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. We at 'Apex Institute' are committed to provide our students best quality education with ethics. Moving in this direction, we have decided that unlike other expensive and 5star facility type institutes who are huge investors and advertisers, we shall not invest huge amount of money in advertisements. It shall rather be invested on the betterment, enhancement of quality and resources at our center. We are just looking forward to have 'word-of-mouth' publicity instead. Because, there is only a satisfied student and his/her parents can judge an institute's quality and it's faculty members coaching. Those coaching institutes, who are investing highly on advertisements, are actually, wasting their money on it, in a sense. Rather, the money should be invested on highly experienced faculty members and on teaching gears. We all at 'Apex' are taking this initiative to improve the quality of education along-with each student's development and growth. Committed to excellence... With best wishes. S . Iqbal ( Motivator & Mentor)

1. SAMPLE PAPER
Class-VII
Foundation
For IIT-JEE
& Medical
MATHEMATICS
HEAD OFFICE: 62, NITIKHAND-III, INDIRAPURAM (NEAR JAIPURIYA MALL)
BRANCH OFFICE: VIDYA BAL BHAWAN PUBLIC SCHOOL SEC-11 VASUNDHARA
BRANCH OFFICE: C-27 R.D.C. RAJNAGAR (NEAR ICICI BANK)
CONT: - 0120-4331180, 09990495952, 09990494712 |Web: www.apexiit.co.in/

2. Head Office: 62, Nitikhand-III, Indirapuram GZB | Cont. +91-9990495952,+91-9990495952 .| www.apexiit.co.in
Sample Paper Foundation for IIT / NTSE / Olympiad
1
Time: 3 hours MM: 90
Instructions:
1. All questions are compulsory.
2. Section A carries 6 parts, one mark for each part.
3. Section B carries 10 blanks, one mark for each blank.
4. Section C carries 6 questions, two marks for each question.
5. Section D carries 8 questions, four marks for each question.
6. Section E carries 6 questions, five marks for each question.
SECTION A
1. Choose the correct option out of the following
i) The number of vertices in a cuboid
(a) 8 (b) 10 (c) 4 (d) 12
ii) (ab)
4
is equal to
(a) ab
4
(b) ba
4
(c) 4ab (d) a
4
b
4
iii) In ΔPQR, the angle opposite to side PQ is
(a) ∠P (b) ∠L (c) ∠Q (d) ∠R
iv) The supplementary angle of 44° is
(a) 36° (b) 136° (c) 44° (d) 144°
v) The product of and is 75 57
(a) 25/49 (b) 1 (c) 49/25 (d) 12 /7
vi) If the integers 11, –6, –10, 7, 8, –4 and –3 are marked on the number line, the integer on the extreme right is
(a) –10 (b) –8 (c) 11 (d) –3
SECTION B
2. Fill in the blanks:
a) 27.3 ÷ 100 = ___________.
b) The mode of 1,2,3,5,5,3,5,7,3,2,2,5 is ___.
c) A sphere has ____ edges.
d) Fractions representing the same value are called ____ fractions.
e) If a ray stands on a line, then the sum of adjacent angles so formed is ____.
f) ____ is a solid which has two edges and no vertex.
g) The reciprocal of
2 3
5 8

 is ____.
h) The value of the expression (5)
0
+ (50)
0
+ (500)
0
is __________
i) Seven times a number equals 56 : The equation for this is _____.
j) Multiplicative inverse of an integer ‘b’ is ___ .
SECTION C
3. Draw a triangular prism and write its number of vertices.
4. Solve for ‘x’ for 7x + 13 – 4x = 4x + 43 – 4x
5. Find the sum of
4 1
&
7 1 4

6. Write down a pair of a negative and a positive integer whose sum is 4.
7. Is it possible to have a triangle with sides 6 cm, 3 cm and 7 cm? Give reason(s).
8. Find the median of the given data: 22, 34, 21, 44, 21, 22, 45, 44, 22
SECTION D
9. (a) Find the probability of choosing E from the word TEMPERATURE.
(b) Find the mean of 2, 4, 8, 6, 5.

3. Head Office: 62, Nitikhand-III, Indirapuram GZB | Cont. +91-9990495952,+91-9990495952 .| www.apexiit.co.in
Sample Paper Foundation for IIT / NTSE / Olympiad
2
10. Solve for ‘p’ :
2 ( 1) 5 1
2
5 3
p p 
 
11. In a class test of 20 questions, 4 marks are awarded for every correct answer, 1 mark is deducted for every incorrect
answer and 0 is awarded for a question not attempted. What will be Nitish's score, if he gets 4 correct and 6 incorrect
answers?
12. Simplify
3
3 2 3
9 7 1 0
3 7 1 0
 
 
13. Evaluate
3 6 2 5 5 1 0
2 1 5 3 6 7 1 4
      
         
     
.
14. Find ‘x’ and 'y', if AB is a straight line.
15. In the given figure, find x, y, z.
16. Simplify: 11.001 – 2.36 + 4.965 – 5.7
SECTION E
17. a) In the given figure, l || m. Find ∠1, ∠2, ∠3 and ∠4.
b) Find the measure of an angle which is three times its supplement.
18. a) A piece of wire is 19.63 m long. If it is cut into 13 equal parts, find the length of each piece.
b) By what fraction should be multiplied to
1 1
6
get
5 5
6
?
19. Find two numbers whose sum is 16 and the first number is 6 more than the second number.
20. a) Simplify: (2
6
x 2
15
) ÷ 2
21
b) Express 231200000000 in the standard form.
21. A tree broke at a point in a storm but did not separate. The top touched the ground at a distance of 12 metre from its
base. Find the height of the tree if the length from the base to the broken point is 5 m.
22. The performance of a student in 1st term and 2nd term is given.
Construct a double bar graph and answer the following questions
i) In which subject the child has shown the maximum improvement?
ii) In which subject the performance has gone down.

4. 60%
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) from
NIT 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. He was our Two years classroom
program Student
AIR 1823(GE)
AIR 5982 (IITAdvanced)
Arindham Roy
AIR 521(GE)
Admission cum Scholarship Test