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Sample MCAP Grade 7 Math Practice Questions

Try these sample questions to review concepts for the MCAP Grade 7 Math exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1A water pump fills $\frac{3}{4}$ of a storage tank in $\frac{1}{6}$ of an hour. What is the unit rate at which the pump fills the tank in tanks per hour?
A.$4.5$ tanks per hour
B.$2.25$ tanks per hour
C.$0.125$ tanks per hour
D.$8.0$ tanks per hour
Explanation: To find the unit rate in tanks per hour, divide the fractional amount of tank filled by the time in hours: $\frac{3}{4} \div \frac{1}{6} = \frac{3}{4} \times \frac{6}{1} = \frac{18}{4} = 4.5$ tanks per hour.
2Elena walks $\frac{2}{5}$ of a mile in $\frac{1}{10}$ of an hour. At this constant speed, what is her walking rate in miles per hour?
A.$2.5$ miles per hour
B.$4$ miles per hour
C.$0.04$ miles per hour
D.$8$ miles per hour
Explanation: Divide the distance by the time: $\frac{2}{5} \div \frac{1}{10} = \frac{2}{5} \times \frac{10}{1} = \frac{20}{5} = 4$ miles per hour.
3The table below shows the cost $y$ for $x$ pounds of organic apples at a local market: - $x = 2$ pounds, $y = \$7.00$ - $x = 4$ pounds, $y = \$14.00$ - $x = 6$ pounds, $y = \$21.00$ - $x = 8$ pounds, $y = \$28.00$ What is the constant of proportionality $k$ in dollars per pound?
A.$2.00$
B.$7.00$
C.$3.50$
D.$0.286$
Explanation: The constant of proportionality is $k = \frac{y}{x}$. Using any pair, such as $\frac{7.00}{2} = 3.50$ or $\frac{14.00}{4} = 3.50$. Thus, $k = \$3.50$ per pound.
4A proportional relationship between the number of hours worked $h$ and total earnings $E$ is represented by the equation $E = 18.25h$. What is the constant of proportionality?
A.$18.25$
B.$1.00$
C.$0.055$
D.$36.50$
Explanation: In a proportional equation of the form $y = kx$, the coefficient of the independent variable $x$ represents the constant of proportionality $k$. Here, $k = 18.25$.
5Which set of ordered pairs $(x, y)$ represents a proportional relationship?
A.$(1, 3), (2, 5), (3, 7), (4, 9)$
B.$(2, 5), (4, 10), (6, 15), (8, 20)$
C.$(0, 2), (2, 4), (4, 6), (6, 8)$
D.$(3, 9), (4, 12), (5, 20), (6, 24)$
Explanation: A set of ordered pairs represents a proportional relationship if $\frac{y}{x}$ is constant for all non-zero pairs. For the set $\{(2, 5), (4, 10), (6, 15), (8, 20)\}$: $\frac{5}{2} = 2.5$, $\frac{10}{4} = 2.5$, $\frac{15}{6} = 2.5$, and $\frac{20}{8} = 2.5$, giving a constant ratio $k = 2.5$.
6A bakery recipe calls for $3$ cups of flour to make $4$ servings of muffins. How many cups of flour are needed to make $14$ servings using the same ratio?
A.$10.5$ cups
B.$12.0$ cups
C.$9.5$ cups
D.$18.6$ cups
Explanation: Set up a proportion: $\frac{3\text{ cups}}{4\text{ servings}} = \frac{x\text{ cups}}{14\text{ servings}}$. Cross-multiply to get $4x = 42 \implies x = 10.5$ cups.
7A grocery store sells Brand A cereal in a 16-ounce box for $\$3.20$ and Brand B cereal in a 24-ounce box for $\$4.56$. Which brand is the better buy per ounce, and by how much?
A.Brand B is cheaper by $\$0.01$ per ounce
B.Brand A is cheaper by $\$0.01$ per ounce
C.Brand B is cheaper by $\$0.05$ per ounce
D.Both brands have equal unit prices
Explanation: Find unit prices: Brand A is $\frac{\$3.20}{16} = \$0.20$ per ounce. Brand B is $\frac{\$4.56}{24} = \$0.19$ per ounce. Brand B is cheaper by $\$0.20 - \$0.19 = \$0.01$ per ounce.
8The quantities $x$ and $y$ are directly proportional. What is the value of $N$ in the table below? - $x = 3, y = 12$ - $x = 5, y = 20$ - $x = 9, y = N$
A.$24$
B.$36$
C.$45$
D.$29$
Explanation: Find the constant of proportionality $k = \frac{y}{x} = \frac{12}{3} = 4$. Apply to $x = 9$: $N = 4 \times 9 = 36$.
9The graph of a proportional relationship passes through the origin $(0, 0)$, $(1, r)$, and $(4, 18)$. What is the value of $r$?
A.$4.5$
B.$14.0$
C.$7.2$
D.$2.25$
Explanation: The point $(1, r)$ gives the unit rate $r$, which is equal to the constant of proportionality $k = \frac{y}{x}$. Using $(4, 18)$, $k = \frac{18}{4} = 4.5$. Therefore, $r = 4.5$.
10The price of a video game increased from $\$45.00$ to $\$54.00$. What was the percent increase in price?
A.$20\%$
B.$16.7\%$
C.$9\%$
D.$25\%$
Explanation: Percent increase $= \frac{\text{Amount of Increase}}{\text{Original Price}} \times 100\%$. The increase is $\$54.00 - \$45.00 = \$9.00$. Then, $\frac{9}{45} = 0.20 = 20\%$.

About the MCAP Grade 7 Math Exam

The Grade 7 assessment is available in English and Spanish. This is an English-language MCQ adaptation, not an official translation or format simulation; it does not replace equation entry, modeling, or constructed reasoning.

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

Assessment

Four sections using selected-response, equation-entry, constructed-response, and technology-enhanced tasks.

Time Limit

Four 40-minute sections (160 minutes total)

Passing Score

Not a pass/fail exam; results are reported in performance levels.

Exam / Certification Fees

No individual candidate fee; administered through eligible Maryland 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.

8 operational items

Ratios and Proportional Relationships

Proportions, percent, and applications.

4 operational items

The Number System

Rational-number operations.

5 operational items

Expressions and Equations

Expressions, equations, and inequalities.

3 operational items

Geometry

Scale, angle, area, volume, and circles.

3 operational items

Statistics and Probability

Sampling, probability, and data.

6 items each

Mathematical Reasoning and Modeling

Reasoning and application/modeling across content domains.

Preparing for the MCAP Grade 7 Math Exam

What You Need to Know

  • Passing score: Not a pass/fail exam; results are reported in performance levels.
  • Assessment: Four sections using selected-response, equation-entry, constructed-response, and technology-enhanced tasks.
  • Time limit: Four 40-minute sections (160 minutes total)
  • Exam / certification fees: No individual candidate fee; administered through eligible Maryland 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

MCAP Grade 7 Math: Suggested Study Strategy

1Show reasoning for multi-step problems.
2Practice equation-entry and modeling tasks.
3Review the official blueprint.

Frequently Asked Questions

How long is it?

Four 40-minute sections in the Spring 2026 manual.

Is there one fixed question count?

No; computer-adaptive forms vary and field-test items may be included.

What languages are official?

English and Spanish versions are available; this site keeps one English-language MCQ bank.