder when P(x) = x³ - 8 is divided by x - 2: _____
- 3.State the restriction for f(x) = (x + 1)/(x - 3): _____
- 4.Evaluate log base 10 of 10000: _____
- 5.Find the remainder when P(x) = x³ - 27 is divided by x - 3: _____
- 6.State the restriction for f(x) = (x + 1)/(x - 4): _____
Show answer key
- Question 1: 3
- Question 2: 0
- Question 3: x ≠ 3
- Question 4: 4
- Question 5: 0
- Question 6: x ≠ 4
Free Practice Worksheets
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Build confidence with approachable problems
Solve each problem. Take your time.
- 1.Evaluate the logarithmic expression: log2(16) + log2(2)
- 2.Given f(x) = x² and g(x) = x + 3, find the composite function f(g(x))
- 3.Find the vertical asymptote of the rational function: f(x) = 1 / (x - 4)
- 4.Calculate the average rate of change for f(x) = x² from x = 1 to x = 3
- 5.Simplify the expression using logarithm power rules: 2 * log(x) + log(y)
- 6.Determine the x-intercepts of the polynomial function: f(x) = (x - 2)(x + 5)
A selection of topic skills
Solve each problem. Show your work.
- 1.Evaluate the expression using logarithmic properties: log2(40) - log2(5).
- 2.Given f(x) = x² - 4 and g(x) = 2x + 1, determine the composite function f(g(x)) and simplify the expression.
- 3.Identify the vertical and horizontal asymptotes of the rational function f(x) = (3x - 6) / (x + 2).
- 4.Calculate the instantaneous rate of change of f(x) = x³ at x = 2 using the difference quotient limit definition: lim(h->0) [f(x+h) - f(x)] / h.
- 5.Word Problem: A bacteria culture grows according to the function P(t) = 500 * 2^(0.5t), where t is time in hours. Determine how many hours it will take for the population to reach 4000 bacteria.
- 6.Word Problem: The profit P(x) in thousands of dollars for a company is modeled by P(x) = -x³ + 9x² - 15x, where x is the number of units sold in hundreds. Find the average rate of change of profit as sales increase from x = 1 to x = 4.
What Your Child Will Learn
Advanced Functions deepens the function concepts from Grade 11 and introduces logarithms as the formal inverse of exponential functions. Students learn the product, quotient, and power laws for logarithms, convert between exponential and logarithmic form, and solve logarithmic and exponential equations that don't yield to simple common-base methods.
Polynomial functions receive rigorous treatment: students analyze end behaviour, multiplicity of zeros, and turning points for functions of degree three and higher, and use the factor theorem and remainder theorem to factor and solve higher-degree polynomials. Rational functions introduce the ideas of vertical, horizontal, and oblique asymptotes, along with holes in a graph caused by common factors — concepts that require careful algebraic analysis rather than just graphing by transformation.
A distinctive feature of this course is the introduction of average and instantaneous rate of change using function values and secant/tangent line reasoning, without yet using derivative notation — this deliberately previews calculus concepts for students who will take MCV4U concurrently or afterward. Students also combine functions through addition, multiplication, and composition, building the technical fluency that calculus assumes on day one.
Skills Covered
- Solving logarithmic and exponential equations using log laws
- Analyzing end behaviour and zeros of polynomial functions
- Applying the factor and remainder theorems
- Identifying asymptotes and holes in rational functions
- Calculating average and instantaneous rate of change from a function
- Combining functions through arithmetic operations and composition
Curriculum Aligned: Core content of Advanced Functions (MHF4U in Ontario), the prerequisite course for Calculus & Vectors, focused on polynomial, rational, and logarithmic functions.
Parent Tip: At this level, most parents genuinely can't verify the algebra by eye, and that's completely normal — lean on the textbook's answer key or a graphing tool to check final answers, and focus your involvement on process questions like 'which rule did you use here, and why did you pick it?' That keeps you engaged without pretending to check math you may not have seen in years.
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.
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Check my 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.