Mock Test Paper

Apex Institute for IIT-JEE / PMT

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Mathematics

APEX INSTITUTE Ghaziabad: 62, Nitikhand-III, Indirapuram 201010. Ph.: 01204331180 | http://apexiit.co.in/.

Sample Paper – 2015

Class – IX Subject – MATHEMATICS

MM-80 (TIME: 21

2 HOURS)

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.

APEX INSTITUTE Ghaziabad: 62, Nitikhand-III, Indirapuram 201010. Ph.: 01204331180 | http://apexiit.co.in/.

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.

APEX INSTITUTE Ghaziabad: 62, Nitikhand-III, Indirapuram 201010. Ph.: 01204331180 | http://apexiit.co.in/.

(b) If 3 2 3 2

,3 2 3 2

x and y

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

13. (a) Evaluate:

2 2

2 2

1 1 1tan 45 8sin 90 .

cos 30 sin 30 2

[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]

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 2 3 1 0,x x find the value of 2

2

1.x

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) If1

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 meet AC at F. Prove that1

3AF AC . [5]

Director's Message

Dear Students/Parents

APEX INSTITUTE has been established with sincere and positive resolve to do something rewarding for

ENGG. / PRE-MEDICAL aspirants. For this the APEX INSTITUTE has been instituted to provide a

relentlessly motivating and competitive atmosphere.

As It is very important to discover the basic weaknesses and problems of students not succeeding in IIT-

JEE / PRE-MEDICAL exams. In fact, as question patterns are changing, now you need to have a different

approach for these exams. As far as ENGG. / PRE-MEDICAL preparations is concerned, students have

been wasting time and energy, studying Physics, Chemistry and Maths at different places. At APEX

INSTITUTE, the scope of the subject has been deliberately made all- inclusive to free them of this

burden. APEX INSTITUTE offers you complete preparation for IIT-JEE/PRE-MED. exams under one

roof.

Grooming at the APEX INSTITUTE is done methodically focusing on understanding of the subject,

tricks of tackling the questions and above all enthusing students with self confidence, ambition and a

'never say give up' spirit. As secrets of success these are no substitutes for hard work and patience. These

qualities, the APEX INSTITUTE ensures will be developed in students in full measure perhaps luck plays

some role in one's life and career. But it is also a universal truth that before proper grasps of subject.

Intelligent preparation and perservance even adverse luck does not stand a chance.

With this mantra success is sure to come your way. At APEX INSTITUTE we strive our best to realize

the Alchemist's dream of turning 'base metal' into 'gold'.

With best wishes.

S. Iqbal (Motivator & Mentor)

APEX INSTITUTE Ghaziabad: 62, Nitikhand-III, Indirapuram 201010. Ph.: 01204331180 | http://apexiit.co.in/.

(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. [5]

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]

APEX INSTITUTE Ghaziabad: 62, Nitikhand-III, Indirapuram 201010. Ph.: 01204331180 | http://apexiit.co.in/.

Space for Rough Work

Admission cum Scholarship Test

29th March,5th & 12th April 2015

60%

Scholarship Upto

100%

Dhwani Jain is pursuing Chemical Engineering from N.U.S. (National university of Singapore) Ranked 2nd University in Asia. she was our two years classroom program Student.

Prakhar Goel is studying in Maulana Azad Medical College Delhi. He was our One year Dropper Batch Student

Prerna Kashyap is pursuing B.Tech (EC) fromNIT Kurukshetra. She was our Two years classroom program Student

Shubham Mukherjee is studying in IIT-Guwahati. He was our One year Dropper Batch Student

Shiddhant Rathore is pursuing B.Tech (Mechanical) from BITS Goa.He was our Three years Classroom Program Student.

AIR 427(GE)

Arindham Roy is pursuing B.Tech from NIT Patna. She was our Two years classroom program Student

AIR 1823(GE)

AIR 5982 (IITAdvanced)

Arindham Roy

AIR 521(GE)