Competition Mathematics Series

Competition Algebra

Name: Competition Algebra
Price: 25.00 USD
Availability: InStock

Foundations and Competition Techniques

MATHCOUNTS and AMC Ready50 Chapters1,000 Practice ProblemsStep-by-Step Solutions

Grades 6–10 ·Competition Ready · Print-Ready PDF

One-time purchase · download for 2 years, always the latest edition (corrections included) · the copy you download is yours to keep. A free account comes with it — that’s how we deliver your PDF and keep it re-downloadable.

About This Book

A competition algebra course in two parts. Part I builds the foundations at contest difficulty: equations and systems, polynomials and factoring, radicals, quadratics, complex numbers, functions, sequences, and logarithms. Part II teaches the techniques contests reward: evaluating without solving, Vieta's formulas, symmetric expressions, telescoping, functional equations, and the AM-GM inequality. Every chapter has a worked example, a 20-problem drill, and step-by-step solutions.

1 Expressions and Substitution

2 Linear Equations

3 Literal Equations and Formulas

4 Word Problems with Linear Equations

5 Ratios, Proportions, and Percent Change

6 Direct, Inverse, and Joint Variation

7 Linear, Compound, and Absolute Value Inequalities

8 Absolute Value Equations

9 Distance, Midpoint, and Dividing a Segment

10 Slope and Equations of Lines

11 Systems of Two Equations

12 Word Problems with Systems

13 Systems in Three Variables

14 Exponent Rules and Scientific Notation

15 Polynomial Arithmetic

16 Factoring

17 Radicals and Radical Expressions

18 Radical Equations

19 Solving Quadratics by Factoring

20 Completing the Square, the Quadratic Formula, and the Discriminant

21 Quadratic Functions: Vertex, Maximum, and Minimum

22 Quadratic Inequalities

23 Complex Numbers

24 Rational Expressions

25 Rational Equations

26 Functions: Notation, Domain, and Range

27 Composition and Inverse Functions

28 Transformations of Graphs

29 Floor, Ceiling, and Piecewise Functions

30 Arithmetic Sequences and Series

31 Geometric Sequences and Series

32 Exponential Growth and Compound Interest

33 Logarithms and Exponential Equations

34 Polynomial Division and the Remainder Theorem

35 The Binomial Theorem

36 Evaluating Without Solving

37 Defined Operations

38 Factoring Tricks: xy + ax + by, and Sums and Differences of Cubes

39 Vieta's Formulas: Sums and Products of Roots

40 Integer and Rational Roots of Polynomials

41 Symmetric Expressions and Power Sums

42 Symmetric and Special Systems

43 Telescoping Sums and Products

44 Infinite Expressions: Nested Radicals and Continued Fractions

45 Functional Equations

46 The AM-GM Inequality

47 Distance, Rate, and Time

48 Work Rate

49 Mixtures

50 Averages: Mean, Weighted, and Pairwise

Free Sample

A free sample for this title is coming soon.

Why This Book?

∞

Infinite Variations

Every practice set uses our AI-powered generator — the same numbers never appear twice.

✓

Answers and Worked Methods

Every problem has an answer, and a full step-by-step solution for its method — nothing is left as just a number.

⚡

Competition Aligned

Difficulty and style are calibrated to AMC 8 and MathCounts standards.

📄

Print Ready

Professionally typeset with LaTeX — sharp on any standard printer.