CBSE Class 09 SA1 Question Paper – Maths

Section A1. Which of the following is irrational:

a) 0.14

b) 0.1416

c) 0.1416

d) 0.4014001400014…..

2. The degree of the polynomial 3x³ – x⁴ + 5x + 3 is:

a) 1

b) 3

c) 4

d) -4

3. Euclid’s fifth postulate is.

a) The whole is greater than the part.

b) A circle may be described with any centre any radius.

c) All right angles are equal to one another.

d) None of these.

4. The sides of a triangle are 3 cm, 4 cm and 5 cm. Its area is:

a) 12 cm²

b) 15 cm²

c) 6 cm²

d) 9 cm²

Section B

5. Express the rational number 0.45 in the form p/q , where p and q are natural number.

6. Find the remainder, when the polynomial 2x⁴ + x³ + 4 x² – 3x -2 is divided by x-3. (without applying long division).

7. Find the value of k if (x-1) is a factor of 4x³ + 3x² -4x +k.

8. If a point C lies between two points A and B such that AC=BC, then prove that AC = 1/2 AB.

9. Show that in a right angled triangle, the hypotenuse is the longest side.

10. In which quadrant or on which axis each of the points (-2,4), (3,-1), (-1,0), (1,2) lie?

Section C

11. Express √5.41 geometrically on a number line.

12. Simplify

(∛343^-2 ) / (∜81 )

13. Use identities to find

(a) (2x³ + 3y)(2x³ + 5y)
(b) (y² + 3/2)(y² – 3/2)

14. If x + 1/x = 4 , find x⁴ + 1/⁴.

15.

∠BAC = 35°
∠CDE = 25°

If AB || DE, then find y.

16. If BO and CO are bisectors of ∠ABC and ∠ACB, then find ∠BOC if ∠BAC=50° .

17. 

∠ABC=45°
∠BAD=35°
∠DCB=50°

Find x

18. Sides AB and AC of △ABC are extended to P and Q respectively. Show that AC > AB is ∠PBC < ∠QCB.

19. △ABC is an isosceles triangle in which AB+AC. Side BA is produced to D such that AD=AB. Show that ∠BCD=90°.

20. Find the area of the given quadrilateral.

AB = 8 cm
BC = 15 cm
DC = 9 cm
AD = 16 cm
∠B = 90°.

Section D

21. Simplify

[(√5 – 2) / (√5 + 2)] – [(√5 + 2) / (√5 – 2)]

22. Locate √11 on a number line.

23. Use suitable identity to solve 35³ – 20³ – 15³.

24. Factorise

(x-2y)³ + (2y-3z)³ + (3z-x)³

25. If x + 1/x = 2 , find x³ + 1/x³ .

26. If a transversal intersects two lines such that the bisectors of a pair of corresponding angles are parallel, then prove that the two lines are parallel.

27. ABCD is a quadrilateral in which AD=BC and ∠DAB = ∠CBA. Prove that △ABD ≅ △BAC.

28. Prove angle DBC=90°, if DM=CM and M is the midpoint of AB.
∠C = 90°.

29. AB and CD are the smallest and the longest sides of a quadrilateral ABCD. Prove ∠A > ∠C.

30. Plot on a graph

(2,0) , (3,5) , (4,7) , (5,-9).

31. The perimeter of a triangle is 120m. The sides are in the ratio 5:12:13. Find the length of the altitude to the longest side of the triangle.