Kerala Class 9 First Term Question Paper 2025 Maths

SAMAGRA S'IIKS"A, KERALA
E-903
SUMMATIVE ASSESSMENT -TERM 2025-26
MATHEMATICS
Class -I V Time: 2—Hrs.
Total Score : 80
Instructions
the questions and think about thc answers.
Use the first 15 tninutes to read
split into 4 parts A, B, C, D
There are 26 questions,
you need answer only one of those.
• Answer all questions; but in questions of the type A or B,
You can answer the questions in any order, writing the correct question number
No need to simplify irrationals like etc. .using approximations unless you are asked to do so.
Answers must be explained, whenever necessary.

Section- A

This section has 8 questions of score 1 each. Select the correct answer.

l. Which of the following equation represents the statements " three times a number added to
five times another number gives 18? "
B) 5x+3y=lO C) 5x-3y=18

2. Which of the following number lies between and ?
1 3
4 2 4
3. In the figure, four parallel lines with same distance apart and
a slanted line are drawn. If AB 2 centimetres.
then BC ..... .centimetres.

4. 20—x10—
1 1 3
4 2 4

5. In the figure, which of the following triangle-has circumcircle on any of its side ?

A) B) C) D)

5 10
5 5
5

7 3 5

E903 1/5

6. For any four consecutive natural numbers.
Sutn of two nutnbers at the ends and sum of two numbers in the middle arc equal.%
8
ii. Product of two nutnbers at the ends and product of two numbers in the middle are equal.
iii. The difference between the product of the two numbers at the ends and product of two
nutnbers in the middle is 2.
iv. Sutn of first two numbers and sum of next two numbers are equal.

A) (i) and (ii) are true
B) (ii) and (iii) are true
C) (i) and (iii) are true
D) (iii) and (iv) are true
7. Read the following statements.
Statement I: - The length of the diagonal of a square with side I metre is metre.
Statement 2: - If another square is drawn on the diagonal of a given square, the area of the second
square is twice the area of the first square.
Choose the correct answer from
those given below.
A) Statement I is true, Statement2 is false.
B) Statement 2 is true, Statement 1 is false.
C) Both are true, statement 2 is the reason for statement I.
D) Both are true, statement 2 is not the reason for statement l.

In triangle ABC, D and E are the midpoints of the sides AB, AC respectively.
Statement 1 : The length of BC is 8 centimetres and the length of DE is 5 centimetres.
Statement 2 : In any triangle, the line joining the midpoints of two sides is half the length of the
third side.
Choose the correct answer from those given below.
A) Statement I is true,Statement 2 is false.
B) Statement 2 is true,Statementl is false.
C) Both are true, statement 2 is the reason for statement l.
D) Both are true, statement 2 is not the reason for statement 1.

Section- B

This section contains 6 questions of 3 score each.
9. Draw an equilateral triangle of perimeter 14 centimetres.
10. Sum of two numbers is 41 and their difference is 15. What are the numbers ?

(V I l. Any odd number can be written as the difference of two perfect squares.
(i) Using this concept, wri!e 15 as the difference of twp perfect squares.
(ii) Draw a square of area 15 square centimetres.

12. (A) The price of 2 bags and I umbrella is 1150 rupees. The price of 2 bags and 3 umbrellas is
1850 rupees. What is the price of a bag? What is the price of an umbrella?

OR
(B) Of two numbers, the larger one is 6 times the smaller one. Subtracting the smaller from the
E903 215

the numbers ?
Inrgcr gives 20.What arc
two digit numbers ending in three is
I.Ä. The algebraic form of
algebrnic form of two digit numbers ending in
(i) Write the algebra. the product of two different two digit numbers ending in 6 alqo
(ii) lixplnin using
ends in 6.

For any two positive numbers x, y
14. (A) (i) ...44 (Fill in the blanks)

(ii) The stun of two even numbers is 26 and their product is 144. What is the product ofthc
even nutnbers next to each ?
OR

(B) The area of a rectangle with length x metre and breadth y metre is 96 square meters. When the
length and breadth are increased by I meter , the area becomes 117 square meters. Then

(i) Find (.v+y).
(ii) What is the perimeter of the first rectangle ?

Section- C
This section contains 6 questions of.4 score each.

15. (A) In the figure, AD is perpendicular to BC. AB = 2
metres, AD CD = 1 metre.
2 1
(iii) Calculate the perimeter of triangle ABC, upto a
centimetre.
D 1 c
OR

(B) In the figure, BCDE is a square. AB 2 centimetres and
3 centimetres. (VIS 2.23 )
(i) What is the area of the square BCDE ?
3
(ii) What is the perimeter of the square BCDE ?
(iii) How much greater in the perimeter of square BCDE c
than the perimeter of triangle ABE ?

16. In any month of a calendar, mark four adjacent numbers which form a square.
(i) Find the difference of the diagonal products.
(ii) .Explain using algebra, why the difference is the same number in all such squares.

17. Of two numbers 13 added to a number gives equal to twice the second number. 7 added to the
second number gives twice the first number. What are the numbers ?

E903 3/5

18. In the trinnglc ABC. DC is parallel to DE.
AB 9 centimetrcs.AD ccntimctrcs.and
AC 6 ccntimctrcs

(i) Al): Aft-

(iii) Find the length of AE and EC.

19. (A) Two tunes a nutnber added to three times another number
gives 52. Six times Ofthe first
nunnber added to five tithes of the second number
gives 108. What are the numbers ?
OR
(B) A fraction
simplified after adding I to its numerator
becomes — If instead , I is added to
the
and then simplified it becomes —. What is the fraction
?
20. (A) All Sides Of the quadrilateral ABCD are
equal and its two corners are joined to the
midpoints of sides AB, CD.
D F
c

(i) Prove that the lines AE and EC are parallel.

(ii) Prove that these lines divide the diagonal BD in to
three equal parts.

OR
(B) In the figure, P, Q, R are the midpoints of the sides of triangle ABC.
X, Y, Z are the midpoints of the sides of triangle APR. Area of triangle XYZ is 3 square
centimetres.

(i) What is the area of triangle AXZ ?
(ii) What is the area of the parallelogram APQR ?
(iii) Find the area of triangle ABC.
Section- D
This section contains 6 questions of 5 score each.
21. Draw a rectangle of perimeter 17 centimetres and sides in the ratio 4:3.

22. Right triangles are drawn as seen in the figure.
1
(i) What is the length of the hypotenuse of the smallest right
triangle?
1
(ii) Find the perimeter of the 4thright triangle ?
1
1
1
E903 4/5

(iii) Continuing like this. how much more would be the perimeter of the 6thtriangle than that of the

23. Two years ago, father's agc i,vassix times the age of son. After two years, this would become four
titnes. What are their ages now ?

24. If the sides of a rectangle are increased by one meter, its area would be 336 square meters.
If decreased by one tneter, it would be 226 square meters.
(i) What is the area of the original rectangle ?
(ii) What is its perimeter ?

25. (A) In the figure, ABC is a right triangle. ED is the 'C
perpendicular drawn from the midpoint of BC to AB.
(i) Prove that ED is half of CA.
(ii) Prove that CE BE.
(iii) Prove that the circumcentre of a right triangle is
the midpoint of the hypotenuse.

OR

(B) In the figure , AQ and BP are the medians of
triangle ABC. S and R are the midpoints of AG
and BG. AB 24 centimetre.

(ii) Find the length of PQ and SR
(iii) Prove that PQRS is a parallelogram.

26. (A) The product of the larger of two numbers increased by one and the smaller decreased by one is
112. The product of the larger decreased by one and the smaller increased by one is 120.
(i) What is the product of numbers ?
(ii) What is their difference ?

OR

(B) The product of two numbers is 4 more than the product of the larger of the numbers increased by
one and the smaller decreased by one.

(i) Find the difference of the numbers.
(ii) How much will be increase in the product if the larger is decreased by one and the
smaller is increased by one.

E903 5/5