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100+ Free CSET Mathematics (211/212/213) Practice Questions

Pass your CSET: Mathematics Subtests I, II, and III (211, 212, 213) exam on the first try — instant access, no signup required.

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ArticleFREE CSET Exam Guide 2026: California Teacher Subject Prep6 min read
2026 Statistics

Key Facts: CSET Mathematics (211/212/213) Exam

211, 212, 213

Three CSET Mathematics Subtest Codes

Official CSET Mathematics test structure

220

Scaled Passing Score Per Subtest

Official CSET score-report guidance

35 MC + 3 CR

Questions on Subtest I (211) and Subtest II (212)

Official CSET Mathematics test structure

30 MC + 2 CR

Questions on Subtest III (213)

Official CSET Mathematics test structure

2h 30m / 2h

Time Limit for Subtests I-II / Subtest III

Official CSET Mathematics test page

$99 / $247

Per-Subtest / Combined Fee

Official CSET fee table

5

SMR Content Domains Across Subtests

CSET Mathematics subtest descriptions

30%

Share of Score from Constructed Responses

Official CSET Mathematics test structure

For 2026 planning, CSET: Mathematics remains three separately scored subtests. Subtest I (211) has 35 multiple-choice and 3 constructed-response items, Subtest II (212) has 35 multiple-choice and 3 constructed-response items, and Subtest III (213) has 30 multiple-choice and 2 constructed-response items. Subtests I and II allow 2 hours 30 minutes each; Subtest III allows 2 hours. A graphing calculator is provided on screen for designated subtests. The official passing standard is a 220 scaled score on each subtest, and the fee is $99 per subtest or $247 for all three in one session. California also allows alternative subject-matter-competence pathways for some routes, so verify whether you need CSET before registering.

Sample CSET Mathematics (211/212/213) Practice Questions

Try these sample questions to test your CSET Mathematics (211/212/213) exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Which statement correctly characterizes the set of real numbers in relation to its subsets?
A.Every rational number is an integer
B.Every integer is a rational number
C.Every real number is rational
D.Every irrational number is an integer
Explanation: Every integer n can be written as n/1, so the integers are a subset of the rational numbers. The rationals are in turn a subset of the reals, which also include irrationals such as sqrt(2) and pi.
2Using the Euclidean Algorithm, what is the greatest common divisor of 252 and 198?
A.6
B.9
C.18
D.54
Explanation: 252 = 1(198) + 54; 198 = 3(54) + 36; 54 = 1(36) + 18; 36 = 2(18) + 0. The last nonzero remainder is 18, so gcd(252, 198) = 18.
3By the Fundamental Theorem of Arithmetic, what is the prime factorization of 360?
A.2^2 * 3^2 * 5
B.2^3 * 3^2 * 5
C.2^3 * 3 * 5^2
D.2^2 * 3^3 * 5
Explanation: 360 = 8 * 45 = 2^3 * (9 * 5) = 2^3 * 3^2 * 5. The Fundamental Theorem of Arithmetic guarantees this factorization into primes is unique up to order.
4A standard proof that sqrt(2) is irrational assumes sqrt(2) = a/b in lowest terms and derives a contradiction. What is that contradiction?
A.Both a and b turn out to be even, contradicting lowest terms
B.a must be negative
C.b must equal zero
D.a/b must be greater than 2
Explanation: If sqrt(2) = a/b in lowest terms, then a^2 = 2b^2, so a is even, say a = 2k. Then 4k^2 = 2b^2 gives b^2 = 2k^2, so b is even too. Both being even contradicts the assumption that a/b was in lowest terms.
5Compute the product (3 + 2i)(1 - 4i), where i = sqrt(-1).
A.11 - 10i
B.-5 - 10i
C.11 + 10i
D.3 - 8i
Explanation: (3 + 2i)(1 - 4i) = 3 - 12i + 2i - 8i^2 = 3 - 10i - 8(-1) = 3 + 8 - 10i = 11 - 10i.
6What is the modulus (absolute value) of the complex number z = -3 + 4i?
A.1
B.5
C.7
D.25
Explanation: The modulus of a + bi is sqrt(a^2 + b^2). Here |z| = sqrt((-3)^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5.
7A recipe requires flour and sugar in a ratio of 5:2. If a baker uses 15 cups of flour, how many cups of sugar are needed to keep the same proportion?
A.4 cups
B.6 cups
C.7.5 cups
D.12 cups
Explanation: Set up 5/2 = 15/x, so 5x = 30 and x = 6 cups of sugar. This proportional reasoning preserves the 5:2 ratio.
8A car travels at 60 miles per hour. Using dimensional analysis, approximately how many feet per second is this? (1 mile = 5280 feet)
A.88 feet per second
B.60 feet per second
C.176 feet per second
D.44 feet per second
Explanation: 60 mi/hr * 5280 ft/mi * 1 hr/3600 s = (60 * 5280)/3600 = 316800/3600 = 88 ft/s. The units of miles and hours cancel correctly.
9Mathematical induction is used to prove that a statement P(n) holds for all natural numbers n. Which two parts must a valid induction proof contain?
A.A base case and an inductive step
B.Two base cases only
C.A contradiction and a converse
D.A limit and a derivative
Explanation: A proof by induction requires a base case (showing P holds for the starting value, often n = 1) and an inductive step (showing that if P(k) holds then P(k+1) holds). Together these establish P(n) for all n at or above the base.
10Which property explains why the set of integers, under ordinary addition and multiplication, forms a ring but not a field?
A.Integers lack an additive identity
B.Multiplication of integers is not commutative
C.Most nonzero integers lack a multiplicative inverse within the integers
D.Integers are not closed under addition
Explanation: A field requires every nonzero element to have a multiplicative inverse in the set. In the integers, only 1 and -1 have integer inverses, so the integers form a commutative ring with unity but not a field.

About the CSET Mathematics (211/212/213) Exam

CSET: Mathematics is the California subject-matter exam for the Single Subject Teaching Credential in Mathematics. The official structure spans five SMR content domains across three separately scored subtests: Subtest I (211) covers Number and Quantity and Algebra, Subtest II (212) covers Geometry and Probability and Statistics, and Subtest III (213) covers Calculus, including trigonometry.

Questions

100 scored questions

Time Limit

7h combined across subtests (2h 30m / 2h 30m / 2h)

Passing Score

220 scaled on each subtest

Exam Fee

$99 per subtest or $247 combined (California Commission on Teacher Credentialing / Pearson Evaluation Systems)

CSET Mathematics (211/212/213) Exam Content Outline

10 MC (Subtest I)

Number and Quantity (SMR Domain 1)

Real and complex number systems, properties and operations, proportional reasoning, dimensional analysis, number theory, the Euclidean Algorithm, the Fundamental Theorem of Arithmetic, and mathematical induction.

25 MC (Subtest I)

Algebra (SMR Domain 2)

Algebraic structures (rings and fields), polynomial equations and inequalities, the Fundamental Theorem of Algebra, rational and conjugate root theorems, functions and their inverses, exponential and logarithmic functions, vectors, matrices, and determinants.

25 MC (Subtest II)

Geometry (SMR Domain 3)

Plane Euclidean geometry and the Parallel Postulate, similarity and congruence, triangle theorems with Law of Sines and Cosines, coordinate geometry and conic sections, polar coordinates, three-dimensional geometry, and transformational geometry.

10 MC (Subtest II)

Probability and Statistics (SMR Domain 4)

Permutations and combinations, conditional probability and independence, expected value, normal and binomial distributions, measures of center and spread, sampling methods, least-squares regression, correlation, chi-square, p-values, and confidence intervals.

30 MC (Subtest III)

Calculus, including Trigonometry (SMR Domain 5)

Trigonometric functions and identities, sum and double-angle formulas, DeMoivre's Theorem, limits and continuity, the Intermediate Value Theorem, derivatives and applications, the Mean Value Theorem, integrals and the Fundamental Theorem of Calculus, and sequences and series.

How to Pass the CSET Mathematics (211/212/213) Exam

What You Need to Know

  • Passing score: 220 scaled on each subtest
  • Exam length: 100 questions
  • Time limit: 7h combined across subtests (2h 30m / 2h 30m / 2h)
  • Exam fee: $99 per subtest or $247 combined

Keys to Passing

  • Complete 500+ practice questions
  • Score 80%+ consistently before scheduling
  • Focus on highest-weighted sections
  • Use our AI tutor for tough concepts

CSET Mathematics (211/212/213) Study Tips from Top Performers

1Study by subtest: 211 for number and algebra, 212 for geometry and statistics, 213 for calculus and trigonometry
2Do not ignore constructed responses; they count for about 30% of each subtest score and require full mathematical reasoning
3Practice proofs explicitly, including induction, irrationality of square roots, and the Pythagorean identity, since the framework demands rigor
4Memorize key theorems by name: Fundamental Theorem of Algebra, Rational Root Theorem, Mean Value Theorem, and the Fundamental Theorem of Calculus
5Drill the on-screen graphing calculator workflow so you do not lose time on Subtest II and III computations
6If your credential program allows a coursework-based subject-matter route, confirm it before scheduling expensive retakes

Frequently Asked Questions

What is the CSET Mathematics exam?

CSET: Mathematics is the California subject-matter exam used to demonstrate competence for the Single Subject Teaching Credential in Mathematics. It is divided into three separately scored subtests, 211, 212, and 213, that together cover number and quantity, algebra, geometry, probability and statistics, trigonometry, and calculus.

How many questions are on each CSET Mathematics subtest?

Subtest I (211) has 35 multiple-choice and 3 constructed-response questions, Subtest II (212) has 35 multiple-choice and 3 constructed-response questions, and Subtest III (213) has 30 multiple-choice and 2 constructed-response questions.

What passing score do I need for CSET Mathematics?

The official passing standard is a scaled score of 220 on each subtest. Because the subtests are scored separately, you must reach 220 on all three (211, 212, and 213) for the full mathematics credential.

How much does CSET Mathematics cost in 2026 planning?

The current official fee is $99 for each individual subtest, or $247 if you register for all three Mathematics subtests in a single session. Always confirm the fee in your registration cart before checkout.

How long is each CSET Mathematics subtest?

Subtest I (211) and Subtest II (212) each allow 2 hours and 30 minutes, while Subtest III (213) allows 2 hours. A graphing calculator is provided on screen for designated subtests, so you do not bring your own.

Do I still need CSET Mathematics in 2026 to show subject-matter competence?

Not always. The California Commission on Teacher Credentialing continues alternative pathways that can satisfy subject-matter competence through an approved program, a degree major, or qualifying coursework in some routes. Verify your specific credential route before paying for the exam.