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Free Practice Questions for MCAS Grade 10 Math

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Key Facts: MCAS Grade 10 Math Exam

The MCAS Grade 10 Mathematics Test is administered by the Massachusetts Department of Elementary and Secondary Education with delivery by Cognia.

MCAS grade 10 math scores are reported on a scale of 440 to 560, with 500 marking the Meeting Expectations level.

The grade 10 test has four achievement levels: Not Meeting, Partially Meeting, Meeting, and Exceeding Expectations.

The test is given in two sessions, with a calculator allowed in one session and prohibited in the other.

The grade 10 math test assesses standards that overlap the Model Algebra I and Model Geometry courses under the 2017 framework.

Massachusetts voters approved a 2024 ballot question that ended MCAS as a statewide high-school graduation requirement.

Students still take the grade 10 MCAS, and a state reference sheet of formulas is provided during both sessions.

The grade 10 Mathematics test is free to students because Massachusetts funds the assessment through its public schools.

The MCAS Grade 10 Mathematics Test is a free, untimed, two-session high-school exam from the Massachusetts DESE covering algebra, functions, geometry, and statistics and probability, reported on a 440-560 scale with 500 marking grade-level proficiency.

Sample MCAS Grade 10 Math Practice Questions

Try these sample questions to review concepts for the MCAS Grade 10 Math exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1What is the value of 27^(2/3)?
A.6
B.9
C.18
D.81
Explanation: A rational exponent a^(m/n) equals the n-th root of a, raised to the m power. So 27^(2/3) = (cube root of 27)^2 = 3^2 = 9.
2Which expression is equivalent to the square root of 50, written in simplest radical form?
A.5 times the square root of 2
B.2 times the square root of 5
C.25 times the square root of 2
D.10 times the square root of 5
Explanation: Factor 50 as 25 times 2. The square root of 25 is 5, which comes out of the radical, leaving 5 times the square root of 2.
3Which statement about the product of a nonzero rational number and an irrational number is always true?
A.The product is always rational
B.The product is always irrational
C.The product is always an integer
D.The product can be either rational or irrational
Explanation: The product of a nonzero rational number and an irrational number is always irrational. If it were rational, dividing by the rational factor would force the irrational number to be rational, a contradiction.
4A car travels 240 miles using 8 gallons of gas. Using unit analysis, what is the fuel efficiency in miles per gallon?
A.24 miles per gallon
B.30 miles per gallon
C.32 miles per gallon
D.248 miles per gallon
Explanation: Fuel efficiency in miles per gallon is found by dividing miles by gallons: 240 divided by 8 equals 30 miles per gallon.
5What is the completely factored form of the expression x^2 - 9?
A.(x - 3)(x - 3)
B.(x + 3)(x + 3)
C.(x - 3)(x + 3)
D.(x - 9)(x + 1)
Explanation: The expression x^2 - 9 is a difference of two squares because 9 = 3^2. A difference of squares a^2 - b^2 factors as (a - b)(a + b), giving (x - 3)(x + 3).
6Solve the equation 3(x - 4) = 2x + 5 for x.
A.x = 1
B.x = 7
C.x = 17
D.x = -7
Explanation: Distribute to get 3x - 12 = 2x + 5. Subtract 2x from both sides to get x - 12 = 5, then add 12 to both sides to find x = 17.
7What are the solutions to the quadratic equation x^2 - 5x + 6 = 0?
A.x = 1 and x = 6
B.x = 2 and x = 3
C.x = -2 and x = -3
D.x = -1 and x = 6
Explanation: Factor the quadratic as (x - 2)(x - 3) = 0 because -2 and -3 multiply to 6 and add to -5. Setting each factor to zero gives x = 2 and x = 3.
8Using the quadratic formula, what are the solutions to 2x^2 + 3x - 2 = 0?
A.x = 1/2 and x = -2
B.x = -1/2 and x = 2
C.x = 2 and x = -2
D.x = 1 and x = -2
Explanation: With a = 2, b = 3, c = -2, the discriminant is 9 + 16 = 25, so the square root is 5. The solutions are (-3 + 5)/4 = 1/2 and (-3 - 5)/4 = -2.
9A rectangle has length (x + 5) and width (x + 2). Which expression represents its area as a polynomial?
A.2x + 7
B.x^2 + 7x + 10
C.x^2 + 10x + 7
D.x^2 + 7
Explanation: Area is length times width: (x + 5)(x + 2). Using the distributive property gives x^2 + 2x + 5x + 10 = x^2 + 7x + 10.
10Solve the system of equations: y = 2x + 1 and y = -x + 7. What is the point of intersection?
A.(2, 5)
B.(3, 7)
C.(2, 4)
D.(1, 3)
Explanation: Set the right sides equal: 2x + 1 = -x + 7, so 3x = 6 and x = 2. Substituting into y = 2x + 1 gives y = 5, so the solution is (2, 5).

About the MCAS Grade 10 Math Exam

The MCAS Grade 10 Mathematics Test is part of the Massachusetts Comprehensive Assessment System administered by the Department of Elementary and Secondary Education (DESE) and aligned to the 2017 Massachusetts Curriculum Framework for Mathematics. The grade 10 test assesses the standards that overlap the Model Algebra I and Model Geometry courses (and Model Mathematics I and II), spanning Number and Quantity, Algebra, Functions, Geometry, and Statistics and Probability. It is delivered in two sessions, most often on a computer, using selected-response, short-answer and constructed-response items; one session allows a calculator and one does not, and a state reference sheet is provided. Results are reported on a 440-560 scale across four achievement levels. Following the November 2024 ballot question, scores no longer function as a statewide high-school graduation requirement, but Massachusetts students continue to take the grade 10 Mathematics test, and it remains a key measure of math readiness.

Exam sponsor: Massachusetts Department of Elementary and Secondary Education (DESE), with test delivery by Cognia.. The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Questions

100 questions

Time Limit

Untimed, given in two sessions; most students finish in about two to three hours total.

Passing Score

A scaled score of 500 (Meeting Expectations) indicates grade-level proficiency on the 440-560 scale. As of the 2024 ballot result, MCAS scores no longer serve as a statewide graduation requirement, but students still take the test.

Exam / Certification Fees

Free for students; Massachusetts funds the assessment through public schools and there is no student registration fee.

Exam sponsor website

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

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.

Approx 60%

Number, Quantity, Algebra and Functions

Rational exponents and radicals, units and quantities, structure of expressions, factoring, creating and solving linear and quadratic equations and inequalities, systems, function notation, sequences, and linear, quadratic and exponential models.

Approx 20%

Geometry

Rigid motions and congruence, similarity and dilations, right-triangle trigonometry, the Pythagorean Theorem, circles and sectors, coordinate geometry with slope and distance, and volume of solids.

Approx 20%

Statistics and Probability

Dot plots, histograms and box plots, center and spread, two-way frequency tables, scatter plots, lines of best fit, the correlation coefficient, conditional probability, and the rules of probability.

Preparing for the MCAS Grade 10 Math Exam

What You Need to Know

  • Passing score: A scaled score of 500 (Meeting Expectations) indicates grade-level proficiency on the 440-560 scale. As of the 2024 ballot result, MCAS scores no longer serve as a statewide graduation requirement, but students still take the test.
  • Exam length: 100 questions
  • Time limit: Untimed, given in two sessions; most students finish in about two to three hours total.
  • Exam / certification fees: Free for students; Massachusetts funds the assessment through public schools and there is no student registration fee. 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

MCAS Grade 10 Math: Suggested Study Strategy

1Focus most of your review on algebra and functions, since standards overlapping Model Algebra I make up the largest share of the test.
2Master quadratics thoroughly, including factoring, the quadratic formula, completing the square, and reading vertex and intercepts from graphs.
3Practice the non-calculator session separately so you can simplify radicals, evaluate functions, and solve equations by hand with confidence.
4Learn the provided reference sheet ahead of time, especially the area, volume, Pythagorean and quadratic formulas, so you do not waste time hunting for them.
5Work official released grade 10 items from recent spring administrations to get used to short-answer and constructed-response formats alongside multiple choice.
6Review statistics and probability topics such as two-way tables, lines of best fit, the correlation coefficient, and conditional probability, which are reliable points if practiced.

Frequently Asked Questions

What is the MCAS Grade 10 Mathematics Test?

It is the high-school mathematics test of the Massachusetts Comprehensive Assessment System, administered by the Department of Elementary and Secondary Education and aligned to the 2017 Massachusetts Curriculum Framework for Mathematics. It measures the standards that overlap the Model Algebra I and Model Geometry courses.

Is the MCAS still required to graduate in Massachusetts?

No. In November 2024, voters approved a ballot question that removed passing the grade 10 MCAS as a statewide graduation requirement. Students still take the test, but a Competency Determination is now earned mainly through coursework rather than the test score.

What topics are on the Grade 10 Mathematics test?

It covers Number and Quantity, Algebra, Functions, Geometry, and Statistics and Probability. Common topics include rational exponents, quadratics, systems of equations, function models, right-triangle trigonometry, circles, two-way tables, and the correlation coefficient.

How is the test scored?

Scores are reported on a scale of 440 to 560 across four achievement levels: Not Meeting, Partially Meeting, Meeting, and Exceeding Expectations. A scaled score of 500 indicates that a student is meeting grade-level expectations.

Can I use a calculator on the MCAS Grade 10 math test?

Partly. The test is given in two sessions; a calculator is permitted in one session but not in the other. A state-provided reference sheet with formulas is available during both sessions.

How much does the MCAS Grade 10 math test cost?

There is no cost to students. Massachusetts funds the Massachusetts Comprehensive Assessment System through its public schools, so students do not pay a registration fee to take the grade 10 Mathematics test.