MathEval 6th Grade

1. 237 + 485

2. 1425 - 567

3. 32 × 25

4. 1248 ÷ 12

5. 346 + 99

6. 2500 - 1750

1. 3578 + 6429

2. 9002 - 3567

3. 807 × 36

4. 3696 ÷ 14

1. Simplify the following fraction: $\frac{36}{48}$

2. Calculate: $\frac{2}{5} + \frac{1}{3}$

3. Calculate: $\frac{3}{4} - \frac{1}{6}$

4. Calculate: $\frac{2}{3} \times \frac{3}{5}$

1. 14.8 + 7.95

2. 35.7 - 12.85

3. 3.6 × 4.5

4. 17.5 ÷ 2.5

1. $2^4$

2. $5^3$

3. $10^2 \times 10^3$

4. $2^3 \times 2^2$

1. A bookstore received a delivery of 450 books. The owner sold 128 in the first week and 175 in the second week. How many books remain after these two weeks?

2. In a class of 30 students, 40% play soccer and 25% play basketball. If 5 students play both sports, how many students don't play either of these sports?

3. A faucet fills a basin in 45 minutes. A second faucet can fill it in 30 minutes. How long will it take to fill the basin if both faucets are running together?

1. A car uses 7 liters of fuel to travel 100 km. How many liters of fuel are needed to travel 350 km?

2. To make a vinaigrette dressing for 6 people, you need 9 tablespoons of oil and 3 tablespoons of vinegar. How many tablespoons of oil and vinegar are needed for 10 people?

3. On a map with a scale of 1:25000, two towns are 12 cm apart. What is the actual distance between these two towns in kilometers?

1. A merchant buys 25 items at $18 each. He wants to make a total profit of $135. At what price should he sell each item?

2. A cyclist travels a route at an average speed of 20 km/h. On the return journey, being tired, he cycles at only 10 km/h. What is his average speed for the entire journey?

3. In an amusement park, the entrance ticket costs $15 for adults and $10 for children. A group of 20 people paid a total of $260. How many adults and children are in this group?

1. A rectangle has a length of 12 cm and a width of 7.5 cm. Calculate its perimeter and area.

2. A square has a side of 8.5 cm. Calculate its perimeter and area.

3. A triangle has a base of 9 cm and a corresponding height of 6 cm. Calculate its area.

4. A circle has a radius of 5 cm. Calculate its perimeter (circumference) and area. Use π ≈ 3.14.

1. In a triangle, the sum of the angles equals how many degrees?

2. In a quadrilateral, the sum of the angles equals how many degrees?

3. An angle inscribed in a semicircle measures how many degrees?

4. A triangle has two angles measuring 45° and 60°. What is the measure of the third angle?

1. A rectangular prism has a length of 10 cm, a width of 6 cm, and a height of 4 cm. Calculate its volume and total surface area.

2. A cube has an edge of 7 cm. Calculate its volume and total surface area.

3. A cylinder has a base radius of 3 cm and a height of 8 cm. Calculate its volume. Use π ≈ 3.14.

1. In a right triangle, the two sides of the right angle measure 6 cm and 8 cm. Calculate the length of the hypotenuse.

2. In a right triangle, the hypotenuse measures 13 cm and one of the sides measures 5 cm. Calculate the length of the third side.

3. A ladder forms a right triangle with the ground. The foot of the ladder is 1.5 m from the wall and the top of the ladder touches the wall at a height of 2 m. What is the length of the ladder?

1. Here are the scores obtained by the students in a class on a test: 8, 12, 15, 10, 14, 9, 13, 7, 11, 15, 16, 10, 13, 12, 9, 14, 11, 8, 10, 13. Calculate the mean, median, and range of this statistical series.

2. The following table represents the distribution of students in a middle school by grade level:\n\nGrade | 6th | 7th | 8th | 9th\nNumber of students | 125 | 130 | 115 | 120\n\nRepresent this data with a bar graph and calculate the percentage of 7th grade students.

Draw the bar graph here.

3. The following pie chart represents the distribution of time a student spends on different activities:\n- Classes: 35%\n- Homework: 15%\n- Leisure: 25%\n- Sleep: 25%\n\nIf a day has 24 hours, calculate the time spent in hours for each activity.

1. In a store, an item costs $80. During a sale, its price is reduced by 25%. What is the new price of the item?

2. The price of a bicycle increased from $200 to $240. What is the percentage increase?

3. An item costs $50 excluding tax. If the sales tax is 20%, what is the price including tax?

1. On a map with a scale of 1:50000, two towns are 6 cm apart. What is the actual distance in kilometers?

2. On a floor plan with a scale of 1:200, a room measures 3.5 cm by 4 cm. What are the actual dimensions of this room in meters?

3. The actual distance between two villages is 15 km. On a map, they are 6 cm apart. What is the scale of the map?

1. Alice, Benjamin, and Clara are three friends whose ages are 12, 13, and 14, but not necessarily in that order. We know that:\n- Alice is younger than Clara.\n- Benjamin is not the oldest of the three.\nWhat are the respective ages of Alice, Benjamin, and Clara?

2. In a race, Paul finishes after Jacques but before Pierre. Antoine finishes after Pierre. Mathieu finishes before Jacques. What is the order of finish for the five runners?

3. A teacher has distributed a test. Students with a score greater than or equal to 12 receive an A, those with a score between 8 inclusive and 12 exclusive receive a B, and the others receive a C. In a class of 30 students, 10 received an A, 14 received a B, and the rest received a C. What is the average score of the class if the average for students with an A is 15, the average for students with a B is 10, and the average for students with a C is 6?

1. Complete this sequence: 3, 7, 11, 15, ..., ...

2. Complete this sequence: 2, 6, 18, 54, ..., ...

3. Complete this sequence: 1, 1, 2, 3, 5, 8, ..., ...

4. What is the rule that generates the following sequence? 1, 4, 9, 16, 25, ...

1. A snail is climbing a 12-meter wall. During the day, it climbs up 4 meters, but each night, it slides down 1 meter. How many days will it take for the snail to reach the top of the wall?

2. Five friends shake hands. How many handshakes are exchanged in total (knowing that each pair of friends shakes hands only once)?

3. A woodcutter cuts a tree trunk into 8 pieces. Each cut takes 1 minute. How long does it take to cut the entire trunk?