Mathematics IX (Term - I) 1

SECTION A

(Question numbers 1 to 8 carry 1 mark each. For each question, four alternative choices

have been provided of which only one is correct. You have to select the correct choice).

1. If (x – 1) is a factor of mx2 – 2 1x + , then the value of m is :

(a) 2 (b) 2 1+ (c) 1 (d) 2 – 1

2. (998)2 + (994)2 – 1996 × 994 is equal to :

(a) 16 (b) 4 (c) 20 (d) 24

3. If x +1

x= 7 , then x2 +

2

1

xis equal to :

(a) 7 (b) 5 (c) 9 (d)7 1

7

+

4. Each equal side of an isosceles triangle is 13 cm and its base is 24 cm. Area of the

triangle is :

(a) 250 3 cm (b) 2

40 3 cm (c) 225 3 cm (d) 60 cm2

5. The sides of a traingle are x, y and z. If x + y = 7 m, y + z = 9 m, and

z + x = 8 m, then area of the triangle is :

(a) 4 m2 (b) 5 m2 (c) 6 m2 (d) 7 m2

6. ( )–1

3 264 is equal to :

(a) 2 (b) 8 (c)1

2(d)

1

8

7. In the figure, a : b : c = 4 : 3 : 5. If AOB is a straight line,

then the values of a, b and c respectively are :

(a) 75°, 45°, 60° (b) 48°, 36°, 60°

(c) 45°, 75°, 60° (d) 60°, 45°, 75°

8. In the figure, it is given that AB = CD and AD = BC.

Therefore :

(a) ∆ADC ≅ ∆ACB (b) ∆ACD ≅ ∆CAB

(c) ∆ABC ≅ ∆DCA (d) ∆DCA ≅ ∆ACB

MODEL TEST PAPER – 4 (UNSOLVED)

Maximum Marks : 90 Maximum Time : 3 hours

General Instructions : Same as in CBSE Sample Question Paper.

2 Mathematics IX (Term - I)

SECTION B

(Question numbers 9 to 14 carry 2 marks each)

9. For what value of k, (x + 1) is a factor of x3 + 2x2 + 5x + k?

10. Factorise : 4x2 + 9y2 + 16z2 + 12xy – 24yz – 16xy.

11. Write whether the follwing statements are true or false? Justify your answer.

(i) Point (0, –2) lies on the y-axis

(ii) The perpendicular distance of the point (4, 3) from the x-axis is 4.

12. A transversal intersects two lines in such a way that the two interior angles on the

same side of a transversal are equal. Will the two lines always be parallel?

OR

In the figure, if x + y = w + z, then prove that AOB is a line.

13. Show that 5 2 is not a rational number...

14. M is a point on side BC of a triangle ABC such that AM is the bisector of ∠BAC.

Is it true to say that perimeter of the triangle is greater than 2AM? Give reason for your

answer.

SECTION C

(Question numbers 15 to 24 carry 3 marks each)

15. Simplify the following by rationalising the denominator : 1

5 – 2 – 7

OR

If 5 = 2.236 and 3 = 1.732, find the value of 2 7

5 3 5 3+

+ −.

16. Prove that the sum of a rational number and an irrational number is an irrational

number.

17. Using factor theorem, show that x – y is a factor of x(y2 – z2) + y(z2 – x2) + z(x2 – y2).

18. Factorise : 23 4

2 3x x− − .

OR

Factorise : a3 + 3a2b + 3ab2 + b3 – 8

19. In the figure, in ∆ABC, ∠DAC = ∠ECA and AB = BC.

Prove that ∆ABD ≅ ∆CBE.

Mathematics IX (Term - I) 3

20. In the given figure, ABCD is a quadrilateral in which AB || DC

and AD || BC. Prove that ∠ADC = ∠ABC.

21. ∆ABC is an isosceles triangle in which AB = AC. D, E and F

are the mid-points of the sides BC, AC and AB respectively. Prove that DE = DF.

OR

In the figure, ABC and DBC are two isosceles triangles on the

same base BC such that AB = AC and DB = DC. Prove that

∠ABD = ∠ACD.

22. Show that in a right angled triangle the hypotenuse is the longest

side.

23. In the figure, AD is the bisector of ∠BAC. Prove that AB > BD.

24. If the side of a rhombus is 10 cm and one diagonal is 16 cm, then find the area of the

rhombus.

SECTION D

(Question numbers 25 to 34 carry 4 marks each)

25. Prove that

–1 –1 2

–1 –1 –1 –1 2 2

2

– –

a a b

a b a b b a+ =

+

26. Express 0.6 + 0.7 0.47+ in the form p

q, where p, q ∈ Z, q ≠ 0

27. Find the value of a so that the polynomial x3 – ax2 + 13x + 15, when divided by

(x – 1), gives 2 as the remainder.

28. Simplify :

2 2 3 2 2 3 2 2 3

3 3 3

( – ) ( – ) ( – )

( – ) ( – ) ( – )

a b b c c a

a b b c c a

+ +

+ +

OR

Factorise : x3 – x2 – x – 15

4 Mathematics IX (Term - I)

29. In the figure, AC > AB and AD is the bisector of ∠A. Show

that ∠ADC > ∠ADB.

30. Prove that a triangle must have atleast two acute angles.

31. In the figure, AC = BC, ∠DCA = ∠ECB and

∠DBC = ∠EAC. Prove that triangles DBC and EAC

are congruent, and hence DC = EC.

OR

Prove that the medians bisecting the equal sides of

an isoscecles triangles are also equal.

32. In the given figure, AP bisects ∠CAD and ∠B = ∠C. Prove that

AP || BC.

33. Find the integral zeroes of the polynomials x3 + x2 + x – 3.

34. From the figure, write the following :

(i) Coordinates of B, C and E

(ii) The points identified by the coordinates (0, 2)