Grade 11 · Level 88 · Abstract & formal reasoning
MATH 88
Families of functions.
Meridian Note
The function concept — met at KS-3 in MATH 75 — now reaches KS-8–9: families of functions compared, composed, inverted, and fitted to data. Logarithms enter at KS-4–6 and must reach KS-7 quickly; exponential modeling is cross-domain synthesis with science coursework.
The Fix Registry
Skills of This Course
Every skill is pinned to the meridian by fix notation — where along the scale, and at what depth. The highlighted state is this course's target: the state an honest instrument must certify before the skill counts as covered here.
| Skill | Fixes | Target at Level 88 |
|---|---|---|
| Linear functions | 75-KS481-KS788-KS9 | KS-9Synthesized |
| Exponential & logarithmic functions | 88-KS690-KS7 | KS-6Understood |
| Ratio & proportional reasoning | 60-KS768-KS888-KS9 | KS-9Synthesized |
| Polynomial functions | 88-KS790-KS8 | KS-7Applied |
| Rational functions | 88-KS690-KS7 | KS-6Understood |
| Sequences & series | 88-KS690-KS8 | KS-6Understood |
Course of Instruction
Units
Unit 1.One Idea, Many Families: Transforming, Composing, Inverting
9 practice itemsIn MATH 75 a function was a rule connecting inputs to outputs. This year it becomes something more: an object you can move, stretch, chain together, and run backwards — the way a number can be added, multiplied, or negated. Algebra II is organized around families of functions (linear, polynomial, rational, exponential), and this unit hands you the tools that work on every family at once: transformations, composition, and inverses. Learn them once here and you will reuse them in every unit that follows.
MatchingMultiple choiceFill in the blankMultiple choice (misconception distractors)Short answer
Unit 2.Polynomial Functions: Zeros, Factors, and End Behavior
7 practice itemsA polynomial is what you get when a variable is allowed to be added, subtracted, and multiplied freely: p(x) = 4x³ − 52x² + 160x is one. Polynomials can rise, dip, and turn several times, yet everything about them is governed by two things you can read straight off the formula: their zeros (where they cross the x-axis) and their leading term (who wins far from the origin). This unit teaches you to take a polynomial apart into factors — and to predict its behavior at the far ends of the graph without plotting a single point.
Multiple choiceFill in the blankMultiple choice (misconception distractors)Short answerTransfer problem
Unit 3.Rational Functions and the Logic of Variation
12 practice itemsDivide one polynomial by another and you leave the polynomial family entirely. The new function can blow up to infinity near a single forbidden input, flatten toward a ceiling it never quite touches, and skip values in its domain. These rational functions describe sharing, draining, averaging, and trade-offs — any situation where a quantity sits in a denominator. This unit also settles a question you have been circling since MATH 60: when is proportional reasoning the right tool, and when does it quietly lie?
Multiple choiceFill in the blankMultiple choice (misconception distractors)Problem solvingTransfer problem
Unit 4.Exponentials and Logarithms: Growth, Decay, and the Great Undo
8 practice itemsLinear functions grow by adding; exponential functions grow by multiplying. That one change of verb produces the most consequential family in this course — the mathematics of interest, population, radioactive decay, and viral spread. And because exponentials answer the question 'multiply how many times?', they come with an inverse that answers 'what exponent?': the logarithm. By the end of this unit those two ideas should feel like one idea read in two directions.
MatchingMultiple choiceFill in the blankMultiple choice (misconception distractors)Short answer
Unit 5.Sequences and Series: Functions on the Counting Numbers
7 practice itemsA sequence is a function whose domain is the counting numbers: term 1, term 2, term 3, and so on. Nothing else about functions changes — which is why the two great sequence families turn out to be old friends wearing name tags. Arithmetic sequences are linear functions in disguise; geometric sequences are exponential functions in disguise. This unit teaches you to see through the disguise, to sum long runs of terms in seconds, and to choose the right family when raw data lands on your desk.
MatchingMultiple choiceFill in the blankMultiple choice (misconception distractors)Problem solving