Class 6 Maths Solved Question Paper (2025–26)
Summative Assessment – 1 | Complete Solutions with Explanation
School: SAGES Lala Lajpat Rai
Class: 6
Subject: Mathematics
Time: 2:30 Hours
Maximum Marks: 50
Q1. Fill in the blanks (with explanation)
1) 1, 1, 1, 1, 1, ___ , ___
Explanation
All the numbers in the sequence are the same.
So the pattern continues with 1.
Answer
1, 1
2) ______ is formed by two rays having a common starting point.
Explanation
When two rays start from the same point, they form an angle.
Diagram
A
\
\
O
/
/
B
Rays OA and OB form ∠AOB.
Answer
Angle
3) 1, 3, 5, 7, 9, 11, 13, 15, ___, ___
Explanation
The pattern increases by 2 each time.
15 + 2 = 17
17 + 2 = 19
These numbers are called odd numbers.
Answer
17, 19
4) A ______ is a straight path that extends endlessly in both directions.
Explanation
A straight path that goes infinitely in both directions is called a Line.
Diagram
<---------------------------->
Line
Answer
Line
5) 1, 3, 6, 10, 15, 21, 28, 36, ___, ___
Explanation
This is a Triangular Number Pattern.
Differences increase by 1.
3 − 1 = 2
6 − 3 = 3
10 − 6 = 4
15 − 10 = 5
21 − 15 = 6
28 − 21 = 7
36 − 28 = 8
Next numbers:
36 + 9 = 45
45 + 10 = 55
Answer
45, 55
6) 1, 8, 27, 64, 125, 216, ___, ___Explanation
These numbers are cube numbers.
1³ = 1
2³ = 8
3³ = 27
4³ = 64
5³ = 125
6³ = 216
Next cubes:
7³ = 343
8³ = 512
Answer
343, 512
7) A ______ has one starting point but no end point.
Explanation
A line that has one starting point and extends infinitely in one direction is called a Ray.
Diagram
A ----------------------->
Starting Point
Answer
Ray
8) 1, 2, 4, 8, 16, 32, 64, 128, ___, ___
Explanation
Each number is multiplied by 2.
128 × 2 = 256
256 × 2 = 512
Answer
256, 512
9) An angle that is more than 180° but less than 360° is called ______.
Explanation
Types of angles:
Acute angle → less than 90°
Right angle → 90°
Obtuse angle → between 90° and 180°
Straight angle → 180°
Reflex angle → more than 180° but less than 360°
Answer
Reflex Angle
10) 1, 3, 9, 27, 81, 243, 729, 2187, ___, ___
Explanation
Each number is multiplied by 3.
2187 × 3 = 6561
6561 × 3 = 19683
Answer
6561, 19683
Q2. Very Short Answer Questions
1. Draw and label an angle with arms ST and SR.
Here S is the vertex.
Diagram
T
\
\
S -------- R
Angle name:
∠TSR
2. What is Mathematics?
Answer
Mathematics is the study of numbers, shapes, patterns, and measurements.
It helps us solve problems in everyday life.
3. Name the angles marked in the given figure
Diagram (similar to question)
P
\
\
L------R
\
Q
Angles formed:
∠PLQ
∠QLR
4. Identify the number marked on the number line and label the remaining positions
On the number line numbers increase by 1.
So the missing numbers are:
15079
15080
15081
15082
5. Name the rays shown in the figure. Is T the starting point of each ray?
Diagram
A
/
/
T -------- N -------- B
Rays
Ray TA
Ray TB
Answer
Yes, T is the starting point of both rays.
Q3. Short Answer Questions
1. How many lines can be drawn through a single point?
Explanation
Through a single point we can draw lines in many directions.
Therefore the number of lines is unlimited.
Answer
Infinite number of lines
2. Draw angles of 160°, 45°, 195°
45° (Acute Angle)
A
\
\
O------B
160° (Obtuse Angle)
A
\
\
O
\
B
195° (Reflex Angle)
A
\
O------B
(large outside angle)
3. Why are 1, 3, 6, 10, 15 called triangular numbers?
Explanation
These numbers can be arranged in the shape of a triangle.
Example
•
• •
• • •
• • • •
Number of dots:
1
3
6
10
Therefore they are called Triangular Numbers.
4. Write three 3-digit numbers whose digit sum is 14.
Examples:
563 → 5 + 6 + 3 = 14
824 → 8 + 2 + 4 = 14
932 → 9 + 3 + 2 = 14
Answer
563, 824, 932
Q4. Long Answer Questions
1 (a) Who am I?
Conditions
Number less than 40
One factor is 7
Sum of digits = 8
Multiples of 7:
7, 14, 21, 28, 35
Digit sums:
7 → 7
14 → 5
21 → 3
28 → 10
35 → 8
Answer
35
1 (b) Who am I?
Number less than 100
Factors include 3 and 5
Multiples of 15:
15, 30, 45, 60, 75, 90
Digits differ by 1
45 → digits 4 and 5 (difference 1)
Answer
45
2. Sum and difference of smallest and largest 5-digit palindrome
Smallest palindrome:
10001
Largest palindrome:
99999
Sum
10001 + 99999 = 110000
Difference
99999 − 10001 = 89998
3. How mathematics helps humanity
Engineering
Mathematics helps engineers design buildings, bridges, and roads.
Technology
Computers, mobile phones, and software depend on mathematical calculations.
Medicine
Doctors use mathematics to calculate medicine doses and analyze medical data.
Space Science
Mathematics helps scientists launch rockets and study planets and satellites.
Q5. Very Long Answer Questions
1. Prime Factorization
(i) 64
64 = 2 × 2 × 2 × 2 × 2 × 2
= 2⁶
(ii) 104
104 = 2 × 2 × 2 × 13
= 2³ × 13
(iii) 320
320 = 2 × 2 × 2 × 2 × 2 × 2 × 5
= 2⁶ × 5
(iv) 243
243 = 3 × 3 × 3 × 3 × 3
= 3⁵
(v) 105
105 = 3 × 5 × 7
2. Smallest number that is a multiple of numbers from 1 to 10
We find LCM of 1–10
LCM = 2520
Answer
2520
3. Bar Graph Question
| Activity | Students |
|---|---|
| Playing | 45 |
| Reading Story Books | 30 |
| Watching TV | 20 |
| Listening to Music | 10 |
| Painting | 15 |
Scale:
1 unit = 5 students
Bar heights:
Playing → 9 units
Reading → 6 units
Watching TV → 4 units
Listening → 2 units
Painting → 3 units