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Free Practice Questions for TCAP Grade 6 Mathematics

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Key Facts: TCAP Grade 6 Mathematics Exam

TDOE

Test Administrator

Tennessee Department of Education (TDOE)

Free

Exam Fee

Free for Tennessee public school students.

On Track

Target Benchmark

Tennessee Academic Performance Levels

100 MCQs

Total Questions

OpenExamPrep Practice Question Bank

Grade 6

Grade Level

Tennessee Academic Standards for Mathematics

Spring

Assessment Window

Annual Statewide Administration

4-Option MCQ

Question Format

Study Adaptation Format

5 Domains

Coverage Domains

RP, NS, EE, G, SP Standards

Prepare for the Tennessee TCAP Grade 6 Mathematics test with 100 independent practice questions covering ratios, number systems, expressions, geometry, and statistics with worked step-by-step explanations.

Sample TCAP Grade 6 Mathematics Practice Questions

Try these sample questions to review concepts for the TCAP Grade 6 Mathematics exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1A basket contains 12 red apples and 16 green apples. What is the simplified ratio of red apples to the total number of apples in the basket?
A.3:7
B.3:4
C.4:3
D.4:7
Explanation: To find the ratio of red apples to total apples, first calculate the total number of apples: 12 + 16 = 28. The ratio of red apples to total apples is 12:28. Simplifying 12:28 by dividing both numbers by their greatest common factor, 4, yields 3:7.
2A car travels 180 miles in 3 hours at a constant speed. What is the unit rate of speed in miles per hour?
A.50 miles per hour
B.60 miles per hour
C.65 miles per hour
D.70 miles per hour
Explanation: To find the unit rate in miles per hour, divide the total distance by the total time: 180 miles / 3 hours = 60 miles per hour. This indicates the car travels 60 miles during each hour.
3A recipe requires 2 cups of flour for every 3 cups of sugar. If Maya uses 12 cups of sugar, how many cups of flour does she need to maintain the same ratio?
A.6 cups
B.7 cups
C.8 cups
D.9 cups
Explanation: Set up an equivalent ratio proportion: 2 cups flour / 3 cups sugar = x cups flour / 12 cups sugar. Since 3 cups of sugar multiplied by 4 equals 12 cups, multiply 2 cups of flour by 4 to get 8 cups of flour.
4A 16-ounce box of cereal costs $4.80. What is the unit cost per ounce of cereal?
A.$0.15 per ounce
B.$0.20 per ounce
C.$0.25 per ounce
D.$0.30 per ounce
Explanation: To find the unit cost per ounce, divide the total price by the number of ounces: $4.80 / 16 ounces = $0.30 per ounce.
5What is 35% of 80?
A.28
B.32
C.35
D.42
Explanation: To find 35% of 80, convert 35% to a decimal (0.35) and multiply by 80: 0.35 * 80 = 28. Alternatively, calculate 10% of 80 = 8, so 30% = 24, 5% = 4, and 24 + 4 = 28.
6If 24 students represent 60% of a 6th-grade class, how many total students are in the class?
A.36 students
B.40 students
C.44 students
D.48 students
Explanation: Set up the percent equation: Part / Whole = Percent / 100, so 24 / Whole = 60 / 100 = 0.60. Dividing 24 by 0.60 gives Whole = 40 students.
7A wooden board is 4.5 feet long. How many inches long is the board? (Note: 1 foot = 12 inches)
A.48 inches
B.52 inches
C.54 inches
D.60 inches
Explanation: To convert feet to inches, multiply the number of feet by 12 inches per foot: 4.5 * 12 = 54 inches.
8Which ratio is equivalent to 5:8?
A.10:14
B.15:20
C.20:30
D.15:24
Explanation: Multiply both terms of the ratio 5:8 by 3: 5 * 3 = 15 and 8 * 3 = 24. Thus, 15:24 is equivalent to 5:8.
9Brand A sells 5 cans of soup for $6.50. Brand B sells 8 cans of the same soup for $9.60. Which brand is cheaper per can, and by how much?
A.Brand B is cheaper by $0.10 per can
B.Brand A is cheaper by $0.10 per can
C.Brand B is cheaper by $0.20 per can
D.Both brands cost the exact same per can
Explanation: Calculate the unit rate for Brand A: $6.50 / 5 = $1.30 per can. Calculate the unit rate for Brand B: $9.60 / 8 = $1.20 per can. Subtract the unit rates: $1.30 - $1.20 = $0.10. Therefore, Brand B is cheaper by $0.10 per can.
10A cyclist rides at a constant speed of 14 miles per hour. How far will the cyclist travel in 2.5 hours?
A.32.5 miles
B.35 miles
C.37.5 miles
D.40 miles
Explanation: Use the distance formula Distance = Rate * Time: Distance = 14 miles per hour * 2.5 hours = 35 miles.

About the TCAP Grade 6 Mathematics Exam

The Tennessee Comprehensive Assessment Program (TCAP) Grade 6 Mathematics assessment evaluates student mastery of 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 6th-grade students practice core Tennessee Academic Standards.

Exam sponsor: Tennessee Department of Education (TDOE). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

100 multiple-choice practice questions covering topics from Tennessee Academic Standards for Grade 6 Math

Time Limit

Untimed (administered in subparts)

Passing Score

On Track (Performance Level 3 of 4)

Exam / Certification Fees

Free for Tennessee public school students.

Exam sponsor website

Reported exam pass rate: ~40-50% On Track or Mastered. This describes exam candidates, not OpenExamPrep users or results from using our resources. Exam sponsor website

Fees, eligibility, and exam policies can change. Confirm them with the exam sponsor before applying or paying.

Official sources

  • Tennessee Department of Education (TDOE) Mathematics Standards
  • TCAP Assessment Blueprints & Item Samplers

Our practice resources: topics covered

We aim to reflect publicly available exam outlines and topic information in our study resources. Coverage, format, and difficulty may differ from the actual exam, and we cannot guarantee that every detail is accurate or current. Confirm exam requirements, fees, and policies with the official exam sponsor.

25%

Ratios Proportional Relationships

Questions covering core Tennessee Academic Standards in ratios proportional relationships.

25%

Number System

Questions covering core Tennessee Academic Standards in number system.

25%

Expressions Equations

Questions covering core Tennessee Academic Standards in expressions equations.

13%

Geometry

Questions covering core Tennessee Academic Standards in geometry.

12%

Statistics Probability

Questions covering core Tennessee Academic Standards in statistics probability.

Preparing for the TCAP Grade 6 Mathematics Exam

What You Need to Know

  • Passing score: On Track (Performance Level 3 of 4)
  • Assessment: 100 multiple-choice practice questions covering topics from Tennessee Academic Standards for Grade 6 Math
  • Time limit: Untimed (administered in subparts)
  • Exam / certification fees: Free for Tennessee public school students. Official sources

Using Our Practice Resources

  • 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 Grade 6 Mathematics: Suggested Study Strategy

1Solve ratio and unit rate problems by constructing ratio tables and using double number lines.
2Master fraction division by understanding multiplying by the reciprocal and simplifying terms.
3Review decimal calculations including column alignment for addition/subtraction and counting decimal places for multiplication/division.
4Evaluate algebraic expressions using the correct order of operations with exponents and grouping symbols.
5Practice calculating areas of composite shapes by decomposing them into triangles and rectangles.
6Analyze data sets by finding the mean, median, interquartile range (IQR), and mean absolute deviation (MAD).

Frequently Asked Questions

What is the TCAP Grade 6 Mathematics Assessment?

The TCAP Grade 6 Mathematics assessment is Tennessee's annual state test measuring 6th-grade student proficiency in Tennessee Academic Standards for Mathematics.

Who administers the TCAP Grade 6 Math test?

The exam is administered by the Tennessee Department of Education (TDOE) in Tennessee public schools during the spring testing window.

What is the cost of taking the TCAP Grade 6 Math test?

Free for Tennessee public school students.

What performance levels are reported on the TCAP Math test?

Tennessee reports student performance in four achievement levels: Below Expectations, Approaching Expectations, On Track, and Mastered.

What main math domains are covered on the TCAP Grade 6 Math exam?

The assessment covers Ratios & Proportional Relationships, The Number System, Expressions & Equations, Geometry, and Statistics & Probability.

Is this practice question bank an official TDOE release?

No. Please note: This 100-question practice bank is an English-language multiple-choice question (MCQ) study adaptation created by OpenExamPrep to help 6th-grade students practice core Tennessee Academic Standards.