Why it trips people up
You must move fluidly between graphs, tables, equations, and verbal descriptions — then connect them to derivative/integral meaning.
Multiple representations + conceptual calculus
Typical study load: ~40–60 hours
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Core · FUNC
Functions and Calculus
Praxis 5165 Category II (~30%): function families, transformations, trig, modeling, and calculus ideas (rates, derivatives, integrals) emphasized conceptually more than heavy computation.
20 flashcards10 MCQs3 high-yield notes
Time
3 hours
MCQs / TBS
20 / 0
Score weight
30% MCQ · 0% TBS
of exam
n/a
Common traps
- Mixing up inverse vs reciprocal functions
- Confusing average rate of change with instantaneous
- Ignoring domain when composing or inverting
How to study FUNC
- 1
For every function family, list parent graph, key features, and common transforms.
- 2
Practice 'what does f′ tell you about f' with graphs, not just formulas.
- 3
Drill unit circle / trig identities that appear in secondary teaching.
- 4
Explain accumulation and net change in words before computing.
Blueprint content areas
Weights are ETS blueprint ranges. Use them to prioritize — do not ignore low-weight areas entirely, but spend more reps where the exam spends more score.
IIA — Functions
~20%- • Function notation & representations
- • Linear, quadratic, exponential, log
- • Trigonometric functions
- • Transformations & inverses
- • Modeling with functions
IIB — Calculus
~10%- • Limits conceptually
- • Derivatives as rate of change
- • Integrals as accumulation
- • Fundamental Theorem intuition
FUNC high-yield notes
Study these, then drill the FUNC flashcards and MCQs.
FUNC · High-yield
Four representations or bust
Functions questions move among graphs, tables, equations, and stories. Practice translating the same feature all four ways.
- Intercepts, asymptotes, monotonicity, and end behavior should be namable from any representation.
- Transformations: outside = vertical; inside = horizontal (and opposite sign).
- Average rate of change is the slope of the secant — always write the formula first.
Exam tip: When stuck, sketch a quick graph even if the item is algebraic.
FUNC · High-yield
Calculus meaning over machinery
5165 emphasizes derivative as rate and integral as accumulation more than heavy symbolic drills.
- f′ > 0 increasing; f′ < 0 decreasing; f′=0 critical.
- f′′ sign ↔ concavity; inflection where concavity changes.
- Net change = integral of rate; total distance needs |rate| thinking.
Exam tip: Read the units in worded calculus items — they often reveal whether you need f, f′, or ∫f.
FUNC · High-yield
NJ CE path reminder
Content study is half the battle — you still need 30 math credits (12 advanced), Praxis 5165 ≥ 159, and the CE application steps.
- This site builds Praxis fluency; college courses create transcript eligibility.
- Physiology & hygiene can be NJ's online test if you lack bio/health credits.
- After CE + job offer comes Provisional Teaching Program coursework.
Exam tip: Keep a running list of completed math courses with levels (100/200 vs 300+).