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6th Grade Math AI Tutor
Mastering 34 Basic Math
Explain your answer
1. What represents a 2/3 ratio?
SOURCE: Arizona Department of Education, Arizona Mathematics Standards 6th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 6th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Ratio and Proportion (RP) 6.RP.A.3.c Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity
means 30/100 times the quantity). Solve percent problems with the
unknown in all positions of the equation.
.
Select your test reviewer question
Type the number
Try again if the selected number did not show up because some devices have slow respond time.
Explain your answer
2. The cube shown has a volume of 125 cm3. What is the area of the base of the cube?
SOURCE: Arizona Department of Education, Arizona Mathematics Standards 6th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 6th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Geometry (G) 6.G.A.2: Find the volume of a right rectangular prism with fractional edge
lengths by packing it with unit cubes of the appropriate unit fraction
edge lengths, and show that the volume is the same as would be
found by multiplying the edge lengths of the prism. Understand
and use the formula V = B · h, where in this case, B is the area of
the base (B = l x w) to find volumes of right rectangular prisms with
fractional edge lengths in mathematical problems and problems in
real-world context.
Explain your answer
3. There are 3 classes of 22 students making ice cream sundaes. A sundae can be made using one of 3 syrups and one of 3 candy toppings. Each student makes one sundae. Which expression can be used to find the total number of sundaes made by the students.
SOURCE: Arizona Department of Education, Arizona Mathematics Standards 6th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 6th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Expressions and Equations (EE) 6.EE.A.2.a: Write expressions that record operations with numbers and variables.
Explain your answer
4. What is the absolute value of the coordinate of the point shown on the number line?
SOURCE: Arizona Department of Education, Arizona Mathematics Standards 6th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 6th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for The Number System (NS) 6.NS.C.7.c: Understand the absolute value of a rational number as its distance
from 0 on the number line; interpret absolute value as magnitude
for a positive or negative quantity in real-world context.
Explain your answer
5. What is the value of the expression 2 + 7(3.8 - 1.4) = ?
SOURCE: Arizona Department of Education, Arizona Mathematics Standards 6th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 6th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Expressions and Equations (EE) 6.EE.A.1: Write and evaluate numerical expressions involving whole-number
exponents.
Explain your answer
6. What is equal to 3√27 ? What is equal to square root of 27?
SOURCE: Arizona Department of Education, Arizona Mathematics Standards 6th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 6th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Expressions and Equations (EE) 6.EE.A.1: Write and evaluate numerical expressions involving whole-number
exponents.
Explain your answer
7. Each stem-and-leaf plot shows the number of points scored by a team in basketball tournament. How many total scores are represented by all stem-and-leaf plots?
SOURCE: Arizona Department of Education, Arizona Mathematics Standards 6th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 6th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Statistics and Probability (SP) 6.SP.B.4: Display and interpret numerical data by creating plots on number line, including histograms, dot plots or scatter plot, stem and leaf plot, and box plots.
Explain your answer
8. Each stem-and-leaf plot shows the number of points scored by a team in basketball tournament. What is the greatest number of points scored by any team in one game?
SOURCE: Arizona Department of Education, Arizona Mathematics Standards 6th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 6th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Statistics and Probability (SP) 6.SP.B.4: Display and interpret numerical data by creating plots on number line, including histograms, dot plots or scatter plot, stem and leaf plot, and box plots.
Explain your answer
9. What are the possible outcomes (sample space) of the spinner?
SOURCE: Arizona Department of Education, Arizona Mathematics Standards 6th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 6th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Statistics and Probability (SP) 6.SP.B.5.a: Reporting the number of observations also called possible outcomes
or solution space.
Explain your answer
10. Look at the sequence. 15, 3, 0.6, 0.12, ... What is the next number in the sequence?
SOURCE: Arizona Department of Education, Arizona Mathematics Standards 6th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 6th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for The Number System (NS) 6.NS.A.1: Interpret and compute quotients of fractions to solve mathematical
problems and problems in real-world context involving division of
fractions by fractions using visual fraction models and equations to
represent the problem. For example, create a story context for 2/3
÷ 3/4 and use a visual fraction model to show the quotient; use the
relationship between multiplication and division to explain that 2/3
÷ 3/4 = 8/9 because 3/4 of 8/9 is 2/3. In general, a/b ÷ c/d = ad/bc
Explain your answer
11. Look at the equation 2 n + 1.4 = 8.6 Which inverse operations will solve the equation?
SOURCE: Arizona Department of Education, Arizona Mathematics Standards 6th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 6th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Expressions and Equations (EE) 6.EE.A.3 Apply the properties of operations to generate equivalent
expressions. For example, apply the distributive property to the
expression 3 (2 + x) to produce the equivalent expression 6 + 3x.
Explain your answer
12. Look at the expression. 6 n + 3 What is the value of the expression when n = 2/3 ?
SOURCE: Arizona Department of Education, Arizona Mathematics Standards 6th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 6th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Expressions and Equations (EE) 6.EE.A.2.c: Evaluate expressions given specific values of their variables. Include
expressions that arise from formulas used to solve mathematical
problems and problems in real-world context. Perform arithmetic
operations, including those involving whole-number exponents, in
the conventional order when there are no parentheses to specify a
particular order (Order of Operations).
Explain your answer
13. What is the total area of the figure?
SOURCE: Arizona Department of Education, Arizona Mathematics Standards 6th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 6th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Geometry (G) 6.G.A.1: Find the area of right triangles, other triangles, special
quadrilaterals, and polygons by composing into rectangles or
decomposing into triangles and other shapes; apply these
techniques to solve mathematical problems and problems in real
world context.
Explain your answer
14. What is the value of the expression 6 / 7 ÷ 3 / 4 = ?
SOURCE: Arizona Department of Education, Arizona Mathematics Standards 6th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 6th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Expressions and Equations (EE) 6.EE.A.1: Write and evaluate numerical expressions involving whole-number
exponents.
Explain your answer
15. Look at points J and K on the number line. Which expression represents the distance between points J and K on the number line?
SOURCE: Arizona Department of Education, Arizona Mathematics Standards 6th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 6th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for The Number System (NS) 6.NS.C.6 Understand a rational number can be represented as a point on
the number line. Extend number line diagrams and coordinate
axes familiar from previous grades to represent points on the line
and in the plane with negative number coordinates.
Explain your answer
16. Kara plans to carpet the entire floor in each of the two rooms shown below. What is the best estimate of the total amount of carpet, in square feet, needed to completely cover both floors?
SOURCE: Arizona Department of Education, Arizona Mathematics Standards 6th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 6th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Geometry (G) 6.G.A.1: Find the area of right triangles, other triangles, special
quadrilaterals, and polygons by composing into rectangles or
decomposing into triangles and other shapes; apply these
techniques to solve mathematical problems and problems in real
world context.
Explain your answer
17. What is the measure, in degrees, of the angle that is complementary to ∠ RVS?
SOURCE: Arizona Department of Education, Arizona Mathematics Standards 6th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 6th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Mathematics Practice 6.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
18. Which diagram represents the prime factorization of 36?
SOURCE: Arizona Department of Education, Arizona Mathematics Standards 6th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 6th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Mathematics Practice 6.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
19. What are the coordinates of the missing vertex of the parallelogram below?
SOURCE: Arizona Department of Education, Arizona Mathematics Standards 6th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 6th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Geometry (G) 6.G.A.3: Draw polygons in the coordinate plane given coordinates for the
vertices; use coordinates to find the length of a side joining points
with the same first coordinate or the same second coordinate.
Apply these techniques to solve mathematical problems and
problems in a real-world context.
Explain your answer
20. Vincent's baseball coach suggested that he drink one-half gallon of water daily. If Vincent drinks one-half gallon of water, how many 8-ounce glasses will he drink?
SOURCE: Arizona Department of Education, Arizona Mathematics Standards 6th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 6th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Ratio and Proportion (RP) 6.RP.A.3.d Use ratio reasoning to convert measurement units; manipulate and
transform units appropriately when multiplying or dividing
quantities.
Explain your answer
21. On the grid below, points Q, R, and S represent three vertices of a rectangle. What are the coordinates of point T, the vertex that will complete rectangle QRST?
SOURCE: Arizona Department of Education, Arizona Mathematics Standards 6th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 6th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Geometry (G) 6.G.A.3: Draw polygons in the coordinate plane given coordinates for the
vertices; use coordinates to find the length of a side joining points
with the same first coordinate or the same second coordinate.
Apply these techniques to solve mathematical problems and
problems in a real-world context.
Explain your answer
22. Which expression is the same as 11%?
SOURCE: Arizona Department of Education, Arizona Mathematics Standards 6th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 6th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Ratio and Proportion (RP) 6.RP.A.3.c Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity
means 30/100 times the quantity). Solve percent problems with the
unknown in all positions of the equation.
Explain your answer
23. Rafael performed an experiment by spinning the arrow on a spinner 200 times. His results are recorded in the table below.
Which is closest to the number of times he should expect the arrow to land on red section?
SOURCE: Arizona Department of Education, Arizona Mathematics Standards 6th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 6th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Statistics and Probability (SP) 6.SP.A.2: Understand that a set of data collected to answer a statistical
question has a distribution whose general characteristics can be
described by its center, spread, and overall shape.
Explain your answer
24. Randy has $7.50 to use on buying notebooks for school. If each notebook costs $1.09 including tax, how many can Randy buy?
SOURCE: Arizona Department of Education, Arizona Mathematics Standards 6th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 6th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Expressions and Equations (EE) 6.EE.C.9: Use variables to represent two quantities that change in
relationship to one another to solve mathematical problems and
problems in real-world context. Write an equation to express one
quantity (the dependent variable) in terms of the other quantity
(the independent variable). Analyze the relationship between the
dependent and independent variables using graphs and tables,
and relate these to the equation.
Explain your answer
25. The scatter plot shows the relationship between the amount of time Casey was at the mall and the amount of money she spent there. Which statement best describes the relationship between the amount of money Casey spent and the amount of time she was at the mall?
SOURCE: Arizona Department of Education, Arizona Mathematics Standards 6th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 6th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Statistics and Probability (SP) 6.SP.B.4: Display and interpret numerical data by creating plots on number line, including histograms, dot plots or scatter plot, stem and leaf plot, and box plots.
Explain your answer
26. Which expression matches the model shown?
SOURCE: Arizona Department of Education, Arizona Mathematics Standards 6th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 6th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Expressions and Equations (EE) 6.EE.A.2.a: Write expressions that record operations with numbers and variables.
Explain your answer
27. Lauren wants to put a brick border around her garden. A drawing of her garden is represented by the shaded section on the grid below. What is closest to the number of meters of brick border Lauren will need to put around her garden?
SOURCE: Arizona Department of Education, Arizona Mathematics Standards 6th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 6th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Geometry (G) 6.G.A.1: Find the area of right triangles, other triangles, special
quadrilaterals, and polygons by composing into rectangles or
decomposing into triangles and other shapes; apply these
techniques to solve mathematical problems and problems in real
world context.
Explain your answer
28. Look at the table of values. Which equation represents the relationship between x and y?
SOURCE: Arizona Department of Education, Arizona Mathematics Standards 6th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 6th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Expressions and Equations (EE) 6.EE.B.5: Understand solving an equation or inequality as a process of
reasoning to find the value(s) of the variables that make that
equation or inequality true. Use substitution to determine whether
a given number in a specified set makes an equation or inequality
true.
Explain your answer
29. Valerie has 35 students in her art class. She asked each student what types of activities they like to do and made a Venn diagram of the results. How many students in Valerie's class told her that they only like to draw and sculpt?
SOURCE: Arizona Department of Education, Arizona Mathematics Standards 6th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 6th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Mathematics Practice 6.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
30. Jim and Don are playing darts. Jim has scored 16, 12, and 2 points. Don's turn is after Jim's. Don has scored 12, 10, and 2 points. They have taken the same number of turns. Who is ahead at this time? Which statement does Kelly need for solving the problem?
SOURCE: Arizona Department of Education, Arizona Mathematics Standards 6th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 6th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Mathematics Practice 6.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
31. Look at the graph. If the water continues to drip at the same rate, how many milliliters of water will have dripped at 14 hours?
SOURCE: Arizona Department of Education, Arizona Mathematics Standards 6th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 6th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Expressions and Equations (EE) 6.EE.C.9: Use variables to represent two quantities that change in
relationship to one another to solve mathematical problems and
problems in real-world context. Write an equation to express one
quantity (the dependent variable) in terms of the other quantity
(the independent variable). Analyze the relationship between the
dependent and independent variables using graphs and tables,
and relate these to the equation.
Explain your answer
32. Which statements explains how to find the area of the figure below?
SOURCE: Arizona Department of Education, Arizona Mathematics Standards 6th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 6th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Geometry (G) 6.G.A.1: Find the area of right triangles, other triangles, special
quadrilaterals, and polygons by composing into rectangles or
decomposing into triangles and other shapes; apply these
techniques to solve mathematical problems and problems in real
world context.
Explain your answer
33. Which graph shows a reflection of the rectangle across the horizontal dotted line?
SOURCE: Arizona Department of Education, Arizona Mathematics Standards 6th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 6th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Mathematics Practice 6.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
34. Scott delivers the 6th grade newsletter to five rooms at his school. He must find the quickest route. The vertex-edge graph shows the rooms that Scott must deliver to and the time, in seconds, it takes him to get from room to room. If Scott begins and ends at his Homeroom, what is the quickest route for him to take and to make sure he visits each room only once?
SOURCE: Arizona Department of Education, Arizona Mathematics Standards 6th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 6th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Mathematics Practice 6.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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