Section A – MCQs
(5 × 1 = 5 Marks)
- Perimeter of a square = 20 cm. What is the side of the square?
a) 4 cm
b) 5 cm
c) 6 cm
d) 10 cm - Which triangle has three lines of symmetry?
a) Scalene triangle
b) Right triangle
c) Equilateral triangle
d) Isosceles triangle - How many whole units are there in ?
a) 2
b) 3
c) 4
d) 5 - Which of the following is a negative integer?
a) 5
b) 0
c) –3
d) 7 - Which shape has four lines of symmetry?
a) Rectangle
b) Square
c) Triangle
d) Parallelogram
Section B – Fill in the Blanks
(5 × 1 = 5 Marks)
- The numbers with a minus sign in front of them (e.g., –2) are called __________ numbers.
- The additive inverse of 7 is __________.
- Negative numbers lie to the __________ of zero on the number line.
- The numbers … –4, –3, –2, –1, 0, 1, 2, 3 … are called __________.
- Zero is neither __________ nor __________.
Section C – Short Answer Questions
(5 × 3 = 15 Marks)
- Compare the following numbers using < or >
a. –2 ☐ +5
b. –5 ☐ +4
c. –5 ☐ –3
- Complete the expressions
a. (+40) + ______ = +200
b. (+40) + ______ = –200
- Complete the subtraction
a. (–5) – (–7)
b. (+10) – (+13)
- Write integers between –4 and 4.
- How many whole units are there in and ?
Section D – Long Answer Questions
(5 × 6 = 30 Marks)
- Complete the following expressions
a. (–50) + ______ = +200
b. (–50) + ______ = –200
c. (–200) – (–40) = ______
- Draw the following triangles
a. A triangle with exactly one line of symmetry
b. A triangle with exactly three lines of symmetry
c. A triangle with no line of symmetry
- Draw a rectangle with sides 4 cm and 6 cm and check whether it satisfies the properties of a rectangle.
- Draw a rectangle of 12 units × 8 units. Draw another rectangle inside it (without touching the outer rectangle) that occupies exactly half the area.
- On a number line, draw
a.
b.
c.
Section E – Application Based Questions
(3 × 10 = 30 Marks)
- The area of a rectangular garden 25 m long is 300 sq m.
Find the width of the garden. - What is the cost of tiling a rectangular plot 500 m long and 200 m wide at the rate of ₹8 per hundred sq m?
- Construct a rectangle where one side is 5 cm and the diagonal is 7 cm.
Section F – Case Study
(1 × 15 = 15 Marks)
Riya is designing a rectangular park for her school.
The park is 25 m long and its area is 300 sq m. She wants to place a square playground inside the park and also draw a border around the park.
Answer the following questions:
- What is the width of the park?
- If the park is rectangular, what is its perimeter?
- If Riya draws a rectangular border 1 cm from the top and bottom and 1.5 cm from the sides, what will be the perimeter of the border?
- If the park area is divided equally into two rectangles, what will be the area of each rectangle?
- Explain whether the park design shows symmetry or not.
✅ Total Marks = 100
Class 6 – Mathematics (STEAM Paper)
Answer Key
Section A – MCQs
- Perimeter of a square = 20 cm → side = 5 cm
Answer: b) 5 cm - Triangle with three lines of symmetry
Answer: c) Equilateral triangle - Whole units in
remainder 1
Answer: b) 3 - Negative integer
Answer: c) –3 - Shape with four lines of symmetry
Answer: b) Square
Section B – Fill in the Blanks
- Negative numbers
- –7
- Left
- Integers
- Positive, Negative
Section C – Short Answers
1. Compare the numbers
a. –2 < +5
b. –5 < +4
c. –5 < –3
2. Complete the expressions
a. (+40) + 160 = +200
b. (+40) + –240 = –200
3. Complete the subtraction
a. (–5) – (–7)
= –5 + 7
= 2
b. (+10) – (+13)
= 10 – 13
= –3
4. Integers between –4 and 4
–3, –2, –1, 0, 1, 2, 3
5. Whole units
→ 1 whole unit
→ 2 whole units
Section D – Long Answers
1. Complete expressions
a. (–50) + 250 = +200
b. (–50) + –150 = –200
c. (–200) – (–40)
= –200 + 40
= –160
2. Lines of symmetry of triangles
a. Isosceles triangle → 1 line of symmetry
b. Equilateral triangle → 3 lines of symmetry
c. Scalene triangle → 0 lines of symmetry
3. Rectangle 4 cm × 6 cm
Properties:
- Opposite sides equal ✔
- All angles = 90° ✔
- Diagonals equal ✔
Therefore it satisfies rectangle properties.
4. Rectangle 12 × 8
Area = 12 × 8
= 96 sq units
Half area = 48 sq units
Example inside rectangle:
8 × 6 rectangle = 48 sq units
5. Fractions on number line
Positions:
(All lie between 0 and 1 on number line)
Section E – Application Questions
1. Width of garden
Area = Length × Width
300 = 25 × Width
Width = 300 ÷ 25
Width = 12 m
2. Cost of tiling
Area = 500 × 200
Area = 100000 sq m
Rate = ₹8 per 100 sq m
Number of units
= 100000 ÷ 100
= 1000
Cost = 1000 × 8
Cost = ₹8000
3. Rectangle construction
Given:
Side = 5 cm
Diagonal = 7 cm
Steps:
- Draw AB = 5 cm
- From A draw a perpendicular line.
- With centre B and radius 7 cm, cut the perpendicular at point C.
- Complete rectangle ABCD.
Section F – Case Study
- Width of park
Area = Length × Width
300 = 25 × Width
Width = 12 m
- Perimeter of park
Perimeter = 2(L + B)
= 2(25 + 12)
= 2 × 37
= 74 m
- Border perimeter
Depends on notebook page size, but rectangle border will have perimeter = 2(length + breadth) after margins are subtracted.
- Area of each rectangle
Total area = 300 sq m
Half area = 150 sq m
- Symmetry
The rectangular park has two lines of symmetry (vertical and horizontal through centre).
✅ Answer Key Complete
