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Sample MTYA High School Math Practice Questions

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

1Simplify $(x^6)^{1/3} \cdot x^2$ for $x > 0$.
A.$x^4$
B.$x^3$
C.$x^8$
D.$x^5$
Explanation: Using the power of a power rule, $(x^6)^{1/3} = x^{6 \cdot (1/3)} = x^2$. Multiplying $x^2 \cdot x^2$ gives $x^{2+2} = x^4$.
2Simplify the radical expression $\sqrt{72 x^4 y^3}$ where $x, y > 0$.
A.$6x^2 y \sqrt{2y}$
B.$36x^2 y \sqrt{2y}$
C.$6x^4 y \sqrt{2y}$
D.$12x^2 y \sqrt{y}$
Explanation: Factor the radicand into perfect squares: $\sqrt{72 x^4 y^3} = \sqrt{36 \cdot 2 \cdot x^4 \cdot y^2 \cdot y} = \sqrt{36} \cdot \sqrt{x^4} \cdot \sqrt{y^2} \cdot \sqrt{2y} = 6 x^2 y \sqrt{2y}$.
3Perform the multiplication and express in standard form $a + bi$: $(3 + 4i)(2 - 5i)$.
A.$26 - 7i$
B.$6 - 20i$
C.$-14 - 7i$
D.$26 + 7i$
Explanation: Expand using FOIL: $(3+4i)(2-5i) = 6 - 15i + 8i - 20i^2$. Since $i^2 = -1$, this becomes $6 - 7i - 20(-1) = 6 + 20 - 7i = 26 - 7i$.
4Find the modulus of the complex number $z = 5 - 12i$.
A.$13$
B.$17$
C.$\sqrt{119}$
D.$7$
Explanation: The modulus of $z = a + bi$ is $|z| = \sqrt{a^2 + b^2}$. Here, $|5 - 12i| = \sqrt{5^2 + (-12)^2} = \sqrt{25 + 144} = \sqrt{169} = 13$.
5Evaluate the numerical expression: $27^{2/3} + 16^{3/4}$.
A.$17$
B.$15$
C.$25$
D.$18$
Explanation: Evaluate each term: $27^{2/3} = (\sqrt[3]{27})^2 = 3^2 = 9$. Also $16^{3/4} = (\sqrt[4]{16})^3 = 2^3 = 8$. Sum = $9 + 8 = 17$.
6Convert a speed of $60\text{ miles per hour}$ into $\text{feet per second}$. (1 mile = 5280 feet, 1 hour = 3600 seconds)
A.$88\text{ ft/s}$
B.$44\text{ ft/s}$
C.$100\text{ ft/s}$
D.$60\text{ ft/s}$
Explanation: Multiply by conversion factors: $\frac{60\text{ mi}}{1\text{ hr}} \times \frac{5280\text{ ft}}{1\text{ mi}} \times \frac{1\text{ hr}}{3600\text{ s}} = \frac{316,800}{3600} = 88\text{ ft/s}$.
7Rationalize the denominator of $\frac{6}{3 - \sqrt{3}}$ and write in simplest form.
A.$3 + \sqrt{3}$
B.$3 - \sqrt{3}$
C.$6 + 2\sqrt{3}$
D.$2 + \sqrt{3}$
Explanation: Multiply numerator and denominator by the conjugate $3 + \sqrt{3}$: $\frac{6(3 + \sqrt{3})}{(3 - \sqrt{3})(3 + \sqrt{3})} = \frac{18 + 6\sqrt{3}}{9 - 3} = \frac{18 + 6\sqrt{3}}{6} = 3 + \sqrt{3}$.
8Simplify the expression $i^{103} + i^{42} - i^{17}$, where $i = \sqrt{-1}$.
A.$-1 - 2i$
B.$-1 + 2i$
C.$1 - 2i$
D.$-1$
Explanation: Divide exponents by 4: $103 = 4(25)+3 \implies i^{103} = i^3 = -i$. $42 = 4(10)+2 \implies i^{42} = i^2 = -1$. $17 = 4(4)+1 \implies i^{17} = i$. Thus, $-i + (-1) - i = -1 - 2i$.
9A pump moves water at a rate of $15\text{ gallons per minute}$. How many liters per hour is this? ($1\text{ gallon} \approx 3.785\text{ liters}$)
A.$3406.5\text{ L/h}$
B.$56.775\text{ L/h}$
C.$237.8\text{ L/h}$
D.$900\text{ L/h}$
Explanation: Convert minutes to hours and gallons to liters: $\frac{15\text{ gal}}{1\text{ min}} \times \frac{60\text{ min}}{1\text{ hr}} \times \frac{3.785\text{ L}}{1\text{ gal}} = 900 \times 3.785 = 3406.5\text{ L/h}$.
10Simplify $(32 x^{10})^{2/5}$ assuming $x > 0$.
A.$4x^4$
B.$8x^4$
C.$4x^5$
D.$16x^4$
Explanation: Apply exponent to coefficient and variable: $32^{2/5} = (\sqrt[5]{32})^2 = 2^2 = 4$. For the variable: $(x^{10})^{2/5} = x^{10 \cdot (2/5)} = x^4$. Combining gives $4x^4$.

About the MTYA High School Math Exam

Statewide assessment for Maine Second Year High School (Grade 10) students measuring high school mathematics proficiency including quadratic functions, exponential growth, geometric proofs, and statistical modeling. This practice bank provides an English-language MCQ study adaptation.

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

Assessment

Computer-adaptive mathematics assessment covering four official reporting domains through seven official item types.

Time Limit

Untimed; testing may be split into multiple sessions.

Passing Score

Not a pass/fail exam; reported across four state achievement levels.

Exam / Certification Fees

No individual candidate fee; administered statewide in Maine public schools.

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.

46–50%

Operations and Algebraic Thinking

Official spring blueprint range, including algebra and functions.

13–15%

The Real and Complex Number Systems

Official spring blueprint range for number and quantity content.

26–30%

Geometry

Official spring blueprint range.

13–15%

Statistics and Probability

Official spring blueprint range.

Preparing for the MTYA High School Math Exam

What You Need to Know

  • Passing score: Not a pass/fail exam; reported across four state achievement levels.
  • Assessment: Computer-adaptive mathematics assessment covering four official reporting domains through seven official item types.
  • Time limit: Untimed; testing may be split into multiple sessions.
  • Exam / certification fees: No individual candidate fee; administered statewide in Maine public schools. 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

MTYA High School Math: Suggested Study Strategy

1Master factoring quadratic expressions.
2Understand key features of quadratic and exponential graphs.
3Use right-triangle trigonometry ratios.

Frequently Asked Questions

What is the MTYA Second Year High School Math assessment?

It is Maine's statewide computer-adaptive assessment for high school sophomores (second year high school), administered in partnership with NWEA.

Is this practice bank the official test format?

No. It is an English-language four-option MCQ study adaptation, not a simulation of the official adaptive assessment or its multi-select, composite, gap-match, graphic gap-match, hot-text, and numeric-entry items.