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Guess Paper – 2013

Class – IX

Subject – Mathematics

A

1. A man goes out at 16:42 and arrives at a post box, 6 km away, at 17:30. He walked part

of the way at 5 km/hr and then, realizing the time, he ran the rest of the way at 10 km/hr.

How far if he have to run?

2. 22

3

pr

q

(i) Find the value of r when 6 5p and q . [1]

(ii) Find both possible values of p when 8 10q and r . [2]

(iii) Make p the subject of the formula. [2]

3. A dishonest dealer professes to sell his goods at cost price, but he uses a weight of 960

grams for 1 kg. Find his gain per cent.

[3]

4. The difference between the compound interest and the simple interest on a certain sum at

12% per annum for 2 years is Rs 90. Find the sum.

[4]

5. If 1

sin )2

A B and 1

cos ( )2

A B , find A and B. [3]

6. Evaluate:

2 2

2 2

1 1 1tan 45 8sin 90 .

cos 30 sin 30 2

[5]

7. If 3 2 3 2

,3 2 3 2

x and y

find the value of 2 2x y . [5]

8. Simplify: (a) 3 54 81 8 216 15. 32 225 (b) 6 312 3. 2.

9. In how many years will a sum of Rs. 3000 at 20% per annum compounded semi-annually

become Rs 3993?

10. If 2 3 1 0,x x find the value of 2

2

1.x

x [3]

11. There are some benches in a class room. If 4 students sit on each bench then three benches are

left unoccupied and if 3 students sit on each bench then 3 students are left standing. How

many students are there in the class?

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12. Solve:

5 21,

15 710.

x y x y

x y x y

[5]

13. Solve the following system of linear equations graphically: 2 3 4 , 5 7.x y x y

Also shade the region between the lines and X – axis.

14. If sinx a and tan ,y b then prove that: 2 2

2 21

a b

x y

. [4]

15. A vertically straight tree, 30 m high, is broken the wind in such a way that its top just touches

the ground and makes an angle of 60 with the ground. At what height from the ground did the

tree break? 3 1.732Use .

16. If the following three equations hold simultaneously for x and y, find p.

3 2 11,2 3 4,4 26.x y x y x py [5]

17. Factorise: (i) 3 3 4 4a b a b

(ii) 2 2 225 9 6x z yz y

18. Factorise: 4

4

11x

x .

19. By using algebraic identities find the values of the following: [6]

(i) 3 3 339 11 50

(ii) 3.59 3.59 2.41 2.41

3.59 2.41

(iii) 8.51 8.51 2 8.51 1.49 1.49 1.49.

20. Viren set up a small factory by investing Rs. 40,000. During the first three successive years his

profits were 5%, 10% and 15% respectively. If each year the profit was on previous year’s

capital, calculate his total profit.

Paper Submitted By:

Name Chandan Singh Ghughtyal

Email chandanganga@gmail.com

Phone No. 7579016459

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Sample Paper – 2013

Class – IX Subject – MATHEMATICS

CSG: 110 MM-80 (TIME: 21

2 HOURS)

B2: MMR

B3: PKJ

B4: CSG

Instructions:

Attempt all questions in Section A.

Attempt any four questions in Section B.

Maximum marks for each question is indicated in [ ] against each question.

Give proper steps and working.

Take the value of 22

7 unless otherwise mentioned in the question.

Section A (40 Marks)

(Attempt all questions)

1. Find a single discount equivalent to the discount series: 25%, 20% and 10%. [4]

2.Simplify :

6 3 3 6

7 7 7 7

2 0 2

3 4 9 2

2 2 2

[4]

3.Solve : (8 3) 4 2log logx x

x [4]

4. Determine (8 )xx if 29 240 9 .x x [4]

5.In the following figure, AB = AC, D and E are point on BC such that BE = DC.

Prove that AD = AE.

2

6. The following data have been arranged in ascending order: [4]

9, 12, 19, 23, 26, x, 35, 39, 40, 45.

If the median of the data is 30, find x.

In the above data, if 45 is replaced by 25, find the new median.

7. Factorize: 2 2 2 22( )ab cd a b c d . [4]

8. The difference between the exterior angle of a n sided regular polygon and an (n+1) sided regular

polygon is 120, find the value of n. [4]

9. Three cubes whose edges are x cm, 8 cm and 10 cm respectively are melted and recast into [4]

a single cube of edge 12 cm. Find x.

10. The sides of an equilateral triangle are (6 3 )x y cm , (8 9 5)x y cm and (10 12 8)x y cm

respectively. Find the length of each side. [4]

Section B (40 Marks)

(Attempt any four questions)

11.(a) A formula for changing temperature in degrees Fahrenheit (F) to degrees in Celsius(C) is [5]

given by 9

32.5

F C

(i) Express C in term of F.

(ii) Find C if F = 50.

(iii) Is it possible for C and F to have the same value?

(b) Solve the following system of equations graphically: [5]

4 5; 5 4 7.x y y x

12. (a) An agricultural field is in the form of a rectangle of length 20m and width 14 m. [5]

A 10 m deep well of diameter 7 m is dug in a corner of the field and the earth taken out of

the well is spread evenly over the remaining part of the field. Find the rise in its level.

(b) If 4tan 3, find the value of sec tan

sec tan

. [5]

13. (a) Evaluate: 2 2 2 24tan 45 8cos 60 sin 60 cos 90 tan30 [5]

(b) The scale of a map is 1:300000. A plot of land of area 90 km2 is to be represented on the [5]

3

map. Find:

(i) The number of km on the ground represented by 1 cm on the map.

(ii) The area in km2

that can be represented by 1 cm2.

(iii) The area on the map that represents the plot of land.

14. (a) If 3 7

2x

, find the value of 2

2

14x

x . [3]

(b) By selling 90 ball pens for 160, a person loses 20%. How many ball pens should be sold for [3]

96, so as to have a profit of 20%.

(c) What sum will amount to 73810 in two years at 10% per annum compound interest? [4]

15. (a) If 1

20xx

, find the value of 3

3

1x

x

. [4]

(b) Factorize: (i) ( 3) ( 3)a a b b (ii) 6 326 27.x x [6]

16. (a) In a triangle ABC, AD is a median and E is the mid- point of AD. BE is joined and produced to [5]

meet AC at F. Prove that 1

3AF AC .

(b) Divide 36 into four parts so that if 2 is added to the first part, 2 is subtracted from the second part,

the third part is multiplied by 2, and the fourth part is divided by 2, then the resulting number is

the same in each case. [5]

17. (a) The heights of the boys in cm of a class are given below. If the mean height is 152.2 cm. Find

the value of p.

Heights ( in cm) 150 151 152 153 154 155

No. of boys. 3 6 p 2 4 2

(b) In the given figure, ABCD is a quadrilateral in which AB = BC, 090 ,B D AD = 3 cm

and CD = 4 cm. Find AC and calculate the area of ABC . [5]

MATHEMATICS

(Two hours and a half)

Answers to this paper must be written on the paper provided separately.

You will not be allowed to write during the first 15 minutes.

This time is to be spent in reading the question paper.

The time given at the head of the paper is the time allowed for writing the answers.

Attempt all questions from Section A and any four questions from Section B.

All working, including rough work, must be clearly shown and must be shown on

the same sheet as the rest of the answer. Omission of essential working will result in

loss of marks.

The intended marks for questions or parts of questions have been mentioned after

each of them.

Please refer to the mathematical tables provided by your school textbook.

Section A (40 marks)

Question 2: 3+3+4=10 marks

a) The perimeter of an isosceles triangle is 42cm. Its base is 2

3times the sum of its

equal sides. Find the length of each side and the area of the triangle.

b) In a right-angled triangle PQR,∟ P=90° and QR= 3PQ. Find the values of cos

Q, cot R and cosec Q.

c) Determine the coordinates of the vertices of the quadrilateral ABCD in each of the

following:

i) ii)

A B A 4 B

3

C 0 D

-4 -3 2 3 -4 -2 2 4

C D

Question 3: 3+3+4=10 marks

a) Express 10.123 as a rational number.

b) If the cost price of 11 shirts is equal to the selling price of 10 shirts, find the

percentage profit or loss.

c) The weights (in kg) of the teachers of a school are recorded as shown below-

60,65,63,70,65,62,65,63,64,60,68,58,62,65,63,65,64,60,62,63

If the collection of data be grouped into class intervals

56-59,59-62,62-65,65-68,68-71 then answer the following:

i) What is the type of these class intervals?

ii) Find the frequency of the class interval 59-62.

iii) Write the tally marks for the frequency of the variate 62 and the class interval

62-65.

iv) What are the class limits and class boundaries of the class interval 68-71?

Question 4: 3+3+4=10 marks

a) In a ∆ABC, AB=AC. Prove that the altitude AD is a median.

b) Prove that any straight line drawn from the vertex of a triangle to the base is

bisected by the straight line which joins the middle points of the other two sides of the

triangle.

c) The ratio of the number of sides of two regular polygons is 3:4 and the ratio of the

sum of their interior angles is 2:3. Find the number of sides of each polygon.

Question 5: 3+3+4=10 marks

a) If 7 – 5 =a+b 35 then find the value of a2

+ 4ab + b2.

7 + 5

b) Prove that log3{9-1/3

÷ (1

3)-4

} is a rational number. Find the number.

c) If the midpoints of the sides of a square are joined in order, prove that the area of

the quadrilateral so formed is half that of the square.

Question 6: 3+3+4=10 marks

a) Ifϴ=60° prove that cosϴ.sin(ϴ/2)+sinϴ.cos(ϴ/2) has a rational value. Also, find

it.

b) Find the LCM of 25x2-9y

2 and 5x

2+2xy-3y

2 by factorization.

c) A man bought a house at Rs.39,20,000. It has three floors-ground floor, first floor

and second floor-and he bought each floor seperately. He decides to sell all the floors

at equal prices. On selling the ground floor, he makes a loss of 12%. But he makes a

profit of 20% from the first floor while he makes neither a profit nor a loss by selling

the second floor. Find the per cent profit or loss he made by selling the house.

Question 7:3+3+4=10 marks

a) Find the radius of a circular field if its area is equal to the area of a circular path

whose inner and outer radius are 175 m and 140 m respectively.

b) If in the figure, AD is perpendicular to BC, find the value of sinϴ+cosϕ. A

10 ϴ 7

8

ϕ

B D C

c) If the polynomial ax2+bx+1 has the values 0 and 15 when x has the values 1 and -2

respectively, determine the polynomial and factorize it.

Question 8: 5+5=10 marks

a) A frequency distribution is displayed by the following histogram:

12

11

10

9

8

7

6

5

4

3

2

1

0 20 40 60 80 100 120

i) Construct a frequency table (with tally marks) of the distribution.

ii) Construct the frequency polygon of the distribution.

b) In the figure, AD=DC and DE is perpendicular to AC. Find DE and cos∟BAC.

A

E

D

4

B 4 3 C

Question 9: 3+3+4=10 marks

a) If the rate of interest is 6% p.a. and the difference of the compound interest and the

simple interest on a sum of money for 2 years is Rs.45 then find the sum of money.

b) Can three angles of a triangle have the measures 35°+x°, x° and 40°-x° for

any value of x? Justify your answer.

c) ABCD is a square. The points P,Q,R and S are taken on AB, BC, CD and DA

respectively, so that AP=BQ=CR=DS. Prove that:

i) PQRS is a square.

ii) PR2+SQ

2=PQ

2+QR

2+RS

2+SP

2

iii) SQ2=2(AP

2+BP

2)

Question 10: 3+3+4=10 marks

a) If x>1 and x-1

𝑥=, find the value of x

4+(1/x

4).

b) If log102=0.3010 and log103=0.4771 then find the value of log10(45)10

, correct to 2

decimal places.

c) A rectangular sheet of tin measuring 60 cm X 44 cm is rolled along the breadth to

form the biggest possible hollow right circular cylinder. What is the area of the extra

sheet of tin required to make it a closed container? Also find the capacity of the

container.

Question 11: 6+4=10 marks

a) In the figure, OX and OY are the x-axis and y-axis respectively, and OABC is a

rectangle. Given OA=3 units, OD=1 unit and ∟BEA=45°.

Y

B

C

D

E 0 X

3 A

ICSE Question Papers For Class 9Mathematics

Publisher : Faculty Notes Author : Panel of Experts

Type the URL : http://www.kopykitab.com/product/4843

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