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Core · ALG

Number & Quantity and Algebra

Praxis 5165 Category I (~30%): real and complex numbers, ratios, radicals, polynomials, equations/inequalities, systems, and algebraic modeling. About a quarter of all Praxis items also wrap content in teaching tasks.

20 flashcards10 MCQs3 high-yield notes

Time

3 hours

MCQs / TBS

20 / 0

Score weight

30% MCQ · 0% TBS

of exam

n/a

Why it trips people up

Questions look elementary until they ask for structure, equivalent forms, or diagnosing a student error. Speed without conceptual clarity fails here.

Procedural fluency + structure sense + teaching diagnosis

Typical study load: ~40–60 hours

Common traps

  • Treating absolute value and inequalities like plain equations
  • Losing domain restrictions on rational/radical equations
  • Confusing factors with zeros of polynomials

How to study ALG

  1. 1

    Rewrite every equation in at least two equivalent forms before solving.

  2. 2

    Drill complex numbers, radicals, and rational exponents until automatic.

  3. 3

    Practice explaining why a student step is wrong — teaching tasks love this domain.

  4. 4

    Mix timed algebra sets with open response: 'justify each step.'

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.

IA — Number & Quantity

~10%
  • • Real number structure & operations
  • • Ratios, rates, percents
  • • Radicals & rational exponents
  • • Quantitative reasoning & units
  • • Complex numbers

IB — Algebra

~20%
  • • Expressions & polynomials
  • • Creating equations & inequalities
  • • Linear / quadratic / systems
  • • Rational & radical equations
  • • Polynomial zeros & factoring

ALG high-yield notes

Study these, then drill the ALG flashcards and MCQs.

ALG · High-yield

See structure before you compute

Algebra items often hide an equivalent form. Pause to factor, complete the square, or rewrite radicals before grinding arithmetic.

  • Ask: can I factor, conjugate, or substitute?
  • Track domain after every rewrite (especially radicals/rationals).
  • Zero product property only after the equation is literally a product = 0.

Exam tip: If two answer choices are algebraically equivalent, you mis-simplified — back up.

ALG · High-yield

Complex numbers on Praxis

Know i-cycle powers, conjugates, and that nonreal roots of real polynomials come in conjugate pairs.

  • i¹=i, i²=−1, i³=−i, i⁴=1, then repeat.
  • Multiply by conjugate to simplify quotients.
  • Discriminant < 0 ⇒ complex conjugate roots for real coefficients.

Exam tip: Reduce exponents of i mod 4 before multiplying big products.

ALG · High-yield

Tasks of Teaching Mathematics

About 25% of Praxis items embed content in teaching moves: diagnose errors, choose representations, evaluate explanations.

  • Name the misconception precisely (not just 'student is wrong').
  • Pick the representation that makes the structure visible.
  • Next instructional step should address the misconception, not pile on new content.

Exam tip: Ask: what would a strong teacher say or show next?

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