6th Maths - Term 1 Exam 2024 - Original Question Paper with Solutions
Standard: 6
Subject: Maths
Assessment: Summative Assessment - September 2024
Marks: 60
Time: 2.00 Hrs
I. Choose the best answer: 5 x 1 = 5
The value of 3+5-7×1 is ______.
Answer: d) 1
Explanation: Using BODMAS, multiplication first: 7×1 = 7. Then 3+5-7 = 8-7 = 1.
Explanation: Using BODMAS, multiplication first: 7×1 = 7. Then 3+5-7 = 8-7 = 1.
Variable means that it ______.
Answer: c) can take different values
If 7:5 is in proportion to x:25, then 'x' is ______.
Answer: c) 35
Explanation: 7/5 = x/25. So, x = (7 × 25) / 5 = 7 × 5 = 35.
Explanation: 7/5 = x/25. So, x = (7 × 25) / 5 = 7 × 5 = 35.
A line is denoted as ______.
Answer: c) A↔B (A line extends infinitely in both directions)
A pictograph is also known as ______.
Answer: b) Pictogram
II. Fill in the blanks: 5 x 1 = 5
Multiplication by ______ leaves a number unchanged.
Answer: 1
If 'P-5' gives 12 then 'P' is ______.
Answer: 17 (Since P = 12 + 5)
Ratio of 75 paise to ₹ 2 = ______.
Answer: 3:8 (75 paise : 200 paise)
A ray has ______ end points.
Answer: one
The collected information is called ______.
Answer: Data
III. Say True / False: 5 x 1 = 5
Successor of a one digit number is always a one digit number.
False (Successor of 9 is 10, which is a two-digit number).
If the cost of 10 rice bags is 't', then the cost of 1 rice bag is t⁄10.
True
If the weight of 40 books is 8 kg, then the weight of 15 books is 3 kg.
True (Weight of 1 book = 8/40 = 0.2 kg. Weight of 15 books = 15 × 0.2 = 3 kg).
88° and 12° are complementary.
False (They sum to 100°. Complementary angles sum to 90°).
The spaces between any two bars in a bar graph are the same.
True
IV. Match it: 5 x 1 = 5
| Question | Given Answer Options | Correct Match |
|---|---|---|
| 16) The whole number that does not have a predecessor is | 5:4 | 0 |
| 17) The value of 'y' in y+7 = 13 is | 9 | 6 |
| 18) Simplify the ratio 25:20 | 60° | 5:4 |
| 19) Find the complementary angle of 30° is | 6 | 60° |
| 20) The tally marks 卌 |||| represents the number count | 0 | 9 |
V. Answer any SIX questions: 6 x 2 = 12
How many thousands are there in 1 million?
1 Million = 10,00,000
1 Thousand = 1,000
Number of thousands = 10,00,000 / 1,000 = 1000.
There are 1000 thousands in 1 million.
1 Thousand = 1,000
Number of thousands = 10,00,000 / 1,000 = 1000.
There are 1000 thousands in 1 million.
Cheran had a bank savings of ₹ 7,50,250. He withdrew ₹ 5,34,500 for educational purpose. Find the balance amount in his account.
Initial Savings = ₹ 7,50,250
Amount Withdrawn = ₹ 5,34,500
Balance Amount = 7,50,250 - 5,34,500 = ₹ 2,15,750.
The balance amount is ₹ 2,15,750.
Amount Withdrawn = ₹ 5,34,500
Balance Amount = 7,50,250 - 5,34,500 = ₹ 2,15,750.
The balance amount is ₹ 2,15,750.
Name the property being illustrated in each of the cases given below:
i) 75+34 = 34+75
ii) 50×1 = 50
i) 75+34 = 34+75
ii) 50×1 = 50
i) Commutative property of addition.
ii) Multiplicative identity.
ii) Multiplicative identity.
If 'u' is an even number, how would you represent (i) the next even number? (ii) the previous even number?
Given 'u' is an even number.
(i) The next even number is u + 2.
(ii) The previous even number is u - 2.
(i) The next even number is u + 2.
(ii) The previous even number is u - 2.
Converting Algebraic statements to verbal statements:
(i) x+6
(ii) 2p-5
(i) x+6
(ii) 2p-5
(i) x+6: "6 added to x" or "The sum of x and 6".
(ii) 2p-5: "5 subtracted from twice p" or "5 less than 2 times p".
(ii) 2p-5: "5 subtracted from twice p" or "5 less than 2 times p".
What is the ratio of 40 minutes to 1 hour?
1 hour = 60 minutes.
Ratio = 40 minutes : 60 minutes
Simplifying by dividing by 20: 2:3.
Ratio = 40 minutes : 60 minutes
Simplifying by dividing by 20: 2:3.
By proportionality law, check whether 3:2 and 30:20 are in proportion.
For a:b and c:d to be in proportion, the product of extremes (ad) must equal the product of means (bc).
Here, a=3, b=2, c=30, d=20.
Product of extremes = a × d = 3 × 20 = 60.
Product of means = b × c = 2 × 30 = 60.
Since 60 = 60, they are in proportion.
Here, a=3, b=2, c=30, d=20.
Product of extremes = a × d = 3 × 20 = 60.
Product of means = b × c = 2 × 30 = 60.
Since 60 = 60, they are in proportion.
Find the supplementary angle of 35°.
Supplementary angles add up to 180°.
Supplementary angle of 35° = 180° - 35° = 145°.
Supplementary angle of 35° = 180° - 35° = 145°.
VI. Answer any SIX questions: 6 x 3 = 18
How many Triangles are there in each of the following figures?
(i) The first figure (2x2 grid with diagonals) has 16 triangles.
(ii) The second figure (triangle with 3 levels) has 13 triangles.
(ii) The second figure (triangle with 3 levels) has 13 triangles.
If ₹ 10,00,000 was distributed in a Government scheme to 500 women in the self help groups, then find the amount given to each woman.
Total Amount = ₹ 10,00,000
Number of women = 500
Amount per woman = Total Amount / Number of women
= 10,00,000 / 500 = 10,000 / 5 = 2,000.
Each woman received ₹ 2,000.
Number of women = 500
Amount per woman = Total Amount / Number of women
= 10,00,000 / 500 = 10,000 / 5 = 2,000.
Each woman received ₹ 2,000.
Simplify: 100+8÷2+{(3×2)-6}÷2
Using BODMAS/BIDMAS rule:
1. Innermost Brackets: (3 × 2) = 6
2. Braces: {6 - 6} = 0
3. Division: 8 ÷ 2 = 4 and 0 ÷ 2 = 0
4. Addition: 100 + 4 + 0 = 104.
1. Innermost Brackets: (3 × 2) = 6
2. Braces: {6 - 6} = 0
3. Division: 8 ÷ 2 = 4 and 0 ÷ 2 = 0
4. Addition: 100 + 4 + 0 = 104.
Athiyan and Mugilan are brothers. Athiyan is 'p' years old and Mugilan is elder to Athiyan by 6 years. Write an algebraic statement for this and find the age of Mugilan if Athiyan is 20 years old.
Athiyan's age = p
Mugilan is 6 years elder, so Mugilan's age = p + 6 (This is the algebraic statement).
If Athiyan's age p = 20, then Mugilan's age = 20 + 6 = 26 years old.
Mugilan is 6 years elder, so Mugilan's age = p + 6 (This is the algebraic statement).
If Athiyan's age p = 20, then Mugilan's age = 20 + 6 = 26 years old.
Complete the table and find the value of 'K' for which K/3 gives 5.
To find K when K/3 = 5, we calculate K = 3 × 5 = 15.
The completed table is:
The completed table is:
| K | 3 | 6 | 9 | 12 | 15 | 18 |
|---|---|---|---|---|---|---|
| K/3 | 1 | 2 | 3 | 4 | 5 | 6 |
Out of 50 students in a class, 30 are boys. Find the ratio of
i) number of boys to the number of girls.
ii) number of girls to the total number of students.
iii) number of boys to the total number of students.
i) number of boys to the number of girls.
ii) number of girls to the total number of students.
iii) number of boys to the total number of students.
Total students = 50
Number of boys = 30
Number of girls = 50 - 30 = 20
i) Ratio of boys to girls = 30 : 20 = 3 : 2
ii) Ratio of girls to total students = 20 : 50 = 2 : 5
iii) Ratio of boys to total students = 30 : 50 = 3 : 5
Number of boys = 30
Number of girls = 50 - 30 = 20
i) Ratio of boys to girls = 30 : 20 = 3 : 2
ii) Ratio of girls to total students = 20 : 50 = 2 : 5
iii) Ratio of boys to total students = 30 : 50 = 3 : 5
A heater uses 3 units of electricity in 40 minutes. How many units does it consume in 2 hours?
2 hours = 2 × 60 = 120 minutes.
In 40 minutes, it uses 3 units.
In 120 minutes, it uses (120 / 40) × 3 units = 3 × 3 = 9 units.
In 40 minutes, it uses 3 units.
In 120 minutes, it uses (120 / 40) × 3 units = 3 × 3 = 9 units.
From the given figure, name the (i) parallel lines (ii) intersecting lines (iii) points of intersection
Based on the visual representation:
(i) Parallel lines: Lines CD, EF and IJ.
(ii) Intersecting lines: Line AB intersects lines CD, EF, GH, and IJ..
(iii) Points of intersection: P, Q, R
(i) Parallel lines: Lines CD, EF and IJ.
(ii) Intersecting lines: Line AB intersects lines CD, EF, GH, and IJ..
(iii) Points of intersection: P, Q, R
Viji threw a die 30 times and noted down the result each time as follows. Prepare a table on the numbers shown using Tally marks.
1 4 3 5 5 6 6 4 3 5 4 5 6 5 2 4 2 6 5 5 6 6 4 5 6 6 5 4 1 1
1 4 3 5 5 6 6 4 3 5 4 5 6 5 2 4 2 6 5 5 6 6 4 5 6 6 5 4 1 1
| Number | Tally Marks | Frequency |
|---|---|---|
| 1 | ||| | 3 |
| 2 | || | 2 |
| 3 | || | 2 |
| 4 | 卌 | | 6 |
| 5 | 卌 |||| | 9 |
| 6 | 卌 ||| | 8 |
Arrange the odd numbers from 1 to 17 without repetition to get a sum of 30 on each side of the magic triangle.
This Solution to the Problem.
VII. Answer the following questions: 2 x 5 = 10
Construct a line segment using ruler and compass
AB = 7.5 cm (OR) QR = 10 cm
Steps to construct AB = 7.5 cm:
1. Draw a line and mark a point 'A' on it.
2. Place the metal tip of the compass on the '0' mark of the ruler.
3. Extend the pencil tip of the compass to the 7.5 cm mark.
4. Without changing the compass width, place the metal tip on 'A' and draw a small arc to cut the line.
5. Mark the point of intersection as 'B'.
6. AB is the required line segment of length 7.5 cm.
(The steps for QR = 10 cm are identical, just using points Q, R and length 10 cm).
AB = 7.5 cm (OR) QR = 10 cm
Steps to construct AB = 7.5 cm:
1. Draw a line and mark a point 'A' on it.
2. Place the metal tip of the compass on the '0' mark of the ruler.
3. Extend the pencil tip of the compass to the 7.5 cm mark.
4. Without changing the compass width, place the metal tip on 'A' and draw a small arc to cut the line.
5. Mark the point of intersection as 'B'.
6. AB is the required line segment of length 7.5 cm.
(The steps for QR = 10 cm are identical, just using points Q, R and length 10 cm).
Draw and label each of the angles.
∠NAS = 90° (OR) ∠BIG = 35°
Steps to draw ∠NAS = 90°:
1. Draw a ray AS.
2. Place the center of the protractor on the vertex A and the baseline along the ray AS.
3. Mark a point 'N' at the 90° mark on the protractor.
4. Remove the protractor and draw a ray AN from the vertex A passing through the point N.
5. ∠NAS is the required right angle of 90°.
Steps to draw ∠BIG = 35°:
1. Draw a ray IG.
2. Place the center of the protractor on the vertex I and the baseline along the ray IG.
3. Mark a point 'B' at the 35° mark on the protractor (using the inner scale).
4. Remove the protractor and draw a ray IB from the vertex I passing through the point B.
5. ∠BIG is the required acute angle of 35°.
∠NAS = 90° (OR) ∠BIG = 35°
Steps to draw ∠NAS = 90°:
1. Draw a ray AS.
2. Place the center of the protractor on the vertex A and the baseline along the ray AS.
3. Mark a point 'N' at the 90° mark on the protractor.
4. Remove the protractor and draw a ray AN from the vertex A passing through the point N.
5. ∠NAS is the required right angle of 90°.
Steps to draw ∠BIG = 35°:
1. Draw a ray IG.
2. Place the center of the protractor on the vertex I and the baseline along the ray IG.
3. Mark a point 'B' at the 35° mark on the protractor (using the inner scale).
4. Remove the protractor and draw a ray IB from the vertex I passing through the point B.
5. ∠BIG is the required acute angle of 35°.
