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100+ Free TCAP Integrated Mathematics III End-of-Course (EOC) Practice Questions

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Key Facts: TCAP Integrated Mathematics III End-of-Course (EOC) Exam

Tennessee Dept of Ed

State authority administering TCAP End-of-Course assessments

Tennessee Department of Education (TDOE)

Graduation Requirement

EOC scores contribute directly to high school final course grades

TN State Board of Education Policy

100 Practice Items

Full 100-question practice set covering all 4 Integrated Math III strands

OpenExamPrep Practice Bank

4 Core Strands

Polynomial & Rational, Trigonometry, Geometry, and Statistics

Tennessee Academic Standards

Calculator Active/Inactive

Assessment features both calculator-permitted and non-calculator subparts

TDOE Testing Guidelines

Free for Students

Provided free to all public high school students in Tennessee

TDOE Funding Model

Spring & Fall Testing

Administered at the conclusion of traditional and block courses

TDOE Testing Calendar

30 / 50 / 20 Ratio

Rigorous difficulty distribution: 30 easy, 50 medium, and 20 hard items

OpenExamPrep Blueprint

Master Tennessee Academic Standards for High School Integrated Math III with 100 realistic practice questions spanning polynomial division, rational equations, unit circle trigonometry, trigonometric modeling, 3D volume & density, normal distributions, and margin of error.

Sample TCAP Integrated Mathematics III End-of-Course (EOC) Practice Questions

Try these sample questions to test your TCAP Integrated Mathematics III End-of-Course (EOC) exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1What is the remainder when the polynomial P(x) = 2x^3 - 5x^2 + 3x - 7 is divided by (x - 2)?
A.-5
B.-3
C.3
D.7
Explanation: According to the Remainder Theorem, the remainder when P(x) is divided by (x - a) is equal to P(a). Evaluating P(2) gives 2(2)^3 - 5(2)^2 + 3(2) - 7 = 16 - 20 + 6 - 7 = -5. Thus, the remainder is -5.
2What are the vertical asymptotes of the rational function f(x) = (x + 3) / (x^2 - 16)?
A.x = -3 only
B.x = 4 only
C.x = 4 and x = -4
D.x = 16 and x = -16
Explanation: Vertical asymptotes occur where the denominator equals zero while the numerator remains non-zero. Setting x^2 - 16 = 0 yields (x - 4)(x + 4) = 0, giving x = 4 and x = -4. Since neither value makes the numerator (x + 3) zero, both x = 4 and x = -4 are vertical asymptotes.
3Solve the radical equation sqrt(3x + 1) = 4 for x.
A.x = 1
B.x = 3
C.x = 5
D.x = 9
Explanation: Square both sides of the equation to eliminate the radical: 3x + 1 = 4^2 = 16. Subtract 1 from both sides to get 3x = 15, then divide by 3 to find x = 5. Checking x = 5 gives sqrt(3(5) + 1) = sqrt(16) = 4, which confirms the solution.
4What is the horizontal asymptote of the rational function g(x) = (6x^2 - 5) / (2x^2 + 7x + 1)?
A.y = 0
B.y = 3
C.y = 6
D.No horizontal asymptote
Explanation: When the degree of the numerator equals the degree of the denominator (both degree 2), the horizontal asymptote is the ratio of their leading coefficients. The leading coefficient of the numerator is 6 and the denominator is 2, so y = 6 / 2 = 3.
5Simplify the rational expression (x^2 - 9) / (x^2 + 5x + 6) for all valid domain values.
A.(x - 3) / (x + 2)
B.(x + 3) / (x + 2)
C.(x - 3) / (x - 2)
D.-9 / (5x + 6)
Explanation: Factor both the numerator and the denominator: x^2 - 9 = (x - 3)(x + 3) and x^2 + 5x + 6 = (x + 2)(x + 3). Canceling the common factor (x + 3) yields (x - 3) / (x + 2).
6Given f(x) = x^2 + 2 and g(x) = 3x - 1, find the value of (f o g)(2).
A.11
B.17
C.27
D.31
Explanation: First evaluate g(2) = 3(2) - 1 = 6 - 1 = 5. Next, substitute this value into f(x) to evaluate f(5) = 5^2 + 2 = 25 + 2 = 27. Therefore, (f o g)(2) = 27.
7What is the inverse function f^(-1)(x) for f(x) = 2x + 8?
A.f^(-1)(x) = (x - 8) / 2
B.f^(-1)(x) = 2x - 8
C.f^(-1)(x) = (x + 8) / 2
D.f^(-1)(x) = -1/2 x + 4
Explanation: To find the inverse, replace f(x) with y: y = 2x + 8. Swap x and y to get x = 2y + 8. Solve for y by subtracting 8 and dividing by 2: y = (x - 8) / 2 = 1/2 x - 4.
8Which cubic polynomial function has zeros at x = -1, x = 2, and x = 4?
A.P(x) = x^3 - 5x^2 + 2x + 8
B.P(x) = x^3 + 5x^2 + 2x - 8
C.P(x) = x^3 - 7x^2 + 14x - 8
D.P(x) = x^3 - 5x^2 - 2x + 8
Explanation: A polynomial with zeros -1, 2, and 4 can be factored as P(x) = (x + 1)(x - 2)(x - 4). Expanding (x - 2)(x - 4) gives x^2 - 6x + 8. Multiplying by (x + 1) yields x^3 - 6x^2 + 8x + x^2 - 6x + 8 = x^3 - 5x^2 + 2x + 8.
9Solve the rational equation 2 / (x - 3) + 1 / x = 6 / (x(x - 3)).
A.x = 3
B.x = 1
C.x = 6
D.No real solution (x = 3 is an extraneous solution)
Explanation: Multiply the entire equation by the common denominator x(x - 3): 2x + 1(x - 3) = 6. Simplifying yields 3x - 3 = 6, so 3x = 9 and x = 3. However, substituting x = 3 into the original equation causes division by zero in (x - 3), making x = 3 an extraneous solution. Thus, no real solution exists.
10Solve the radical equation sqrt(2x + 3) - x = 0.
A.x = -1 and x = 3
B.x = 3 only
C.x = -1 only
D.x = 9 only
Explanation: Isolate the radical: sqrt(2x + 3) = x. Square both sides: 2x + 3 = x^2, which rearranges to x^2 - 2x - 3 = 0. Factoring gives (x - 3)(x + 1) = 0, so x = 3 or x = -1. Check both: sqrt(2(3) + 3) - 3 = 3 - 3 = 0 (valid); for x = -1, sqrt(2(-1) + 3) - (-1) = 1 + 1 = 2 != 0 (extraneous). Thus, x = 3 is the only valid solution.

About the TCAP Integrated Mathematics III End-of-Course (EOC) Exam

The Tennessee Comprehensive Assessment Program (TCAP) Integrated Mathematics III End-of-Course (EOC) assessment evaluates high school student proficiency in advanced algebra, polynomial and rational functions, trigonometry, 3D geometric modeling, and inferential statistics based on Tennessee Academic Standards. Please note: This 100-question practice bank is an English-language multiple-choice question (MCQ) study adaptation created by OpenExamPrep to help high school students practice core Tennessee Academic Standards.

Assessment

100 multiple-choice practice questions (English-language MCQ study adaptation for TCAP Integrated Math III EOC) covering Polynomial, Rational, & Radical Functions (35%), Trigonometric Functions & Modeling (25%), Geometric Measurement & Modeling (20%), and Statistical Inferences (20%).

Time Limit

Untimed state subparts (approx. 35–50 min per subpart)

Passing Score

Performance Level 3 (On Track) or Level 4 (Mastered)

Exam Fee

Free for Tennessee public school students. (Tennessee Department of Education (TDOE))

TCAP Integrated Mathematics III End-of-Course (EOC) Exam Content Outline

35%

Polynomial, Rational, & Radical Functions

Polynomial operations, factor and remainder theorems, rational root theorem, solving radical and rational equations, function composition/inverses, and vertical/horizontal asymptotes.

25%

Trigonometric Functions & Modeling

Radian measure, unit circle trigonometry, transformations of periodic functions (amplitude, period, phase shift), Pythagorean identities, and Law of Sines and Law of Cosines.

20%

Geometric Measurement & Modeling

Volume formulas for 3D figures, cross-sectional geometry, solids of revolution, modeling density and optimization, circle arc lengths, and sector areas.

20%

Statistical Inferences

Sampling methods, random assignment in experiments, normal distributions, standard error, margin of error, confidence intervals, and evaluating statistical claims.

How to Pass the TCAP Integrated Mathematics III End-of-Course (EOC) Exam

What You Need to Know

  • Passing score: Performance Level 3 (On Track) or Level 4 (Mastered)
  • Assessment: 100 multiple-choice practice questions (English-language MCQ study adaptation for TCAP Integrated Math III EOC) covering Polynomial, Rational, & Radical Functions (35%), Trigonometric Functions & Modeling (25%), Geometric Measurement & Modeling (20%), and Statistical Inferences (20%).
  • Time limit: Untimed state subparts (approx. 35–50 min per subpart)
  • Exam fee: Free for Tennessee public school students.

Keys to Passing

  • Work through all 100 available questions
  • Review every answer and explanation
  • Track weak areas and revisit them
  • Use our AI tutor for tough concepts

TCAP Integrated Mathematics III End-of-Course (EOC) Study Tips from Top Performers

1Review polynomial long division and synthetic division to quickly find rational roots, factors, and asymptotes.
2Memorize special right triangle ratios (30-60-90 and 45-45-90) to easily determine exact unit circle values for sine, cosine, and tangent.
3Practice solving radical and rational equations while remembering to check for extraneous solutions in denominators or radicals.
4Understand the parameters of y = A sin(B(x - C)) + D, noting that amplitude is |A|, period is 2pi/B, and phase shift is C.
5Apply normal distribution z-score formulas z = (x - mu)/sigma and the Empirical Rule (68-95-99.7) for statistical probability problems.
6Use margin of error formulas ME = z* sqrt(p_hat(1-p_hat)/n) or ME = 2 * sigma / sqrt(n) when calculating confidence intervals.

Frequently Asked Questions

What is the structure of the TCAP Integrated Math III EOC assessment?

The official TCAP Integrated Math III EOC assessment consists of multiple subparts containing operational multiple-choice and constructed-response items. This practice bank adapts those state standard expectations into a 100-question multiple-choice study bank.

Are graphing calculators permitted on the TCAP Integrated Math III EOC?

Yes, graphing calculators (such as TI-84 Plus) are permitted on specified calculator-active subparts of the test, while non-calculator subparts test core algebraic and trigonometric fluency.

How are student results scored on the TCAP Integrated Math III assessment?

Student results are scored into four performance levels: Level 1 (Below Expectations), Level 2 (Approaching Expectations), Level 3 (On Track), and Level 4 (Mastered). Achieving Level 3 or Level 4 indicates solid mastery of high school mathematics.

Does the TCAP Integrated Math III EOC grade count toward high school graduation?

Yes, under Tennessee State Board of Education rules, the EOC score accounts for a percentage (typically 15–25%) of the student's final course grade in Integrated Math III.

What specific topic domains are emphasized on Integrated Math III?

The assessment places strong emphasis on polynomial algebra, rational/radical equations, unit circle and sinusoidal functions, 3D geometric volume and modeling, and inferential statistics (normal distribution and margin of error).

Is this practice question bank officially affiliated with TDOE?

No, this practice bank is an independent educational prep resource developed by OpenExamPrep aligned to Tennessee Academic Standards and is not affiliated with or endorsed by TDOE.