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7th Grade Math AI Tutor
Mastering 34 Basic Math

Explain your answer

1. A microwave oven is on sale for 20% off the regular price. The sale price is $250. What is the regular price of the microwave oven?

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 7th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 7th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Ratio and Proportion (RP) 7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems (e.g., simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error).

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2. If two parallel lines are cut by a non-perpendicular transversal, which type of angles are not congruent?

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 7th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 7th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Mathematics Practice 7.MP.6 Attend to precision. Mathematically proficient students clearly communicate to others using appropriate mathematical terminology, and craft explanations that convey their reasoning. When making mathematical arguments about a solution, strategy, or conjecture, they describe mathematical relationships and connect their words clearly to their representations. Mathematically proficient students understand meanings of symbols used in mathematics, calculate accurately and efficiently, label quantities appropriately, and record their work clearly and concisely.

Explain your answer

3. The circumference of a circle measures 12.56 inches. What is the measure of the radius of the circle?

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 7th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 7th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Geometry (G) 7.G.B.4: Understand and use the formulas for the area and circumference of a circle to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

Explain your answer

4. The number of students (class size) in each of 7 classes is shown as 15, 25, 25, 29, 31, 32, 37 Which class size affects the range of all 7 classes the most?

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 7th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 7th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Statistics and Probability (SP) 7.SP.A.1: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

Explain your answer

5. Becky created the line graph below to show the distance she traveled during one day. Which activity could be represented by the circled portion of the line?

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 7th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 7th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Mathematics Practice 7.MP.4 Model with mathematics. Mathematically proficient students apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. When given a problem in a contextual situation, they identify the mathematical elements of a situation and create a mathematical model that represents those mathematical elements and the relationships among them. Mathematically proficient students use their model to analyze the relationships and draw conclusions. They interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

Explain your answer

6. For which of the following would the use of a table of values not be helpful?

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 7th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 7th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Mathematics Practice 7.MP.3 Construct viable arguments and critique the reasoning of others. Mathematically proficient students construct mathematical arguments (explain the reasoning underlying a strategy, solution, or conjecture) using concrete, pictorial, or symbolic referents. Arguments may also rely on definitions, assumptions, previously established results, properties, or structures. Mathematically proficient students make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. Mathematically proficient students present their arguments in the form of representations, actions on those representations, and explanations in words (oral or written). Students critique others by affirming or questioning the reasoning of others. They can listen to or read the reasoning of others, decide whether it makes sense, ask questions to clarify or improve the reasoning, and validate or build on it. Mathematically proficient students can communicate their arguments, compare them to others, and reconsider their own arguments in response to the critiques of others.

Explain your answer

7. The Venn diagram below shows the number of students in a class who have visited the Grand Canyon, Carlsbad Caverns, or both. There are 34 students in the class, and all of the students have visited at least one of the locations. What is the number of students, x, who have only visited the Grand Canyon?

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 7th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 7th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Mathematics Practice 7.MP.3 Construct viable arguments and critique the reasoning of others. Mathematically proficient students construct mathematical arguments (explain the reasoning underlying a strategy, solution, or conjecture) using concrete, pictorial, or symbolic referents. Arguments may also rely on definitions, assumptions, previously established results, properties, or structures. Mathematically proficient students make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. Mathematically proficient students present their arguments in the form of representations, actions on those representations, and explanations in words (oral or written). Students critique others by affirming or questioning the reasoning of others. They can listen to or read the reasoning of others, decide whether it makes sense, ask questions to clarify or improve the reasoning, and validate or build on it. Mathematically proficient students can communicate their arguments, compare them to others, and reconsider their own arguments in response to the critiques of others.

Explain your answer

8. What is the value of the expression (1/2)y - x ?

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 7th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 7th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Expressions and Equations (EE) 7.EE.A.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

Explain your answer

9. The graph below shows the increase in average gasoline prices from Jan. through May. If the gasoline prices continue to increase at the same rate, what will be the average gasoline price in July of that same year?

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 7th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 7th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Ratio and Proportion (RP) 7.RP.A.2.d: Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

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10. Max, Owen, Elise, and Cara went to a school carnival. They each played the dart throw, ring toss, water shoot, and basketball throw. Each student won a different game. Clues: Max didn't score any points at the dart throw. Elise correctly tossed 2 rings, but did not win the ring toss. Cara won a bear for outscoring everyone at the water shoot. Owen score more than anyone at the basketball throw. Based on the clues, which game did Max win?

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 7th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 7th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Mathematics Practice 7.MP.3 Construct viable arguments and critique the reasoning of others. Mathematically proficient students construct mathematical arguments (explain the reasoning underlying a strategy, solution, or conjecture) using concrete, pictorial, or symbolic referents. Arguments may also rely on definitions, assumptions, previously established results, properties, or structures. Mathematically proficient students make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. Mathematically proficient students present their arguments in the form of representations, actions on those representations, and explanations in words (oral or written). Students critique others by affirming or questioning the reasoning of others. They can listen to or read the reasoning of others, decide whether it makes sense, ask questions to clarify or improve the reasoning, and validate or build on it. Mathematically proficient students can communicate their arguments, compare them to others, and reconsider their own arguments in response to the critiques of others.

Explain your answer

11. Which expression has a value of -3?

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 7th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 7th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Expressions and Equations (EE) 7.EE.A.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

Explain your answer

12. Between which two consecutive integers is the value of this irrational number?

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 7th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 7th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for The Number System (NS) 7.NS.A.1: Add and subtract integers and other rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

Explain your answer

13. Using the results in the tables, what is the probability of a spinner landing on the letter P in both experiments?

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 7th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 7th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Statistics and Probability (SP) 7.SP.C.6 Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.

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14. The radius of a circular fish pond is 4 feet. What is the circumference of the pond in terms of π?

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 7th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 7th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Geometry (G) 7.G.B.4: Understand and use the formulas for the area and circumference of a circle to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

Explain your answer

15. On a winter Monday in Prescott, the temperature at 8 a.m. was -8°F. At 1 p.m. it was 27°F. By how many degrees did the temperature change from morning to afternoon?

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 7th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 7th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Ratio and Proportion (RP) 7.RP.A.2.b: Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

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16. Dave's neighbors are going on a trip to Japan. He wants them to bring him a souvenir t-shirt, but Japan has its own unit of currency. Conversion 1 US dollar = about 94.73 Japanese yen. Dave gives his neighbors $20.00. About how many Japanese yen will Dave's neighbors be able to spend on his t-shirt?

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 7th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 7th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Ratio and Proportion (RP) 7.RP.A.2.c: Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn

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17. Karen wants to visit all of the points of interest near her home. She will leave from her home and then visit each place on her vertex-edge graph only once. What is the shortest distance that Karen will travel to each site and then return home?

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 7th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 7th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Mathematics Practice 7.MP.4 Model with mathematics. Mathematically proficient students apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. When given a problem in a contextual situation, they identify the mathematical elements of a situation and create a mathematical model that represents those mathematical elements and the relationships among them. Mathematically proficient students use their model to analyze the relationships and draw conclusions. They interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

Explain your answer

19. Alfredo bought 3 new notebooks for school. He paid $2.49 for all the notebooks. Which equation can be used to find n, the cost of each notebook?

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 7th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 7th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Expressions and Equations (EE) 7.EE.B.4: Use variables to represent quantities in mathematical problems and problems in real-world context, and construct simple equations and inequalities to solve problems.

Explain your answer

20.The table shows a sequence of numbers. What is the rule for the sequence?

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 7th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 7th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for The Number System (NS) 7.NS.A.2.c c. Apply properties of operations as strategies to multiply and divide rational numbers.

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21.Look at the figure. Which statement can be used to find the total area of the figure?

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 7th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 7th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Mathematics Practice 7.MP.2 Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. Students can contextualize and decontextualize problems involving quantitative relationships. They contextualize quantities, operations, and expressions by describing a corresponding situation. They decontextualize a situation by representing it symbolically. As they manipulate the symbols, they can pause as needed to access the meaning of the numbers, the units, and the operations that the symbols represent. Mathematically proficient students know and flexibly use different properties of operations, numbers, and geometric objects and when appropriate they interpret their solution in terms of the context.

Explain your answer

22. Which polygon has the same perimeter as the one below?

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 7th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 7th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Geometry (G) 7.G.A.1: Solve problems involving scale drawings of geometric figures, such as computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

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23. Which two points on circle Q form an arc?

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 7th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 7th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Geometry (G) 7.G.A.2: Draw geometric shapes with given conditions using a variety of methods. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

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24. What is the value of the expression?

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 7th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 7th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for The Number System (NS) 7.NS.A.1.c: Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world context.

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25. What is the solution to the equation?

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 7th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 7th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for The Number System (NS) 7.NS.A.1.b: b. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world context.

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26. What is 7.29 x 10⁵ written in standard form?

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 7th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 7th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for The Number System (NS) 7.NS.A.2.d: d. Convert a rational number to decimal form using long division; know that the decimal form of a rational number terminates in 0’s or eventually repeats.

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27. Which pair of events is dependent?

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 7th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 7th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Mathematics Practice 7.MP.7 Look for and make use of structure. Mathematically proficient students use structure and patterns to assist in making connections among mathematical ideas or concepts when making sense of mathematics. Students recognize and apply general mathematical rules to complex situations. They are able to compose and decompose mathematical ideas and notations into familiar relationships. Mathematically proficient students manage their own progress, stepping back for an overview and shifting perspective when needed.

Explain your answer

28. Which figure is a right prism with a hexagonal base?

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 7th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 7th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Geometry (G) 7.G.B.6: Solve mathematical problems and problems in a real-world context involving area of two-dimensional objects composed of triangles, quadrilaterals, and other polygons. Solve mathematical problems and problems in real-world context involving volume and surface area of three-dimensional objects composed of cubes and right prisms.

Explain your answer

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 7th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 7th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Ratio and Proportion (RP) 7.RP.A.2.a Decide whether two quantities are in a proportional relationship (e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin).

Explain your answer

30. Which figure shows the triangle below reflected over the x-axis, then reflected over the y-axis?

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 7th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 7th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Mathematics Practice 7.MP.7 Look for and make use of structure. Mathematically proficient students use structure and patterns to assist in making connections among mathematical ideas or concepts when making sense of mathematics. Students recognize and apply general mathematical rules to complex situations. They are able to compose and decompose mathematical ideas and notations into familiar relationships. Mathematically proficient students manage their own progress, stepping back for an overview and shifting perspective when needed.

Explain your answer

31. Which table of values can be used to graph the equation below?

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 7th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 7th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Ratio and Proportion (RP) 7.RP.A.2.a Decide whether two quantities are in a proportional relationship (e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin).

Explain your answer

32. Jose is having a party and will invite all of his friends. He will supply the following items for each person. 3 slices of pizza, 2 bottles of sports drink, and 1 piece of cake. What information is needed to make sure that Jose has pizza, sports drink, and cake for each person?

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 7th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 7th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Mathematics Practice 7.MP.4 Model with mathematics. Mathematically proficient students apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. When given a problem in a contextual situation, they identify the mathematical elements of a situation and create a mathematical model that represents those mathematical elements and the relationships among them. Mathematically proficient students use their model to analyze the relationships and draw conclusions. They interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

Explain your answer

33. What is the solution to the equation ?

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 7th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 7th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Expressions and Equations (EE) 7.EE.A.1: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients

Explain your answer

34. What situation could the graph best represent?

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 7th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 7th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Mathematics Practice 7.MP.2 Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. Students can contextualize and decontextualize problems involving quantitative relationships. They contextualize quantities, operations, and expressions by describing a corresponding situation. They decontextualize a situation by representing it symbolically. As they manipulate the symbols, they can pause as needed to access the meaning of the numbers, the units, and the operations that the symbols represent. Mathematically proficient students know and flexibly use different properties of operations, numbers, and geometric objects and when appropriate they interpret their solution in terms of the context.

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