Class IX - Mathematics Practice Paper - 2 - Answers

Subject: Mathematics

Class IX

Time Allowed: 3 hours

Max Marks: 80

Section – A (Q1 – Q16)

1. The coefficient of x² in 4x² + 3x + 1 is

a) 1 b) 3 c) 4 d) 0

View Answer

Ans. (C)

2. Which of the following is a polynomial?

a) 1/x b) 1/x² c) x^3/2/ √x d) None of these

View Answer

Ans. (C)

3. Zero of the zero polynomial is

a) 0 b) 1 c) any real number d) not defined

View Answer

Ans. (D)

4. In figure l₁ ∥ l₂, the value of x is

a) 80^o b) 100^o c) 110^o d) 70^o

View Answer

Ans. (A)

5. In a triangle if the measure of an angle is equal to sum of the measures of remaining two angles, then the triangle is

a) right angled triangle b) acute angled triangle c) obtuse angled triangle d) equilateral triangle

View Answer

Ans. (A)

6. The measure of an angle is 5 times its complement. The angle measures

a) 25^o b) 35^o c) 65^o d) 75^o

View Answer

Ans. (D)

7. The length of each side of an equilateral triangle of area 4√3 sq.cm is

a) 4 cm b) 4/√3 cm c) √3/4 cm d) 3 cm

View Answer

Ans. (A)

8. The mid – value of a class interval is 42. If the class size is 10, Then the upper and the lower limits of the class interval are

a) 37 and 47 b) 47 and 37 c) 37.5 and 47.5 d) 47.5 and 37.5

View Answer

Ans. (B)

9. The mode of the following numbers is

2, 3, 4, 5, 0, 1, 3, 3, 4, 3

a) 2 b) 3 c) 4 d) 5

View Answer

Ans. (B)

10. The median of the first 20 natural numbers is

a) 10.5 b) 10 c) 11 d) None of these

View Answer

Ans. (A)

11. Find the mean of the first 10 whole numbers

(a) 5.5 b) 55 (c) 4.5 (d) 45

View Answer

Ans. (C)

12. In figure, if PQ ∥ RS, then the value of x is

a) 20^o b) 30^o c) 40^o d) 50^o

View Answer

Ans. (C)

13. The equation of the x – axis is

a) x = 0 b) y = 0 c) x = y d) x = -y

View Answer

Ans. (B)

14. The graph of a linear equation in two variables is a

a) a straight line b) parabola c) a circle d) None of these

View Answer

Ans. (A)

15. In figure, if AB ∥ CD, then x is

a) 100^o b) 80^o c) 60^o d) 150^o

View Answer

Ans. (A)

16. If the area of an isosceles right triangle is 8 sq.cm, then the length of its hypotenuse is

a) √32 cm b) √16 cm c) √48 cm d) √24 cm

View Answer

Ans. (A)

Section – B

Case Studies (Q17-Q20)

Each sub part is of 1 mark

17. Read the following and answer the following questions:

A shopkeeper sells two types of rice, Brown Rice (BR) and Golden Sella Rice(GSR). Study the details of his stock, purchase and sale of rice during a particular week. Total quantity of rice he had in the beginning of the week = 10 Quintals. He bought BR at the rate of ₹ 75 per kg and GSR at the rate of ₹ 25 per kg. His total purchase (cost price) = ₹ 56250 He sold BR rice at the rate of ₹ 100 per kg and GSR at the rate of ₹ 30 per kg. His total profit at the end of the week = ₹ 26250

Assume that the shop keeper bought x kg of BR and y kg of GSR, answer the following questions

i) Frame the equation for the above

a) x + y = 10 b) x + y = 1000 c) x + y = 100 d) x + y = 10000

View Answer

Ans. (B)

ii) The linear equation that represents the total amount of purchase of both the types of rice is

a) 25x +75y = 56250 b) 75x + 25y = 56250 c) 75 x + 25y = 26250 d) None of these

View Answer

Ans. (B)

iii) The shopkeeper used the linear expression 100x + 30 y to calculate his total sale amount at the end. He got the amount equals to

a) ₹ 56250 b) ₹ 75000 c) ₹ 82500 d) ₹ 150000

View Answer

Ans. (C)

iv) A linear equation in two variables has

a) unique solution b) two solutions because it has two variables

c) infinite solutions d) none of these

View Answer

Ans. (C)

18. Read the following and answer the following questions:

A graphic designer divided 10cm x 8cm rectangular sheet ABCD into four triangles as shown in the figure to create a logo design for his client.

i) Length of the common side of the ∆ AFD and∆ FED

a) 14 cm b) 15 cm c) 10.5 cm d) 10 cm

View Answer

Ans. (D)

ii) Length of the common side of ∆ FBE and ∆ FED

a) 5 cm b) 7 cm c) 5.5 cm d) 4 cm

View Answer

Ans. (A)

iii) Length of the common sides of ∆ DEC and ∆ FED approximately equal to (√5 = 2.2)

a) 11.5 cm b) 11 cm c) 12 cm d) 11.19 cm

View Answer

Ans. (B)

iv) Area of the ∆ FED is approximately equal to

a) 4√39 cm² b) 624 cm² c) 39 cm² d) 78 cm²

View Answer

Ans. (A)

19. Read the following and answer the following questions:

Look at the petite pedant giving dainty dazzle, crafted in white gold. It is triangular in shape studded with three sparkling diamonds. The sketch originally drawn by the artist designer and its details are for tour reference to answer the given questions.

∆ABC is isosceles with AB = AC and ∆ DBC is isosceles with BD = DC.

i) ∆ ABD is congruent to

a) ∆ BDP b) ∆ DPC c) ∆ ACD d) ∆ ABC

View Answer

Ans. (C)

ii) ∆ ABP is congruent to

a) ∆ ABD b) ∆ ACD c) ∆ ABC d) ∆ ACP

View Answer

Ans. (D)

iii) If ∠ BDC = 1000, then ∠ DBC =

a) 35^o b) 40^o c) 50^o d) 30^o

View Answer

Ans. (B)

iv) If the equal sides AB and AC of the given pendant are 13mm and its height from A to BC is 5mm then BC =

a) 12 mm b) 24 mm c) 41 mm d) 0.25 mm

View Answer

Ans. (B)

20. Corona virus disease (COVID-19) is an infectious disease caused by a newly discovered variation of corona virus.

The following data shows the number of confirmed and recovery case of COVID-19 pandemic in 4 states/Union Territories of India as on 9^th December 2020, 9.05 a.m. IST

State/UT	Confirmed Cases (in Lakh)	Recovery Cases (in Lakh)
Maharashtra (MH)	18.59	17.37
Delhi (DL)	5.97	5.65
Karnataka (KA	8.95	8.58
Uttar Pradesh (UP)	5.58	5.28

Study the table and its bar graph given below to answer the following questions:

(Data Source: Ministry of Health and Family Welfare)

i) Which State/UT shows maximum number of confirmed cases?

a) MH b) DL c) KA d) UP

ii) Which two States/state and UT together exceed the confirmed number of cases then MH?

a) DL and KA b) KA and UP c) DL and UP d) None of these

iii) If the confirmed cases = Recovery cases + (Active cases + Deceased), then find out number of (Active cases + Deceased) in thousand in Delhi

a) 23 b) 0.32 c) 3.2 d) 32

iv) Which two States/state and UT shows less than 6 lakh recovery cases in the bar graph?

a) MH and KA b) KA and UP c) DL and MH d) DL and UP

Section – C (Q21 – Q36)

21. Find the value of k, for which the polynomial x – 3x + 3x + k has 3 as its zero.

View Answer

Ans. k = -9

22. Find the value of 249² – 248² using a suitable identity.

View Answer

Ans. 497

23. Find the value of the polynomial 2x³ + 3x² – 11x – 6, at x = – 3

View Answer

Ans. 0

24. What is the area of an equilateral triangle with side 18cm?

View Answer

Ans. 81√3 cm²

25. In the given figure, AB∥ CD. If ∠ AOC = 300 and ∠1000, then find ∠OCD

View Answer

Ans. 130^o

26. Find the zero of the polynomial, P(x) = 3x – 5

View Answer

Ans. 5/3

27. Express 6x – 7 in the form of ax + by + c = 0 and find the values of a, b and c.

28. If two supplementary angles are in the ratio 3 : 2. Find the angles.

View Answer

Ans. 108^o and 72^o

29. Find whether 2x – 1 is a factor of 2x² + x – 1.

View Answer

Ans. Yes

30. Expand (2x – 10) (2x + 10)

View Answer

Ans. 4x² – 100

31. (x + 1/x)² = x² + 1/x² + 2

32. If x =3, y = -2 is a solution of the linear equation 3x – ky = 1, then find the value of k.

View Answer

Ans. k = -4

33. In ∆ ABC, ∠ ABC = 66 and ∠ ACB = 60. If the bisector of ∠ A meets BC at D, then find ∠ADB.

View Answer

Ans. 87^o

34. In figure, ABC is an equilateral triangle and BDC is an isosceles right triangle, right angled at D. Find ∠ ABD.

View Answer

Ans. 105^o

35. The following observations have been arranged in ascending order. If the median of the data is 65, find the value of x.

30, 35, 48, 55, x, x + 3, 75, 79, 85, 99

View Answer

Ans. 63.5

36. In the give figure, find the value of p.

View Answer

Ans. 60^o

Section – D Q37 – Q40 (2 Marks Each)

37. In a quadrilateral ABCD, AB = AD and AC bisects ∠ A. Show that BC = DC

38. If two lines intersect each other, then prove that the vertically opposite angles so formed are equal.

39. Factorise: 25x² – 35x + 12

View Answer

Ans. (5x – 4) (5x – 3)

40. Without actually calculating the cubes, find the value of (-12)³ + (7)² + (5)³

View Answer

Ans. – 1260

Section – E (Q41 – 43) (3 Marks Each)

41. Factorise: x³ – 2x² – x + 2

View Answer

Ans. (x – 1) (x + 1) (x – 2)

42. Draw the graph of x + y =10

43. In figure PR = QR, ∠ PRA = ∠ QRB and ∠ BPR = ∠ AQR. Prove that BP = QA.

Section – F (Q44 – 46) (5 Marks Each)

44. The sides of a triangular plot are in the ratio of 3 : 5 : 7 and its perimeter is 300m. Find its area .

45. A random survey of the number of children of various age group playing in a park was found as follows: Draw a histogram to represent the data.

46. In the given figure ABC is a right triangle right angled at C, M is the mid – point of hypotenuse AB, C is joined to M and produced to a point D such that DM = CM. Point D is joined to B. Show that: CM = ½ AB.

Class IX – Mathematics Practice Paper – 2 – Answers