6th Std Maths Quarterly Exam 2024 - Solutions
I Choose the correct answer. (10 X 1 = 10)
1. 1 billion is equal to
Explanation: 1 billion = 1,000,000,000. 1 crore = 1,00,00,000. Therefore, 1 billion = 100 x 1,00,00,000 = 100 crore.
2. The estimation to the nearest hundred of 76812 is
Explanation: To round to the nearest hundred, we look at the tens digit. In 76812, the tens digit is 1. Since 1 is less than 5, we keep the hundreds digit (8) as it is and change the tens and ones digits to zero. So, the estimated number is 76800.
3. Which of the following expressions is not zero?
Explanation: Division by zero is undefined, not zero. 0 X 0 = 0, 0 + 0 = 0, and 0 / 2 = 0.
4. The number of days in 'w' weeks is
Explanation: There are 7 days in one week. So, in 'w' weeks, the number of days is 7 multiplied by w, which is 7w.
5. The ratio of the number of sides of a triangle to the number of sides of a rectangle is
Explanation: A triangle has 3 sides. A rectangle has 4 sides. The ratio is 3 to 4, written as 3:4.
6. An equivalent ratio of 4 : 7 is
Explanation: To find an equivalent ratio, multiply both parts of the ratio by the same non-zero number. 4 x 3 = 12 and 7 x 3 = 21. So, 4:7 is equivalent to 12:21.
7. If a barbie doll costs Rs. 90, then the cost of 3 such dolls is Rs.
Explanation: Cost of 1 doll = Rs. 90. Cost of 3 dolls = 3 x 90 = Rs. 270.
8. A line is denoted as
Explanation: A line extends indefinitely in both directions, which is denoted by a double-headed arrow over the letters representing two points on the line.
9. The tally marks for the number 7 in standard form is
Explanation: Tally marks are grouped in fives. The number 7 is represented as a group of five (||||) and two additional marks (||).
10. The representation of "one picture to many objects" in a pictograph is called
Explanation: In a pictograph, scaling is the key used to define how many objects each picture represents (e.g., 1 car picture = 100 cars).
II Fill in the blanks. (5 X 1 = 5)
11. The largest 8 digit number is ____________.
12. The algebraic statement of 'S divided by 5' is ____________.
13. Ratio of 75 paise to Rs. 2 = ____________.
Explanation: Convert Rs. 2 to paise: Rs. 2 = 200 paise. The ratio is 75 : 200. Dividing both by their greatest common divisor (25), we get 3 : 8.
14. A line through two end points 'A' and 'B' is denoted by ____________.
15. The tally marks for number 8 in standard form is ____________.
III True (or) False. (5 X 1 = 5)
16. Successor of a one digit number is always a one digit number.
Explanation: The successor of 9 (a one-digit number) is 10 (a two-digit number).
17. Both addition and multiplication are associative for whole numbers.
Explanation: The associative property (a + b) + c = a + (b + c) and (a × b) × c = a × (b × c) holds for whole numbers.
18. The product of 'q' and 20 is '20q'.
19. The ratio of 130cm to 1m is 13 : 10.
Explanation: 1m = 100cm. The ratio is 130cm : 100cm. Dividing by 10, we get 13 : 10.
20. 20° and 70° are complementary.
Explanation: Complementary angles are two angles that add up to 90°. 20° + 70° = 90°.
IV Answer any 10 of the following. (10 X 2 = 20)
21. How many thousands are there in 1 lakh?
1 lakh = 1,00,000
1 thousand = 1,000
Number of thousands in 1 lakh = 1,00,000 / 1,000 = 100.
There are 100 thousands in 1 lakh.22. Use the properties of whole numbers and simplify: 50 X 102.
Using the distributive property of multiplication over addition:
50 x 102 = 50 x (100 + 2)
= (50 x 100) + (50 x 2)
= 5000 + 100
= 5100
Answer: 510023. Arivazhagan is 30 years younger to his father. Write Arivazhagan's age in terms of his father's age.
Let the father's age be 'f' years.
Since Arivazhagan is 30 years younger, his age is the father's age minus 30.
Arivazhagan's age = f - 3024. Find the simplified form of the following ratio 15 : 20.
To simplify the ratio 15 : 20, we find the greatest common divisor (GCD) of 15 and 20, which is 5.
Divide both parts of the ratio by 5:
15 ÷ 5 = 3
20 ÷ 5 = 4
The simplified form is 3 : 4.25. Which of the two ratios is larger? 4 : 5 or 8 : 15.
To compare the ratios, we can convert them to fractions: 4/5 and 8/15.
Find a common denominator, which is 15.
4/5 = (4 x 3) / (5 x 3) = 12/15
Now compare 12/15 and 8/15. Since 12 > 8, 12/15 is larger.
Therefore, the ratio 4 : 5 is larger.26. Fill in the box: 3 : 5 :: [ ] : 20.
Let the missing number be x. The proportion is 3/5 = x/20.
To get from 5 to 20, we multiply by 4.
So, we multiply the numerator by 4 as well: x = 3 x 4 = 12.
The missing number is 12.27. Find the complementary angle of a) 30° b) 26°
Complementary angles add up to 90°.
a) Complement of 30° = 90° - 30° = 60°
b) Complement of 26° = 90° - 26° = 64°
28. Draw any 3 lines to have a point of concurrency.
To draw three concurrent lines:
- Draw a single point on the paper and label it 'O'.
- Draw a straight line that passes through point O.
- Draw a second straight line that also passes through point O.
- Draw a third straight line that also passes through point O.
All three lines intersect at the same single point P, which is the point of concurrency.
29. How many triangles are there in the given figure.
The figure shows a large triangle with its interior divided by connecting the midpoints of its sides. This creates 4 smaller triangles inside and 1 large outer triangle.
- The top small triangle.
- The bottom-left small triangle.
- The bottom-right small triangle.
- The central inverted small triangle.
- The large outer triangle itself.
Total number of triangles = 5.
30. Define: "Ray".
Ray: A ray is a part of a line that has one fixed starting point (called an endpoint) and extends infinitely in one direction.
31. Name the following angles as shown in the figure. i) ∠1 = ? ii) ∠2 = ?
Based on the typical labeling in the figure provided:
i) ∠1 = ∠DBC (or ∠CBD)
ii) ∠2 = ∠EBD (or ∠DBE)
V Answer any 5 of the following. (5 X 3 = 15)
32. Arrange the following numbers in the descending order : 128435, 10835, 21354, 6348, 25840.
Descending order means arranging numbers from the largest to the smallest.
- 128435 (the only 6-digit number)
- 25840 (largest of the 5-digit numbers)
- 21354
- 10835
- 6348 (the only 4-digit number)
33. The number of people who visited the public library for the past 5 months were 1000, 2000, 2450, 3060 and 3200 respectively. How many people visited the library in the last 5 months.
To find the total number of visitors, we add the numbers for each month:
Total visitors = 1000 + 2000 + 2450 + 3060 + 3200
1000 + 2000 = 3000
3000 + 2450 = 5450
5450 + 3060 = 8510
8510 + 3200 = 11710
A total of 11,710 people visited the library in the last 5 months.34. What is the value of 'S' if '2S - 6' gives 30?
We are given the equation: 2S - 6 = 30
Step 1: Add 6 to both sides of the equation.
2S - 6 + 6 = 30 + 6
2S = 36
Step 2: Divide both sides by 2.
S = 36 / 2
S = 18
The value of S is 18.35. The cost of parking a bicycle is Rs. 5 and the cost of parking a scooter is Rs. 15. Find the simplest ratio of the parking cost of the a bicycle to that of a scooter.
Cost of parking a bicycle = Rs. 5
Cost of parking a scooter = Rs. 15
The ratio of the cost of parking a bicycle to a scooter is 5 : 15.
To simplify, divide both numbers by their greatest common divisor, which is 5.
5 ÷ 5 = 1
15 ÷ 5 = 3
The simplest ratio is 1 : 3.36. A line segment 63cm long is to be divided into two parts in the ratio 3 : 4. Find the length of each part.
Total length = 63 cm
Ratio = 3 : 4
Sum of the ratio parts = 3 + 4 = 7
This means the line segment is divided into 7 equal parts.
Length of one part = 63 cm / 7 = 9 cm
Length of the first part (3 parts) = 3 x 9 cm = 27 cm
Length of the second part (4 parts) = 4 x 9 cm = 36 cm
The lengths of the two parts are 27 cm and 36 cm.37. Draw a pictograph for the given data.
| Month | June | July | August | September |
|---|---|---|---|---|
| Number of Computers sold | 300 | 450 | 600 | 550 |
Pictograph: Computers Sold Last 4 Months
Scale: Each 💻 symbol represents 100 computers.
| Month | Number of Computers (Pictorial) |
|---|---|
| June | 💻 💻 💻 |
| July | 💻 💻 💻 💻 (and a half symbol) |
| August | 💻 💻 💻 💻 💻 💻 |
| September | 💻 💻 💻 💻 💻 (and a half symbol) |
VI Answer any one of the following. (1 X 5 = 5)
38. Construct a line segment using ruler and compass AB = 7.5cm. (OR)
Steps for Construction:
- Draw a line and mark a point 'A' on it.
- Place the metal tip of the compass on the '0' mark of the ruler.
- Extend the pencil tip of the compass to the 7.5 cm mark on the ruler.
- Without changing the compass width, place the metal tip on point 'A'.
- Draw a small arc on the line to cut it at a point. Mark this point as 'B'.
- The line segment AB is the required segment of length 7.5 cm.
39. Draw the following angle using the protractor ∠NAS = 90°.
Steps for Construction:
- Draw a ray AS. This will form one side of the angle.
- Place the center of the protractor on the vertex 'A'.
- Align the base line of the protractor with the ray AS.
- Look for the 90° mark on the protractor scale and make a small dot. Label this point 'N'.
- Remove the protractor.
- Draw a ray from the vertex 'A' through the point 'N'.
- The resulting angle, ∠NAS, is the required 90° angle.
