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Mathematics Grade-9 Aptitude
Assessment Tests
This book contains nine Aptitude Assessment Tests and is useful for
students and learners who are preparing for Standardized Tests,
Achievement Tests, Aptitude Tests and other competitive examinations
all over the world
Er. Sanjiva Dayal, B.Tech. (I.I.T. Kanpur)
First Edition 2015
Sanjiva Dayal Classes For Mathematics
Head Office: A-602, Twin Towers, Lakhanpur, Kanpur-208024, INDIA.
Phone: +91-512-2581426. 
Mobile: +91-9415134052. 
Email: sanjivadayal@yahoo.com.
Website: www.amazon.com/author/sanjivadayal.
ISBN-13: 978-1511696920 ISBN-10: 1511696923
Copyright © Sanjiva Dayal, Author
All rights reserved. No part of this publication may be reproduced,
distributed or transmitted in any form or by any means electronic,
mechanical, photocopying and recording or otherwise, or stored in a
database or retrieval system, including, but not limited to, in any
network or other electronic storage or transmission, or broadcast for
distance learning without the prior written permission of the Author.
i
ABOUT THE AUTHOR
Indian Institute of Technology Joint Entrance Examination (IIT-JEE) is
considered to be one of the toughest competitive entrance examinations in the
world with success ratio well below 1%. The author of this book Sanjiva
Dayal was selected in IIT-JEE in his first attempt. After completing B.Tech.
from IIT Kanpur, since the last more than 25 years, he has been teaching IIT-
JEE Mathematics to the students aspiring for success in IIT-JEE and other
engineering entrance examinations with an objective to provide training of
the highest order by way of specialized and personalized oral coaching,
teaching, training, guidance, educational facilities including tutorials, tests,
assignments, reading materials etc. and all such facilities which are helpful to
the students seeking admission in the IIT and other Engineering Institutes of
India.
His excellent teaching and result-oriented methods have combined to produce
outstanding performance by his students in the past years. A large number of
his students were selected in their First Attempt with top ranks. Most of his
students have secured admission in the IIT and other Engineering Institutes of
India and they are doing well in their engineering education and professional
career also.
Conceptual understanding of Mathematics provided by him not only helps his
students to do well in the IIT-JEE and other engineering entrance
examinations but also helps them to do well in their engineering studies
where they are pitted against the best students of the country and competition
is much more intense.
ii
ACKNOWLEDGEMENTS
I thank the Almighty God for my very existence and for providing me the
opportunity and resources to write this book.
Mother is the first teacher and father is the second teacher. My respects and
deepest gratitude to my mother Late Pushpa Dayal, my father Late Chandra
Mauleshwar Dayal, my grandfather Late Lakshmeshwar Dayal, my
grandmother Late Sarju Dayal, my maternal grandfather Late Ranbir Jang
Bahadur and my maternal grandmother Late Chandra Kishori Bahadur who
are no longer in this world but their blessings are always with me.
I am extremely thankful to all my school teachers and all my IIT Kanpur
Professors who have taught and trained me.
I am also extremely thankful to all my batch mates in IIT Kanpur because
studying and training with such brilliant persons was an amazing experience
for me which will be cherished by me throughout my life.
I am also extremely thankful to all my students because teaching and
interacting with such brilliant minds has been an amazing learning experience
for me which will be cherished by me throughout my life.
I am also extremely thankful to my wife Dr. Vidya Dayal, my sister Ms.
Smita Prakash and my niece Ms. Somya Prakash for their love, cooperation
and moral support.
I am also extremely thankful to my childhood friends Mr. Navneet Butan,
Mr. Pankaj Agarwal, Mr. Akhil Srivastava and Mr. Subir Nigam for their
love, cooperation and moral support.
I am also thankful to all other persons who have ever helped me directly or
indirectly.
I am also thankful to my student Mr. Ashutosh Verma for his help and efforts
in publishing this book.
Place: Kanpur, India.
Date: 12thApril, 2015. Sanjiva Dayal iii
PREFACE TO THE FIRST EDITION 2015
"If there is a God, he's a great mathematician."~Paul Dirac "How is an
error possible in mathematics?"~Henri Poincare "Go down deep enough
into anything and you will find mathematics."~Dean Schlicter
This book contains nine Aptitude Assessment Tests and is useful for students
and learners who are preparing for Standardized Tests, Achievement Tests,
Aptitude Tests and other competitive examinations all over the world.
All readers and students are requested and welcome to send their feedback,
comments, corrections, suggestions, improvements, mathematical theory and
questions on my email ID sanjivadayal@yahoo.com. This will help in
continuous improvement and updation of this book. All readers and students
are invited to join me as friends on Facebook at URL
www.facebook.com/sanjiva.dayal and they are also invited to join my
Facebook Group "Mathematics By Sanjiva Dayal".
Place: Kanpur, India.
Date: 12th April, 2015. Sanjiva Dayal iv
CONTENTS
About The Author i
Acknowledgements ii
Preface iii
Test Paper No. 1 1.1 
Test Paper No. 2 2.1 
Test Paper No. 3 3.1 
Test Paper No. 4 4.1 
Test Paper No. 5 5.1 
Test Paper No. 6 6.1 
Test Paper No. 7 7.1 
Test Paper No. 8 8.1 Test Paper No. 9 9.1
GRADE 9 ASSESSMENT OF MATHEMATICS
Multiple-Choice Questions: Question no. 1.1 to 1.12 
Short-Answer Questions: Question no. 2.1 to 2.5 
Tasks: Question no. 3.1 to 3.3
Test Paper No. 1 
PREPARED BY:
Sanjiva Dayal (sanjivadayal@yahoo.com)
Multiple-Choice Questions
1.1 
A car is moving on a circular path with a 
constant speed. The distance of the car from
the center of the circular path is d. Which of
the following graph shows the relationship 
between d versus time?
Circular path
Car 
Center of the circular path
(a) 
time (b) 
time
(c)
time (d) 
time
The line joining the points
x, x 2 and 2x 1,x 1 has slope equal to 1. What is the equation of this line?
(a) y x 3 (b) y x 4 (c) y 2x 1 (d) y x 2
1.3 
Which of the following pair of lines are the diagonals of a rhombus?
(a) 2x 3y 5 0 and 2x 3y 5 0
(b) 3x 4y 5 0 and 4x 3y 7 0
(c) 3x 4y 5 0 and 3x 4y 2 0
(d) 2x 3y 1 0 and 4x 6y 1 0
1.4 
Find the ratio of the perimeter of the square to the circumference of the circle.
(Use 22 ) 7
(a) 1:1 (b) 2:1 (c) 11:7 (d) 14:11
1.5
Population of the world is about 6 billion. Population of U.S.A. is about
281,000,000. What percentage of world’s population lives in U.S.A.? (1
billion = 109 )
(a) 
28.1 108
6 109 100%
7
(b) 2.81 10 100%6 109
2
.
81
10
8
(c)6 109 100%
9
(d) 6 10 100%281 108
A box contains cookies. w is the weight of the box along with n cookies in it.
w, in kg, is given by the formula 
w = 1.5 + 0.3n.
Weight of how many cookies is equal to the weight of the empty box?
(a) 4 
(b) 5 
(c) 6 
(d) 7
1.7 
Peter is x years old. Peter’s brother is 2 years older than Peter. Peter’s sister is
3 years younger than Peter. Age of Peter’s father is equal to the product of
the ages of his three children. What is the age of Peter’s father?
(a) x3 x2 6x (b) x3 x2 6x (c) x3 x2 6x (d) x3 x2 6x
1.8 
The coordinates of the two opposite corners of a rhombus are (2,3) (2,3) and
(5,7). What is the equation of the diagonal that is not passing
through these corners?
(a) 3x 4y 30 0
(b) 6x 8y 61 0
(c) 2x 3y 15 0 (5,7)(d) 2x 3y 15 0
1.9 
Triangle ABC is a right-angled triangle. What is the length of the median AD?
A
4 
(a) 5 units
(b) 6 units
(c) 7.5 unitsB D C (d) 13 units 6 What is the perimeter of the shaded square?
(a) 6 units 3 (b) 7 units
(c) 7.5 units
(d) 8.5 units
5 
1.11 
Which of the following pair of lines have the same x-intercept?
(a) 2x 3y 5 0 and 5y 4x 10 0 (b) 2x 3y 3 0 and 4x y 6 0 (c) x y 1 0 and x 3y 1 0
(d) 4x 3y 3 0 and4x y 3 0
1.12 
The sum of the interior angles of a polygon is 1080 . How many sides this
polygon has?
(a) 5 
(b) 6 
(c) 7 
(d) 8
Short-Answer Questions
2.1 
John is standing between two walls, wall A and wall B. His distance from
wall A is 6 m and from wall B is 5 m.
Wall A Wall B John 
6 m 5 m
John moved towards wall B such that his distance from wall A increased by
8%. What is the percentage decrease in his distance from wall B?
Show your work 
Answer: _____%
Equation of a line is
Ax By C 0
and A:B:C = 1:2:4. Find the slope, x-intercept and y- intercept of this line.
Draw this line on the coordinate plane given below.
y
10
9 
8 
7 
6 
5 
4 
3 
2
1 x -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
Show your work 
Answer: Slope = _______, x-intercept = _______, y-intercept = _______
ABCD is a square and points D, E, F, G are the midpoints of its A G D sides.
What percentage area of the square is shaded?
D F 
B E C Show your work 
Answer: ______%
2.4 
2000 people lived in a village in the year 1999. By the year 2004, the male
population has increased by 10% and the female population has decreased by
6%, but the total population has remained unchanged. How many males were
in the village in the year 1999?
Show your work
Answer: _______ males. Find the volume of a hollow sphere whose outer
diameter is 4 cm and thickness is 1 cm. (Use 22 ) 7
Show your work Answer: _______ cubic cm.
Tasks
3.1 
Station X and station Y are 300 km apart. Car A is at station X and car B is at
station Y.
Station 300 km Station X Y
At time t = 0, car A and car B start moving simultaneously. The movement of
the cars is in the following manner:
Stage 1: For 1 hr., car A moves towards station Y with speed 100 km per
hour and car B
moves towards station X with speed 50 km per hour.
Stage 2: For the next 1 hr., car A stops and remains stationary but car B
keeps moving towards station X with speed 50 km per hour.
Stage 3: For the next 1 hr., car A moves towards station Y with speed 100
km per hour but car B stops and remains stationary.
Stage 4: For the next 1 hr., car A keeps moving towards station Y with speed
100 km per hour and car B moves towards station X with speed 50 km per
hour.
(a) Complete the following graph for stages 2, 3 and 4. Graph for stage 1 has
been drawn.
300 Car B 
250 
200 
150 
100 
50 
Car A
0 1 2 3 4 Time, t (hr.) Show your work 
(b) Look at both the graphs and answer the following questions. (i) After
what time the cars meet?
Answer: _____ hrs. 
(ii) When car A reaches station Y, how far is car B from station X?
Answer: _____ km. 
(iii) What is the distance between the cars after 1 hr.?
Answer: _____ km. 
(iii) What is the distance between the cars after 2 hr.?
Answer: _____ km.
Show your work In a triangle ABC, AD BC, BE AC and CF AB.A AD, BE and
CF meet at P. 
ABC = 56 and ACB = 42 . 
E (a) Write the correct answers. F P (i) BAC = _____ 
(ii) FPA = _____ 
(iii) APE = _____
(iv) EPC = _____ B D C (v) CPD = _____ 
(vi) DPB = _____ 
(vii) BPF = _____
Show your work 
(b) To make the following statements true, write one of the triangles ACD,
ACF, ABD in the spaces below.
(i) FPA is similar to _______ (ii) PEA is similar to _______ (iii) EPC is
similar to _______
Show your work Peter has a rectangular piece of paper with corners 5 cm C
marked A, B, C, D. Length of the sides of the paper 
are 3 cm and 5 cm. Peter folded the paper such that 
the corner D touches side AB as shown in figure.E 3 cm
(a) Write the correct answers.
(i) Length of side BD = ______ cm
(ii) Length of side AD = ______ cm A D B
Show your work 
(b) Are BDC and DAE similar? Yes No Explain your answer.
Show your work (c) Write the correct answers.
(i) Length of side AE = ______ cm
(ii) Length of side DE = ______ cm
(iii) Area of DEC = _______ sq. cm 
(iv) Area of trapezoid ABCE = ______ sq. cm
(v) Ratio of area of DEC to area of trapezoid ABCE = _________
Show your work
ANSWERS
1.1 The car is moving on the circular path, hence the distance of the car from
the center of the circular path is a constant and it does not change with time. 
Answer: (d)
1.2 Slope of the line = 1
x 1 x 212x 1 x
1 1x 1
x 1 1
x 2
Hence, the points are (2,4) and (5,3) 
Hence, the equation of the line is 
y 4 1 x 2
y x 2. 
Answer: (d) 
1.3 Diagonals of a rhombus are perpendicular to each other.
Slope of line 3x 4y 5 0 is 3 and slope of line 4x 3y 7 0 is 4 . 4 3
Hence, the product of their slopes is –1. Hence these lines are perpendicular
and they can be the diagonals of a rhombus. The other three pair of lines are
not perpendicular. Hence, they cannot be the diagonals of a rhombus.
Answer: (b)
1.4 Let the diameter of the circle = d
Hence, length of the side of the square = d
Hence, perimeter of the square = 4d
Hence, circumference of the circle =
d22d7
Hence, Perimeter : circumference = 4d : 22d = 28 : 22 = 14 : 117
Answer: (d) 
1.5 Population of the world = 6 billion = 6 109
Population of U.S.A. = 281,000,000 = 2.81 108
Hence, percentage of world’s population living in U.S.A. =
2.81 108 6 109 100%
Answer: (c)
1.6 w = 1.5 + 0.3n
Hence, if 1 cookie is added, the weight changes by 0.3 kg
Hence, weight of 1 cookie = 0.3 kg 
When there is no cookie in the box, n = 0, w = 1.5 kg
Hence, weight of empty box = 1.5 kg
Number of cookies whose weight equals weight of empty box =
1.5 50.3
Answer: (b) 
1.7 Age of Peter = x years
Age of Peter’s brother = x + 2 years 
Age of Peter’s sister = x – 3 years
Age of Peter’s father = x x 2 x 3 x x2 2x 3x 6 x x2 x 6 x3 x2 6x
Answer: (c)
1.8 Slope of the diagonal passing through the given corners =
7 3 4
5 2 3
Diagonal of a rhombus are perpendicular and they bisect each other.
Hence, the slope of the other diagonal =
3
4
Hence, midpoint of the diagonals is 2 5,3 7 , which is 7,52 2 2
Hence, equation of the other diagonal is
y
5
3x 7
4 2
4
y
20
3
x
21
2
8y 40 6x 21
6x 8y 61 0
Answer: (b)
1.9 D is the mid point of BC
Length of BC = 6 units 
Hence, length of BD = 3 units 
ABD is right angled triangle
Hence, by Pythagorus theorem, 
AD2 AB2 BD2
AD2 42 32 16 9 25
AD 5 units
Answer: (a) 
1.10 Let the length of the side of the square = x unitsAHence, BD = DE = x 3-x E AB
= 3, hence AD = 3 – x D x 
DE BC, hence DEA = BCA (corresponding 
angles) B C ADE = ABC = 90
Hence, ADE and ABC are similar because two angles are equal. 
AD DEHence, AB BC
3 x x
3 5
15 5x 3x
8x 15
15x 8
Hence, perimeter of the square = 4x 415 7.5 units8
Answer: (c)
1.11 x-intercept of the line Ax By C 0 is C . A
x-intercept of the line 2x 3y 5 0 and 5y 4x 10 0 is 5 , hence they have the 2
same x-intercept. 
Answer: (a) 
1.12 Sum of the interior angles of a n-sided polygon = n 2 180
Hence, n 2 180 1080
1080n 2 180
n 2 6
n 8
Answer: (d) 
2.1 John’s distance from wall A = 6 m
Increase in distance from wall A = 8 612 m 100 25
Hence, decrease in distance from wall B = Increase in distance from wall A =
12 m 25
John’s distance from wall B was = 5 m
Hence, percentage decrease in his distance from wall B = 12 1 100 9.6%25 5
Answer: 9.6%
2.2 A:B:C = 1:2:4 
Slope = A 1 ; x-intercept = C 4; y-intercept = C 4 2B 2 A B 2
y 
Answer: Slope =
10
9 
8 
7 
6 
5 
4 
3 
2
1 x -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
1 ; x-intercept = 4; y-intercept = 22
2.3 Let the length of the side of the square = 2xA G D D, E, F, G are
midpoints of the sides. 
Hence, AD = AG = CE = CF = xF Hence,D (area of ADG) + (area of CEF)B E
C
= 
1x2 1x2
2 2
= x2
Hence,
area of the shaded region 
= area of square ABCD (area of ADG) (area of CEF) = 2x2 x2
= 3x2
Hence, percentage of shaded area = 
3x2
4x2 100 75%
Answer: 75%
2.4 Let the number of males in the year 1999 = n 
Hence, number of females in the year 1999 = 2000 n
Male population increased by 10% by the year 2004.
Hence, male population in the year 2004 =
n10 n110n11n100 100 10
Female population decreased by 6% by the year 2004. Hence, female
population in the year 2004
= 2000 n6 2000 n100
2000 n 1206 n100188094 n100
Total population remained unchanged.
Hence, 11n 188094 n 200010 100
16 n 120100
n 120100 75016
Answer: 750 males 
2.5 Outer diameter of the sphere = 4 cm
Hence, outer radius of the sphere = 2 cm
Thickness = 1 cm
Hence, radius of the spherical hollow region = 2 cm – 1 cm = 1 cm 
Hence, volume of the hollow sphere
= Volume of the outer spherical region – Volume of the spherical hollow
region
=
4 23 4 13 cubic cm 3 3
=4 22 84 22 cubic cm 3 7 3 7
4 22 7 cubic cm3 7
=88 cubic cm 3
=291 cubic cm 3
Answer: 291 cubic cm 3
3.1 (a) 
During stage 2, car A remains stationary. Hence, distance of the car A from
station X is a constant and so its graph must be a horizontal line. Car B
moves towards station X with speed 50 km per hour, hence during one hour,
distance of car B from station X decreases by 50 km. 
During stage 3, car A moves towards station Y with speed 100 km per hour,
hence during one hour, distance of car A from station X increases by 100 km.
Car B remains stationary, hence distance of car B from station X remains
constant.
During stage 4, car A moves towards station Y with speed 100 km per hour,
hence during one hour, distance of car A from station X increases by 100 km.
Car B moves towards station X with speed 50 km per hour, hence during one
hour distance of car B from station X decreases by 50 km.
300 Car B
250 
200 
150 
100 
50 
Car A
0 1 2 3 4 
Time, t (hr.)
3.1 (b) 
(i) Answer: 3 hrs.
(ii) Answer: 150 km. 
(iii) Answer: 150 km. 
(iv) Answer: 100 km.
3.2 (a) 
(i). A 
BAC = 180 ABC ACB 
= 180 56 42 = 82E
(ii).F P 
ABD is a right angled triangle
Hence, BAD = 90 ABD = 90 56 = 34
AFP is a right angled triangleB D C 
Hence, FPA = 90 FAP = 90 34 = 56
(iii).
ADC is a right angled triangle
Hence, DAC = 90 ACD = 90 42 = 48
AEP is a right angled triangle
Hence, APE = 90 EAP = 90 48 = 42
(iv).
AFC is a right angled triangle
Hence, ACF = 90 FAC = 90 82 = 8
CEP is a right angled triangle
Hence, EPC = 90 ECP = 90 8 = 82
(v). 
CPD = FPA = 56 (They are vertical angles)
(vi).
DPB = APE = 42 (They are vertical angles)
(vii).
BPF = EPC = 82 (They are vertical angles)
3.2 (b) 
(i) FPA is similar to ABD because both are right angled triangle and FAP is 
common to both 
(ii) PEA is similar to ACD because both are right angled triangle and EAP is 
common to both 
(iii) EPC is similar to ACF because both are right angled triangle and ECP is 
common to both 
3.3 (a) 
(i) DBC is a right angled triangle, BC = 3 cm, CD = 5 cm
Hence, by Pythagorus theorem
BD2 CD2 BC2 52 32 25 4 16
So, BD = 4 cm 
(ii) AD = AB – BD = 5 cm – 4 cm = 1 cm
3.3 (b) AED and BDC are complimentary angles of ADE hence they are
equal. 
Hence BDC and DAE are similar because both are right angle triangle and
one of
their other angle are equal.
3.3 (c) 
(i) BDC and DAE are similar
hence AE BD AE4 14 cm AD BC 3 3
(ii) BDC and DAE are similar
hence DE CD DE5 15 cm AD BC 3 3
(iii) Area of DEC = 1 DE CD1 5 525 sq. cm2 2 3 6
(iv) Area of trapezoid ABCE =1 AE BC AB1 4 3 51 13 585 sq. 2 2 3 2 3 6
cm 
(v) Ratio of area of DEC to area of trapezoid ABCE =25:85 5:136 6
THIS PAGE IS INTENTIONALLY LEFT BLANK GRADE 9
ASSESSMENT OF MATHEMATICS
Multiple-Choice Questions: Question no. 1.1 to 1.12 
Short-Answer Questions: Question no. 2.1 to 2.5 
Tasks: Question no. 3.1 to 3.3
Test Paper No. 2 
PREPARED BY:
Sanjiva Dayal (sanjivadayal@yahoo.com)
Multiple-Choice Questions
1.1 
A cone of height 4.5 cm is melted and formed into a sphere of diameter 9 cm.
What is the radius of the cone?
(a) 9 cm 
(b) 10 cm
(c) 11 cm
(d) 12 cm
1.2 
$1000 is to be divided among Tom, Jack, Mary and Kate. 30% of the money
was given to Tom, 30% of the balance amount was given to Jack, 30% of the
balance amount was given to Mary. The remaining amount of money was
given to Kate. Who received the largest amount of money?
(a) Tom (b) Jack (c) Mary (d) Kate
1.3 
Two sides of the right-angled triangle are x y 1 0 and 2x 4y 7 0. Which of the
following line cannot be the third side of the triangle?
(a) x y 2 0 (b) 2x 2y 7 0 (c) 2x y 1 0 (d) 2x 3y 7 0
1.4 
Two trains are 1000 km apart. They start moving towards each other. One
train is moving with a speed of 110 km per hour and the other train with a
speed of 90 km per hour. The distance between the trains after time t is d.
What is the formula of d, in km, as a function of time t, in hr?
(a) d = 1000 – 20t (b) d = 1000 + 20t (c) d = 1000 – 200t (d) d = 1000 + 200t
Which of the following line does not have x-intercept?
(a) y x (b) y x (c) y 3 (d) x 4
1.6 
A hollow cylindrical vessel has radius 3 inches and height 8 inches. What is
the greatest length of the stick that can be kept inside the vessel? (Stick
should not be bent or broken and no part of the stick should be outside the
vessel)
(a) 6 inch (b) 8 inch (c) 10 inch (d) 12 inch
1.7 
Length of bacteria is about 0.000003 inch. How many bacteria would fit in 1
mm length? (1 inch = 2.54 cm)
2.54(a) 3 107 10 (b) 
10
3 106 2.54 (c)
2.54 10
3 106
1(d) 3 106 2.54 10
1.8 
Lines 2x 3y 7 0 and x y 3 0 are the diameter of a circle. Which of the
following point is the center of the circle?
(a) (1,2) (b) (3,2) (c) (2,1) (d) (2,3) The length, width and height of a
rectangular prism are x y units, 2x y units and x 2y units respectively. What is
the surface area of the rectangular prism?
(a) 8x2 20xy 8y2 sq. units (b) 10x2 22xy 10y2 sq. units (c) 4x2 10xy 4y2 sq.
units (d) 5x2 11xy 5y2 sq. units
1.10 
Peter scored 20% marks in an examination and he failed by 30 marks. Mary
scored 30% marks in the same examination and she failed by 10 marks. What
is the passing percentage of marks in the examination?
(a) 35% (b) 40% (c) 45% (d) 50%
1.11 
The angles of a hexagon are x , x 10 , x 20 , x 30 , x 40 and x 50 . What is x?
(a) 75
(b) 85
(c) 95
(d) 105
1.12 
ABC is an isosceles triangle. AB = AC, EF BC and
EAC = 128 . What is BAC? E A F
(a) 52
(b) 54
(c) 66
(d) 76
B C
Short-Answer Questions
2.1 
The height of a tree, h, and the diameter of the tree, d, are tabulated below at
different time, t.
t (years) 1 3 4 7 
h (ft) 3 4 5 6 
d (inch) 2 4 5 8
Plot these values in the graphs given below and check whether h and d are
linear functions or non- linear functions of time. 
8 8 
7 7 6 6 
5 5 4 4 
3 3 2 2 
1 1 
0 1 2 3 4 5 6 7 t (years)
0 1 2 3 4 5 6 7 t (years)
Show your work
Answer: 
h is a Linear function d is a Linear function Non-linear function Non-linear
function The vertices A, B, C of a triangle are (3, 1), (2,3) and A (1,1)
respectively. What is the equation of the median
AD? 
B D C Show your work 
Answer: Equation of the median AD is __________________
2.3 
Peter has a rectangular piece of board. He cut out a circular disk and a
semicircular disk from the board. What percentage area of the board is left
with him?
(Use 3.14. Round off your answer to the nearest tenth)
Show your work 
Answer: ______ % The midpoints of the sides of a triangle are (1,4), (4,8)
andA (5,6). What is the equation of the side BC?
(1,4) (5,6) 
B (4,8) C Show your work
Answer: Equations of the side BC is ________________________ Figure
ABCD is a square having side length a. Figure CEFG is a A a D rectangle
having width b. Figure DBF is a straight line. Perimeter of
the square ABCD is equal to the perimeter of the rectangle CEFG.
What is the ratio a:b?
E B C b 
F G
Show your work Answer: a:b = _______
Tasks
3.1 
When wheels of a car make one revolution, the distance moved by the car is
equal to the circumference of the wheel.
d 
d 
When the diameter of the wheels is d, in meters; and the wheels are rotating
at the rate of n revolutions per second, the velocity of the car v, in meters per
second, is given by the formula
v dn (Use 22 ).7
(a) Diameter of the wheels of a car is 70 cm.
(i) Express v as a function of n.
Answer: ________ 
(ii) What is the speed of the car when the wheels are rotating at the rate of 5 
revolutions per second?
Answer: _______ meters per second.
Show your work (b) Due to the leakage of air, the diameter of the wheels
decreases by 50%. (i) Expressv as a function of n after leakage of air.
Answer: ____________
(ii) What should be the rate of rotation of wheels after leakage of air in order
to 
maintain the same speed as before?
Answer: _______ revolutions per second.
(iii) What is the percentage increase in the rate of rotation of wheels?
Answer: ____ %
Show your work 
(c) Draw graphs of v versus n before the leakage of air and after the leakage
of air.
12
10
8 
6 
4 
2 
0 1 2 3 4 5 6 7 8 9 10 11
n (revolutions per second) Show your work
There are two rectangular sheet of paper of same size, each measuring 22 cm
in length and 11 cm in width. A cylinder A was made by rolling one sheet of
paper along its length and another cylinder B was made by rolling the other
sheet of paper along its width.
(Use
22 ) 7
11 cm 22 cmPaper Paper 22 cm11 cm
Cylinder
A Cylinder B (a) The radius of Cylinder A = _____ cm
Show your work 
(b) Volume of Cylinder A = _____ cubic cm
Show your work (c) The radius of Cylinder B = _____ cm
Show your work 
(d) Volume of Cylinder B = _____ cubic cm
Show your work 
(e) Ratio of volume of Cylinder A to volume of Cylinder B = _______
Show your work In the ABC, ACB=78 . AP is the angular bisector ofC CAB.
BP is the angular bisector of CBA. 
78
P 
Answer the following questions. A B 
(a) Is APB = 180 ( PAB + PBA)? Yes No
Show your work 
(b) Is APB = 1801 CAB CBA ? Yes No2
Show your work (c) Is APB = 901 ACB? Yes No2
Show your work 
(d) APB = _____ degrees.
Show your work 
ANSWERS
1.1 Let the radius of the cone = x cm
Given; height of the cone = 4.5 cm
Hence, volume of the cone = 1 x2 4.5 cubic cm3
Given; diameter of sphere = 9 cm, hence radius = 4.5 cm
Hence, volume of the sphere = 4 4.53 cubic cm3
Both the volumes should be equal 
1 x2 4.54 4.53
3 3
x2 4 4.52
x 9 cm 
Answer: (a) 
1.2 30% of $1000 was given to Tom
Hence, money received by Tom = 30 $1000 = $300 100
Hence, balance amount = $1000 $300 = $700
30% of balance amount was given to Jack
Hence, money received by Jack = 30 $700 $210100
Hence, balance amount = $700 $210 = $490 
30% of balance amount was given to Mary
Hence, money received by Mary = 30 $490 $147100
Hence, remaining amount received by Kate = $490 $147 = $343 Hence, Kate
received the largest amount of money 
Answer: (d)
1.3 Slope of the line
x y 1 0 is 1 
Slope of the line 
2
x
4
y
7
0
is
1
2
These two given sides are not perpendicular, hence the third side must be
perpendicular to one of these sides 
Slope of the line 2x 3y 7 0 is 2 and so this line is not perpendicular to any of3
the given sides and so it cannot be the third side. The other three lines are
perpendicular to one of the given sides and they can be the third side.
Answer: (d)
1.4 Trains are moving towards each other at speeds 110 km per hour and 90
km per hour. Hence, the distance between them is decreasing at the rate of
110 + 90 = 200 km per hour. Initially the distance between them is 1000 km.
Hence, d = 1000 – 200t
Answer: (c)
1.5 Line y = 3 is parallel to x-axis and so it does not have x-intercept. 
Answer: (c)
1.6 The position of the largest stick is as shown in the figure
Diameter of the cylindrical vessel = 2 3 = 6 inches
Let the length of the stick = l8 Hence, by Pythagorus theorem
l2 62 82 36 64 1006 l 10 inches
Answer: (c)
1.7 Length of bacteria = 0.000003 inch = 3 106 inch = 3 106 2.54 10 mm
1Hence, number of bacteria in 1 mm = 3 10 6 2.54 10
Answer: (d) 
1.8 Diameters of a circles meet at the center 
Hence, the center of the circle is the point which lies on both the 
diameters
Point (2,1) lies on the diameter 2x
2 2 3 1 7 0
Point (2,1) lies on the diameter x 3y 7 0 because
y 3 0 because 2 1 3 0 The other three points do not lie on both the diameters
Hence, center of the circle is (2,1)
Answer: (c)
1.9 Surface area of the prism 
2 l b l h b h
2 x y 2x y x y x 2y 2x y x 2y
2 2x2 xy 2xy y2 x2 2xy xy 2y2 2x2 4xy xy 2y2 2 5x2 11xy 5y2
10x2 22xy 10y2
Answer: (b) 
1.10 Let the maximum marks in the examination = x
Peter scored 20% marks
Hence, Peter scored =
20 x marks 100
Peter failed by 30 marks
Hence, passing marks = 20 x 30 marks100
Mary scored 30% marks
Hence, Mary scored = 30 x marks100
Mary failed by 10 marks
Hence, passing marks = 30 x 10 marks100
Hence,
20 x 30 30 x 10100 100
10 x 20100
x 200
Hence, passing marks = 30 200 10 60 10 70 marks100
Hence, percentage passing marks = 70 100 35%200
Answer: (a) 
1.11 Sum of the angles of n-sided polygon = (n – 2) 180
Hence, sum of the angles of a hexagon = (6 – 2) 180 = 720
Hence,
x x 10 x 20 x 30 x 40 x 50 720
6x 150 720
6x 570
x 95
Answer: (c)
1.12 FAC = 180 EAC = 180 128 = 52E A F (Supplementary angles)
BCA = FAC = 52 (Alternate angles)
CBA = BCA = 52 (Equal angles of isosceles 
triangle) 
BAC = 180 CBA BCA B C = 180 52 52 = 76
Answer: (d) 
2.1
8 8 
7 7 6 6 
5 5 4 4 
3 3 2 2 
1 1 
0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 t (years) t (years)
Graph of h versus t is non-linear but graph of d versus t is linear. Answer:
h is a non-linear function of t.
d is a linear function of t.
2.2 D is the midpoint of BC 
Coordinates of B and C are (2,3) and (1,1) respectively Hence, coordinates of
D are
2 1,3 1 , which is 3,22 2 2
Coordinates of A are (3, 1)
Hence, slope of AD = 2 1 3 2 6 23 3 3 6 3
2
Hence, equation of AD is y 1 2 x 3 or y 1 2x 6 or 2x y 5 0 Answer: Equation
of the median AD is 2x y 5 0.
2.3 Let the radius of the disks = r
Hence, area of the circular disk = r2
Hence, area of the semicircular disk = 
1r2 2
Length of the rectangle = 3 r
Width of the rectangle = 2r 
Area of the rectangle = 3r 2r 6r2
Area of the board left =
6
r
2 r2 1 r2 6r2 3 r2
2 2
6r2 3 r2 63 3.14 Percentage area of the board left =
2
6r2 100%2 100% 21.5%6
Answer: 21.5%
2.4 Line joining midpoints of the two sides of a triangle is parallel to the third
side.
6 4 1Slope of the line joining points (1,4) and (5,6) = 5 1 2
1Hence, slope of BC = 2
BC passes through the point (4,8) 
Hence, equation of BC is y 81 x 4 or 2y 16 x 4 or x 2y 12 02
Answer: Equation of the side BC is x 2y 12 0
. 
2.5 ADB = 45 (Angle between diagonal and side of a square)A a D
AD EC, hence, EBF = ADB = 45
FEB = 90 , hence EFB = 180 90 45 = 45 = EBF
Hence, BE = EF = b E B C 
Hence, length of the rectangle = EC = BE + BC = b + ab 
F G Hence, perimeter of rectangle = 2(a + b + b) = 2a + 4b
Hence, perimeter of the square = 4a 
Perimeter of square and rectangle are equal
2a + 4b = 4a 
2a = 4b 
a = 2b
Hence, a: b = 2:1 
Answer: 2:1
3.1 (a) 
(i) Diameter of the wheel = d = 70 cm = 0.7 m 
Hence,
v22 0.7 n 2.2n7
v 2.2n
(ii) Given; n = 5 revolutions per second 
Hence, v 2.2 5 11 meters per second 
v 11 meters per second
3.1 (b) 
(i) Diameter of the wheel decreases by 50%
Hence, after leakage, d = 50 0.7 0.35 cm 100
Hence, v22 0.35 n 1.1n7
v 1.1n (After leakage of air)
(ii) Speed after leakage is same as before, which is 11 meters per second
Hence, 11 1.1n n11 10 revolutions per second 1.1
n 10 revolutions per second
(iii) Rate of rotation has increased from 5 revolutions per second to 10
revolutions per second
Hence, percentage increase in the rate of rotation of wheels =10 5 100%
100%5
Percentage increase in the rate of rotation of wheels = 100%
3.1 (c) v 2.2n (Before leakage of air)
v 1.1n (After leakage of air)
12
10 Before
8 leakage Afterof air leakage of 6 air 
4 
2 
0 1 2 3 4 5 6 7 8 9 10 11
n (revolutions per second)
3.2 (a) Let the radius of Cylinder A = r cm
Length of the paper = circumference of the Cylinder A = 22 cm Hence, 2 r 22
222 r 227
r 227 1 cm 22 2
r 3.5 cm 
Answer: The radius of Cylinder A = 3.5 cm
3.2 (b) Width of the paper = height of the Cylinder A = 11 cm Hence,
volume of Cylinder A = 
r
2 height22 3.52 1122 7 2 7 7 2 11 423.5 cubic cm
Answer: Volume of Cylinder A = 423.5 cubic cm 3.2 (c) Let the radius of
Cylinder B = R cm
Width of the paper = circumference of the Cylinder B = 11 cm Hence, 2 R 11
222 R 117
R 117 1 cm 22 2
R 1.75
cm 
Answer: The radius of Cylinder B = 1.75 cm
3.2 (d) Length of the paper = height of the Cylinder B = 22 cm Hence,
volume of Cylinder B
22
1
.
75
2
22
227
2
= R2 height7 7 4 22 211.75
cubic cm
Answer: Volume of Cylinder B = 211.75 cubic cm
3.2 (e) Ratio of volume of Cylinder A to volume of Cylinder B =
423.5:211.75 = 2:1
Answer: Ratio of volume of Cylinder A to volume of Cylinder B = 2:1 3.3
C 78
P 
A B (a) APB + PAB + PBA = 180 (Angles of a triangle) Hence, APB = 180 (
PAB + PBA) 
Answer: Yes
3.3 (b) PAB =
1 CAB (AP is angular bisector of CAB) 2
PBA = 1 CBA (BP is angular bisector of CBA) 2
Hence, APB = 180 ( PAB + PBA) = 1801 CAB CBA2
Answer: Yes
3.3 (c) CAB + CBA + ACB = 180 (Angles of a triangle) 
APB = 1801 CAB CBA2
= 1801 180 ACB2
= 180 901 ACB2
= 901 ACB2
Answer: Yes
3.3 (d) APB = 901 ACB 901 78 90 39 1292 2
Answer: 129
THIS PAGE IS INTENTIONALLY LEFT BLANK GRADE 9
ASSESSMENT OF MATHEMATICS
Multiple-Choice Questions: Question no. 1.1 to 1.12 
Short-Answer Questions: Question no. 2.1 to 2.5 
Tasks: Question no. 3.1 to 3.3
Test Paper No. 3 
PREPARED BY:
Sanjiva Dayal (sanjivadayal@yahoo.com)
Multiple-Choice Questions
1.1 
Peter has 50 coins. n coins are nickel and the rest are dimes. Q, in dollars, is
the total amount of money with Peter. What is the formula of Q?
(a) Q = 5 – 0.05 n
(b) Q = 50 – 
(c) Q = 500 – 
(d) Q = 50 – 0.1n
1.2 
Which of the following geometrical objects has same number of triangular
faces as square pyramid?
(a) Triangular prism (b) Triangular pyramid (c) Cone
(d) Hexagonal pyramid
1.3 
Speed of light is 300,000,000 meter per second. Distance of Sun from Earth
is 150,000,000 km. How many minutes light takes to reach Earth from Sun?
(a)
1.5 108 1000 minutes3 108 60
(b) 15 108 1000 minutes3 108 60
(c)
1.5 108
3 108 60 minutes 15
10
8
(d) 1000 minutes3 108
1.4
Vertices A, B, C of a triangle are (2,1), (3,2) and A (5, 4) respectively. What is the
equation of the line
which passes through A and is perpendicular to the 
median AD?
(a) x y 1 0
(b) x y 1 0B D C (c) x y 1 0
(d) x y 1 0
A car is moving on a road with constant speed. A building is situated away
from the road. d is the distance of the car from the building.
Building
d 
Car Road
Which of the following graphs show the relationship between d versus time?
(a) d 
time 
d 
(b) 
time 
(c)d 
time 
(d) d 
time
1.6 
Cost price of 10 toys is equal to the selling price of 16 toys. What is the profit
or loss percentage?
(a) 28% profit (b) 37.5 % profit (c) 28% loss (d) 37.5% loss a3b2c6 4 balls are
distributed equally among a2b5c4 2 boys. How many balls each boy
has? 
(a)
a6c16 b2
a
8c16
(b) b2
8c14
(c)
a
b2
a
6 c14
(d) b
1.8 
Which of the angle is three times of its complementary angle?
(a) 135 (b) 67.5 (c) 50.5 (d) 45
1.9 
Surface area of the square based pyramid is 75 sq. cm. What is the area of
each triangular face?
(a) 18.75 sq. cm (b) 25 sq. cm (c) 12.5 sq. cm (d) 15 sq. cm
5 cm
1.10 
A point A is in second quadrant and a point B is in fourth quadrant. Which of
the following statement is always true?
(a) Line joining A and B has negative slope (b) Line joining A and B has
positive slope (c) Line joining A and B has slope greater than 1 (d) Line
joining A and B has slope between 0 and 1 A line is drawn through the points
(x,1) and (3,2). The slope of this line is 1 . What is x? x
(a) 1 
(b) 
3
2
(c) 2 
(d) 3
1.12 
Which of the following statement is always true?
(a) Similar triangles are congruent (b) Congruent triangles are similar (c)
Similar triangles are equal in area (d) Similar triangles are equal in perimeter
Short-Answer Questions
2.1 
Draw the lines y x 2 and y 2x 3 on the coordinate plane given below and find
the coordinates of their point of intersection.
y
10
9 
8 
7 
6 
5 
4 
3 
2 
1
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10x 
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
Show your work 
Answer: Coordinates of point of intersection is _______. Find the number x
such that the area of the figure given below is 50 sq. units.
6 x 4 
12 Show your work
Answer: x = _____ units. The ratio of number of boys to girls is 2:3. Number
of girls increased from 12 to 16. What is the ratio of boys to girls now?
Show your work 
Answer: _____.
2.4 
The average age of 5 children in a family is 9 years. The average age of these
5 children together with their parents is 20 years. The father is 5 years older
than the mother. What is the age of the father?
Show your work 
Answer: Age of the father is _____ years. What is the ratio of the total area
of the three circles to the A D area of the rectangle ABCD?
B C Show your work 
Answer: Ratio is _______
Tasks
3.1 
A tank contains 180 liters of alcohol. Everyday 60 liters of liquid is taken out
of the tank and
60 liters of water is put in it.
(a) Calculate the quantity of alcohol remaining in the tank after 1 day, 2 days
and 3 days and complete the table given below. (Round off your answer to
the nearest tenth) 
Days 0 1 2 3 
Quantity of alcohol 180in the tank (liters) 
Show your work 
(b) Complete the graph of quantity of alcohol in the tank versus days.
180
170
160
150
140
130
120
110
100
90
80
70
60
50
40
30
20
10
0
01 23 Days
(c) Look at the graph and check whether the quantity of alcohol as a function
of days is a linear function or a non-linear function. Explain your answer.
Linear function Non-linear function
Explain your answer
3.2 
A metal cylinder has height 12 cm and diameter 10 cm. A 
conical hole is drilled in this metal cylinder. The height and 10 radius of
conical hole is same as that of the cylinder. The solid 
remaining after drilling the conical hole is shown in the figure.
(Use = 3.14)
12 
(a) What is the volume of the conical hole? Answer: ______ cubic cm
Show your work 
(b) What is the volume of the remaining solid? Answer: ______ cubic cm
Show your work (c) What is the slant height of the conical hole? Answer:
______ cm
Show your work 
(d) What is the surface area of the remaining solid? Answer: ______ sq. cm
Show your work 
3.3 
A circle is drawn with center O. A point P is taken on its Q circumference. From the point P,
two chords PQ and PR are drawn. Lengths of PQ and PR are equal to the
radius of the circle. 
P O 
(a) QPR = ______ R 
Show your work 
(b) PQO = ______ 
Show your work 
(c) PRO = ______ 
Show your work 
(d) QOR = ______ 
Show your work 
(e) Is figure PQOR a rhombus? Yes No
Show your work
ANSWERS
1.1 Peter has 50 coins out of which n coins are nickel.
Hence, number of coins which are dimes = 50 – n
Value of n nickel coins = $0.05n
Value of (50 – n) dimes = $(50 – n) 0.10 = $(5 – 0.1n) Total value of coins =
$(0.05n + 5 – 0.1n) = $(5 – 0.05n) Hence, Q = 5 – 0.05n
Answer: (a)
1.2 Square pyramid and triangular pyramid both have 4 triangular faces
Answer: (b) 
1.3 Speed = 300,000,000 meters per second= 3 108 meters per second
Distance = 150,000,000 km = 1.5 108 km = 1.5 108 1000 meters
Distance
1
.
5
10
8 1000 seconds = 1.5 108
Time =1000 minutesspeed 3 108 3 108 60
Answer: (a) 
1.4 D is the midpoint of BC.
Hence, coordinates of D are 3 5,2 4 or (4, 1)2 2
Coordinates of A are (2,1) 
Hence, slope of AD =1 1 2 14 2 2
Hence, slope of line which is perpendicular to AD is 1
Hence, equation of line which is perpendicular to AD and passes through A is
y 1 1 x 2 or x y 1 0
Answer: (d)
1.5 As the car moves along the road, its distance decreases with time and then
it increases with time. The least distance between the car and the building is
the distance between the building and the road.
Answer: (d)
1.6 Let the cost price of 1 toy = $ x
Hence, cost price of 10 toys = $10x
Hence, selling price of 16 toys = cost price of 10 toys = $10x
10x $5xHence, selling price of 1 toy = $16 8
5x x, hence selling price is less than cost price8
x 5
Hence, loss percentage = 8 x 3 100% 37.5%x 100%8
Answer: (d) 
1.7 Number of balls with each boy = 
a3b2 c64 a3 4b2 4c6 4 a12b8c24 a12 4c24 8 a8c16
2a2 2b5 2c4 2a4b10c8b10 8b2a2b5c4
Answer: (b) 
1.8 Let the angle = x
Hence, complementary angle = 90 x
Angle is three times its complementary angle
Hence, x = 3(90 x) 
x = 270 3x 
4x = 270
x =
270 67.53
Answer: (b) 
1.9 Base is square of side length = 5 cmHence, area of base = 5 5 sq. cm = 25 sq. cm
Pyramid has 4 triangular faces.
Hence,
Surface area of the pyramid = Area of square base + Area of four triangular
faces
Hence, Area of four triangular faces = 75 sq cm – 25 sq. cm = 50 sq. cm
Hence, area of each triangular face = 50 12.5 sq. cm4
Answer: (c)
1.10 Line joining point A and B will be always slant downward from left to
right, hence slope 
is always negative.
Answer: (a)
1.11 Slope of the line joining the two given points =
2 1 1 3 x 3 x
1The slope is given to be x
1 1Hence, 3 x x
x 3 x
2x 3
3x 2
Answer: (b) 
1.12 Congruent triangles are similar because their angles are equal.
Answer: (b)
2.1 Line
y x 2 has slope 1 and y-intercept 2 Line y 2x 3
has slope 2 and y-intercept 3 
y
10
9 
8 
7 
6 
5 
4 
3 
2 
1
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10x 
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
Answer: Coordinates of point of intersection is (5,7).
2.2 Draw a rectangle with dotted lines as shown in 
the figure2 
One side of the rectangle with dotted sides is6 x 
6 – 4 = 2 units and the other side is x units4 The area of the given figure
= (Area of rectangle of sides 12 units and 6 12 units) (Area of rectangle of
sides 2 units and x units)
= 12 6 – 2 x
= 72 – 2x
Area given is 50 sq. units
Hence, 72 – 2x = 50 2x = 72 – 50 2x = 22 x = 11 units Answer: x = 11 units.
2.3 Ratio of boys to girls = 2:3 
Number of girls = 12 
Hence, number of boys =
2 12 83
Now, number of girls increased to 16 Hence, ratio of boys to girls = 8:16 =
1:2 Answer: 1:2
2.4 Let the age of father = x years 
Hence, age of mother = x – 5 years
Average age of 5 children = 9 years 
Hence, total age of children = 9 5 = 45 years
Hence, average age of children together with their parents =
45 x x 5 40 2x 7 7 years
But average age of the family is 20 years (Given)
Hence, 40 2x 207
40 2x 140
2x 100
x 50
Answer: Age of the father is 50 years.
2.5 Let the diameter of the two small spheres = x units A D Hence, diameter
of the large sphere = 2x unitsx Hence, radius of the large sphere = x units2x
Hence, sides of the rectangle are 2x units and 3x units 
Hence, the total area of the three circlesB C 
= 
x
2 x2 x2 3 x2
4 4 2 sq. units
Hence, the area of the rectangle = 2x 3x 6x2 sq. units Hence, ratio of the total
area of three circles to the area of rectangle is
3 x2
2 :6x2 or : 4
Answer: Ratio is : 4. 
3.1 (a) 
After first day
60 liters of liquid taken out is alcohol 
Hence, amount of alcohol in the tank = 180 – 60 = 120 liters
60 liters of water is added
Hence, fraction of alcohol in the liquid =
120 2
180 3
After second day
60 liters of liquid taken out is 2 alcohol 3
Hence, quantity of alcohol taken out = 2 60 40 liters 3
Hence, quantity of alcohol in the tank = 120 – 40 = 80 liters 60 liters of water
is added 
Hence, fraction of alcohol in the liquid =
80 4
180 9
After third day
60 liters of liquid taken out is 4 alcohol 9
Hence, quantity of alcohol taken out =4 60 26.7 liters 9
Hence, quantity of alcohol in the tank = 80 – 26.7 = 53.3 liters 
Days 0 1 2 3 Quantity of alcohol 180 120 80 53.3in the tank (liters) 
3.1 (b)
180
170
160
150
140
130
120
110
100
90
80
70
60
50
40
30
20
10
0
01 23 Days
3.1 (c) The points on the graph does not lie on a straight line. Hence, quantity
of alcohol as a function of days is a non-linear function. 
3.2 (a) Radius of the conical hole = 5 cm
Height of the conical hole = 12 cm 10 Hence, volume of the conical hole
=
1 r2h1 3.14 52 12 314 cubic cm 3 3 12
Answer: 314 cubic cm 
3.2 (b) Volume of the cylinder before drilling the hole
= r2h 3.14 52 12 942 cubic cm 
Hence, volume of the remaining solid = 942 – 314 = 628 cubic cm
Answer: 628 cubic cm 
3.2 (c) Let slant height of the conical hole = l cm 
By Pythagorus theorem, l2 122 52 144 25 169 132
Hence, l 13
Answer: 13 cm 
3.2 (d) Surface area of the remaining solid
= Area of the outer cylindrical curved surface + Area of the base + Area of
the inner 
conical curved surface
= 2 rh r2 rl
= 2 3.14 5 12 3.14 52 3.14 5 13
= 376.8 + 78.5 + 204.1 sq. cm
= 659.4 sq. cm 
Answer: 659.4 sq. cm
3.3 (a) Join the center O to the point P 
PQ = PO = OQ = PR = OR (Their lengths are equal to theQ radius of the
circle) 
Hence, POQ and POR are equilateral triangles as their P O sides are equal
and all their angles are 60
Hence, QPR = QPO + OPR = 60 + 60 = 120R Answer: QPR = 120
3.3 (b) PQO = 60 (Angle of an equilateral triangle)
3.3 (c) PRO = 60 (Angle of an equilateral triangle)
3.3 (d) QOR = QOP + POR = 60 +60 = 120
Answer: QOR = 120
3.3 (e) All the sides of the figure PQOR are equal to the radius of the circle,
hence all the four sides are equal; hence figure PQOR is a rhombus.
Answer: Yes
THIS PAGE IS INTENTIONALLY LEFT BLANK GRADE 9
ASSESSMENT OF MATHEMATICS
Multiple-Choice Questions: Question no. 1.1 to 1.12 
Short-Answer Questions: Question no. 2.1 to 2.5 
Tasks: Question no. 3.1 to 3.3
Test Paper No. 4 
PREPARED BY:
Sanjiva Dayal (sanjivadayal@yahoo.com)
Multiple-Choice Questions
1.1 
In an examination, Peter, Mary and John got 40%, 50% and 60% of the
maximum marks respectively. They got 450 marks together. What is the
maximum marks?
(a) 250
(b) 300
(c) 350
(d) 400
1.2 
In ABC, what is DPE? A 
E P
(a) 144
(b) 138
(c) 102
(d) 100 36 42 B D C
1.3 
Mean weight of a group of n persons is 40 kg. One person, having weight w,
in kg, is included in the group. The mean weight of the group is now 41 kg.
What is w in terms of n?
(a) w = 40n – 41 (b) w = 40n + 41 (c) w = n + 41 (d) w = n + 81
1.4 
Area of Canada is about 9,970,000 sq. km and population of Canada is about
31,900,000. What is the number of persons per sq. km?
(a)
319 107 9.97 106
3
.
19
10
7
(b) 99.7 106 3
.
19
10
7
(c) 9.97 106 9
.
97
10
6
(d) 3.19 107
What is the area of the shaded figure?
13 
(a) 12 sq. units3 4 (b) 24 sq. units
(c) 36 sq. units
(d) 48 sq. units
1.6 
There are (2x – 1) barrels of oil. Each barrel contains (x + 1) liters of oil. Cost
of oil is $( x + 2) per liter. What is the total cost of oil in all the barrels?
(a) $ 2x3 5x2 x 2
(b) $ 2x3 7x2 x 2
(c) $ 2x3 5x2 x 2
(d) $ 2x3 5x2 3x 2
1.7 
A line passes through the points (a,2) and (3,1). y-intercept of this line is 1.
What is the slope of this line?
(a)
1
3
(b) 
1 3 (c)
2 3 (d) 
2 3
1.8 
Twelve iron balls, each of diameter 7 cm, are melted and formed in the shape
of a cylinder of radius 7 cm. What is the height of the iron cylinder?
(a) 14 cm (b) 56 cm (c) 72 cm (d) 112 cm Peter, Mary, Tom and Kate go for
a walk. The distances traveled by them are shown on the graph.
Peter
Mary
Tom
Kate
time
Who has the highest average speed?
(a) Peter (b) Mary (c) Tom (d) Kate
1.10 
An elevator has the capacity of 12 adults or 20 children. How many adults
can board the elevator with 15 children?
(a) 3 
(b) 4 
(c) 5 
(d) 6
1.11 
One of the diagonals of a rhombus is equal to its side. What are the angles of
the rhombus?
(a) 70 and 110
(b) 60 and 120
(c) 80 and 100
(d) 50 and 130
During a war, 1 of a platoon of solders were killed, 1 died of disease and 1
were taken 5 3 25
prisoners. What fraction of the platoon is left?
(a) 
29 75 (b) 
2 5 (c)
32 75 (d) 
7 15
Short-Answer Questions
2.1 
Draw the line 2x y 1 0. This line cuts the circle that is drawn on the graph.
What are the coordinates of the points of intersections of this line and the
circle?
y
10
9 
8 
7 
6 
5 
4 
3 
2 
1
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10x 
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
Show your work
Answer: Coordinates of the points of intersections are _______ and
________. Peter purchases toys at the rate of 11 toys for $10 and sells the
toys at the rate of 10 toys for $11. What is his percentage profit?
Show your work 
Answer: _____ %
2.3 
A racing track is shown below. What is the length of the racing track in km?
(Use
22 ) 7
84 m
200 m 
Show your work
Answer: ____ km. A pizza shop sells large and small pizzas. 30% of the
pizzas are large and the remaining pizzas are small. A Large pizza is sold for
$5 and a small pizza is sold for $4. Totalsale on a particular day was $817.
How many pizzas were sold on that particular day?
Show your work 
Answer: _____ pizzas.
2.5 
An insect is at one corner of the floor of the room. A lizard is at the midpoint
of one of the edge of the roof. What is the distance between the insect and the
lizard?
Lizard
12 m 
Insect 6 m 
4 m 
Show your work Answer: _____ meters
Tasks
3.1 
Peter wants to visit his friend who lives 160 km away. Peter noticed that the
fuel tank of his car has a hole and fuel is leaking at the rate of I liter per hour.
Peter knows that if he drives his car at the speed of 50 km per hour then the
fuel consumption rate of his car is 10 km per liter of fuel, but if he drives his
car at the speed of 100 km per hour then the fuel consumption rate of his car
is 8 km per liter of fuel. At the start of his journey, there is 20 liters of fuel in
the tank of his car. Peter wants to know how he can reach his friends house
with the leaking fuel tank?
(a) What is the distance traveled by Peter till his fuel tank is empty if he
drives at the speed of 100 km per hour? (Round off your answer to the
nearest hundredth) Answer: ________ km
Show your work
(b) What is the distance traveled by Peter till his fuel tank is empty if he
drives at the speed of 50 km per hour? (Round off your answer to the nearest
hundredth) Answer: ________ km
Show your work
(c) At what speed should Peter drive his car so that he reaches his friends
house that is 160 km away? 
Answer: ____ km per hour
Show your work A building is in the shape of a triangular prism. 120 ft 
90 ft 100 ft (a) What is the volume of the building?
Answer: _________ cubic feet 150 ft 
Show your work 
(c) What is the area of the floor? Answer: _________ sq feet 
Show your work 
(c) What is the surface area of walls excluding the floor? Answer: _________
sq feet 
Show your work Figure ABCD is a trapezoid. Its sides D C CD and CB are equal in
length. 
126
Write the correct answers.
(a) CBD = ______ A B 
Show your work 
(b) DBA = ______ 
Show your work 
(c) DAB = ______ 
Show your work
ANSWERS
1.1 40 50 60 of maximum marks = 450 100 100 100
150 of maximum marks = 450 100
Maximum marks = 100 450 300150
Answer: (b) 
1.2 Figure BDPE is a quadrilateral and so sum of its internal angles is 360
Hence, EBD + BDP + DPE + PEB = 360
36 + 90 + DPE + 90 = 360
DPE = 360 36 90 90 = 144
Answer: (a) 
1.3 Mean weight of a group of n persons is 40 kg
Hence, total weight of n persons = 40n
Total weight of the group including the person having weight w kg = 40n + w
Hence, the mean weight =
40n w
n 1
Mean weight is given to be 41 kg
Hence, 40n w 41n 1
40 n w 41 n 1
40n w 41n 41
w 41n 41 40n
w n 41
Answer: (c)
1.4 Area of Canada = 9,970,000 sq. km = 9.97 106 sq. km 
Population of Canada = 31,900,000 = 3.19 107 persons
Hence, number of persons per sq. km = 
3.19 107
9.97 106 persons per square km
Answer: (c)
1.5 By Pythagorus theorem, 
BC2 32 42 9 16 25 52 A Hence, BC = 5 units 
By Pythagorus, theorem, 12 13
AB2 132 52 169 25 144 122 D Hence, AB = 12 units 3 4 Hence, area of shaded
figure B 5 C = Area of ABC Area of BDC
= 1 5 121 3 4 sq. units2 2
= 30 6 sq. units 
= 24 sq. units
Answer: (b)
1.6 There are (2 x – 1) barrels of oil and each barrel contains (x + 1) liters of
oil. Hence, total amount of oil in all the barrels = (2x – 1) (x + 1) liters
Cost of oil is $( x + 2) per liter.
Hence, the total cost of oil in all the barrels
= $ 2x 1 x 1 x 2
= $ 2x2 2x x 1 x 2
= $ 2x2 x 1 x 2
= $ 2x3 x2 x 4x2 2x 2
= $ 2x3 5x2 x 2
Answer: (a)
1.7 A line passes through the points (a,2) and (3,1). 
Hence, the equation of the line is 
y 12 1 x 3a 3
1 y 1a 3 x 3
1 3y a 3x a 31 y
1
a
3
x
3 a 3 a 3
1 x a 6y a 3 a 3
y
-intercept of this line is
a 6
a 3
Given; y-intercept of this line is 1.
Hence, a 6 1a 3
a 6 a 3
2a 9
9a 2
1 1 2 2 Hence, slope of this line = a 3 9 3 9 6 3 2
Answer: (d)
1.8 Let the height of the cylinder = h cm
Diameter of iron ball = 7 cm
Hence, radius of iron ball = 7 2 = 3.5 cm Volume of 12 iron balls = Volume
of cylinder
124 3.53 72 h3
h 124 3.53 1 cm 3 72
h 14 cm Answer: (a) 
1.9 Average speed = 
Totaldistance
Total time
Hence, the person who travels largest distance in least time will have highest
average speed.
Mary travels the highest distance in least time, and hence Mary has highest
average speed.
Answer: (b)
1.10 Weight of 20 children = weight of 12 adults
Hence, weight of 5 children = weight of 3 adults
Capacity of elevator 
= weight of 20 children
= weight of 15 children + weight of 5 children
= weight of 15 children + weight of 3 adults
Hence, 3 adults can board the elevator with 15 children
Answer: (a)
1.11 All the sides of a rhombus are equal. D C Given; one diagonal is equal to the side
Hence, BD = AB = AD = BC = CD
Hence, ABD and BCD are equilateral trianglesB Hence, A
DAB = ABD = ADB = BDC = BCD = DBC = 60 Hence, ADC = ABC = 120
Hence, angles of rhombus are 60 and 120
Answer: (b)
1.12 Fraction left =
1
1 1 1 75 15 25 3 32
5 3 25 75 75
Answer: (c)
2.1 Line 2x y 1 0 is y 2x 1
Hence, its slope is 2 and y-intercept is 1. 
y
10
9 
8 
7 
6 
5 
4 
3 
2 
1
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10x 
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
Answer: Coordinates of the points of intersection are (3,7) and ( 2, 3). 2.2
Peter purchases toys at the rate of 11 toys for $10.
Hence, purchase price of one toy = $
10
11
Peter sells the toys at the rate of 10 toys for $11.
Hence, sale price of one toy = $
11
10
Hence, percentage profit = 
11 10 11 11 100
10 11 100%10 11 11 100% 121 100 % 21%10 10
11
Answer: 21%
2.3 Length of the semi-circular portion = 22 841m 132 m 7 2
Length of the racing track = 200 m + 132 m + 200 m + 132 m = 664 m =
0.664 km. Answer: 0.664 km.
2.4 Let the number of pizzas sold = n
30% of pizzas are large, hence (100% 30%) = 70% pizzas are small 
Hence, number of large pizzas sold =30 n100
A large pizza is sold for $5. 
Hence, amount of sale of large pizzas = $30 n 5100
Hence, number of small pizzas sold =70 n100
A small pizza is sold for $4. 
Hence, amount of sale of small pizzas = $70 n 4100
Total amount of sale = $817, hence 
30 n 570 n 4 817100 100
150 280n 817100
430 n 817100
n 817100 190430
Answer: 190 pizzas.
2.5 Draw lines AC, CD and AD as shown in the figure.
D Lizard
12 m 
C Insect 6 m
A 4 m B D is the midpoint of the side, hence, C is the mid point of the side
having length 6 m Hence, BC = 3 m
ABC is a right angles triangle, hence by Pythagorus theorem
AC2 AB2 BC2 42 32 16 9 25 52
Hence, AC = 5 m
ACD is a right angles triangle, hence by Pythagorus theorem
AD2 AC2 CD2 52 122 25 144 169 132
Hence, AD = 13 m 
Answer: = 13 m
3.1 (a) Let the time of traveling till the fuel tank becomes empty = t hours
Fuel is leaking at the rate of 1 liter per hour 
Hence, quantity of fuel leaked in t hours = t liters 
Distance traveled at the speed of 100 km per hour = 100t km
Fuel consumption rate of the car at 100 km per liter = 8 km per liter
Hence, fuel consumed =
100t liters 8
Fuel in the tank at the start of the journey = 20 liters
Hence, Fuel leaked + Fuel consumed = 20 liters
t 100t208
108t208
t20 8 hours108
Hence, distance traveled = 10020 8 148.15 km 108
Answer: 148.15 km
3.1 (b) Let the time of traveling till the fuel tank becomes empty = T hours 
Fuel is leaking at the rate of 1 liter per hour 
Hence, quantity of fuel leaked in T hours = T liters 
Distance traveled at the speed of 50 km per hour = 50T km
Fuel consumption rate of the car at 50 km per liter = 10 km per liter Hence,
fuel consumed = 50T 5T liters 10
Fuel in the tank at the start of the journey = 20 liters Hence, Fuel leaked +
Fuel consumed = 20 liters T 5T 20
6T 20
T20 10 hours6 3
Hence, distance traveled = 5010 166.67 km 3
Answer: 166.67 km
3.1 (c) Hence, at the speed of 100 km per hour, Peter can drive up to 148.15
km only, 
whereas at the speed of 50 km per hour, Peter can drive up to 166.67 km. His
friend
lives 160 km away. Hence, to reach his friends house with leaking fuel tank,
Peter 
should drive at the speed of50 km per hour.
Answer: 50 km per hour 
3.2 (a) The triangular face of the building has side lengths 90 ft, 150 ft and
120 ft.
902 1202 8100 14400 22500 1502
Hence, the triangular faces are right angled triangles with hypotenuse 150 ft
Hence, area of triangular face = 1 90 120 5400 sq. ft2
Length of the building is 100 ft
Hence, volume of the building = 5400 100 = 540,000 cubic ft 
Answer: 540,000 cubic ft
3.2 (b) Floor is in the shape of a rectangle with sides 150 ft and 100 ft
Hence, area of the floor = 150 100 = 15,000 sq. ft
Answer: 15,000 sq. ft
3.2 (c) Surface area of walls excluding the floor
= Area of two triangular faces + Area of two slanting rectangular walls = 2
5400 + 90 100 + 120 100 sq. ft
= 31,800 sq. ft
Answer: 31,800 sq. ft
3.3 (a) BCD is an isosceles D C triangle because CD = CB126Hence,
CBD =
180 126 272
Answer: CBD = 27
3.3 (b) CDB = CBD = 27 (They A B 
are equal angles of the isosceles triangle BCD)
DC and AB are parallel sides of the trapezoid
Hence, DBA = CDB = 27 (Alternate angles) 
Answer: DBA = 27
3.3 (c) DAB + ADB + ABD = 180 (They are angles of triangle ABD)
Hence, DAB = 180 ADB ABD = 180 90 27 = 63
Answer: DAB = 63
GRADE 9 ASSESSMENT OF MATHEMATICS
Multiple-Choice Questions: Question no. 1.1 to 1.12 
Short-Answer Questions: Question no. 2.1 to 2.5 
Tasks: Question no. 3.1 to 3.3
Test Paper No. 5 
PREPARED BY:
Sanjiva Dayal (sanjivadayal@yahoo.com)
Multiple-Choice Questions
1.1 
Water is filled with a constant rate in the container shown in the figure.
Which of the following graph shows the relationship between the height of
water level versus time?
(a) height
time 
(b) height
time 
(c) height
time 
(d) height
time
1.2 
Slope of line A is m. m is a non-zero number. Line B is perpendicular to line
A. Which of the following statement is always true?
(a) Slope of line B is greater than m
(b) Slope of line B is less than to m
(c) Slope of line B is equal to m
(d) Slope of line B and m have opposite signs A cylindrical vessel is partly
filled with water. The diameter of the vessel is 12 cm. A ball of diameter 6
cm is dropped into the vessel such that the ball is completely dipped in water.
By how many cm will the surface of water rise?
(a) 0.5 cm (b) 1 cm (c) 2 cm (d) 3 cm
1.4 
Which natural number is 80% of the next natural number?
(a) 3 
(b) 4 
(c) 6 
(d) 8
1.5 
Peter and his 15 friends went to a coffee shop. The total bill amount was
$114.40. Peter paid for himself and 5 of his friends. How much did Peter
pay?
(a) $36.80
(b) $38.60
(c) $42.90
(d) $43.20
1.6 
A man takes 150 steps in walking 120 meters. He takes 3 steps in one second.
What is his speed?
(a) 1.2 meter per second (b) 2.4 meter per second (c) 3.6 meter per second (d)
4.2 meter per second A train travels at the speed of 3x2 xy 2y2 km per hour for
x y hours and at the
speed of x y km per hour for 2x2 xy 3y2 hours. What is the total distance
traveled by the train?
(a) 5x3 8x2y 7xy2 y3 km (b) 5x3 5x2y 3xy2 y3 km (c) 5x3 3x2y 4xy2 y3 km (d)
5x3 3x2y 5xy2 y3 km
1.8 
Which of the following statements is always true for all isosceles right-angled
triangles?
(a) All isosceles right-angled triangles are congruent (b) All isosceles right-
angled triangles have same area (c) All isosceles right-angled triangles are
similar (d) All isosceles right-angled triangles have same perimeter
1.9 
What is the value of x? 
x
(a) 100 80140(b) 120 20(c) 140
(d) 150
1.10 
From 84 boys of the schools, three-seventh were selected for school sports
and were divided equally into six teams. How many boys are there in each
team?
(a) 4 
(b) 6 
(c) 7 
(d) 8 
A triangular board is shown in the figure. What is A the height AD?
(a) 6 units 9 12 (b) 6.5 units
(c) 7 units
(d) 7.2 units
B D 15 C
1.12 
20 men working 12 hours a day can complete a piece of work in 60 days.
How many men can complete the same piece of work in 90 days working 8
hours a day?
(a) 15
(b) 18
(c) 20
(d) 22
Short-Answer Questions
2.1 
A tent is in the shape of a cone. Tent is made of thick canvas cloth. The
canvas cloth costs $7 per sq. ft. What is the cost of the cloth that is required
to make the tent?
(All dimensions in the figure are in ft) (Use
22 ) 7
12 
9 
Show your work 
Answer: $______ 
2.2 
Figure ABC is a right-angled triangle, right angled at C. D is B the midpoint of side AC. E is
the midpoint of side BC. Length of side AB is 4 units. What is the value of
AE2 BD2
. E 4 
C D A 
Show your work
Answer: ____ sq. units There are two vessels. First vessel contains 10 liters
mixture of alcohol and water in the ratio 5:3. Second vessel contains 5 liters
mixture of alcohol and water in the ratio 7:5. The contents of both the vessels
are poured in a third vessel that was empty. What is the percentage of alcohol
in the third vessel?
Show your work 
Answer: ______ %
2.4 
The minute hand of a clock is 7 cm long. What is the distance covered by the
tip of the minute hand in 15 minutes? (Use
22 ) 7
Show your work
Answer: ____ cm Three points A, B, C are shown on the graph. Two of these
points are joined to form three lines, AB, BC and AC. 
(a) Which of these lines has the greatest positive slope?
(b) Which of these lines has the greatest y-intercept? 
(b) Which of these lines has the greatest x-intercept?
y 
B A
C
x 
Show your work
Answer:
Line that has the greatest positive slope is AB BC AC Line that has the
greatest y-intercept is AB BC AC Line that has the greatest x-intercept is AB
BC AC
Tasks
3.1 
A pizza shop sells pizzas and ice creams. After 11:00 pm, the shop charges
night fees per person but gives 25% discount on pizza and ice cream. A group
of n persons want to know the total amount paid by them, P, in dollars, for
eating p pizzas and m ice creams. The shop manager told them the formula of
P after 11:00 pm. The formula is given below.
P = 1.25n + 3.75p + 2.25m
(a) What the number 1.25 in the formula stands for?
Answer:
_____________________________________________________________
Show your work 
(b) What the number 3.75 in the formula stands for?
Answer:
_____________________________________________________________
Show your work 
(c) What the number 2.25 in the formula stands for?
Answer:
_____________________________________________________________
Show your work (d) What is the formula of P before 11:00 pm? Answer: P =
_______________________
Show your work
(e) If John eats 1 pizza and 1 ice cream only, then should he eat before 11:00
pm or after 11:00 pm to save money?
Answer: Before 11:00 pm After 11:00 pm
Show your work 
3.2 
Diagonals of a rhombus are 6 cm and 8 cm long.
(a) Draw both the diagonals and the four sides of the rhombus on the grid?
= 1 cm 
(b) Calculate the length of the sides of the rhombus. Answer: _____ cm 
Show your work 
(c) Calculate the perimeter of the rhombus. Answer: _____ cm 
Show your work (d) Calculate the area of the rhombus. Answer: _____ sq.
cm 
Show your work 
3.3 
In the given figure, AD = BD = CD and BDC = x . C 
(a) Write ADC in terms of x.xAnswer: ADC = ____ A D B 
Show your work. Explain your answer. 
(b) Write DAC in terms of x. Answer: DAC = ____
Show your work. Explain your answer. (c) Write DBC in terms of x. Answer:
DBC = ____
Show your work. Explain your answer.
(d) What is the measure of ACB? Discuss whether ACB depends on x or not?
Answer: ACB = ____
Show your work. Explain your answer.
ANSWERS
1.1 When water is filled with a constant rate, the height of the water level will
rise faster in the container having smaller area. The bottom part of the
container has the largest area. Area of the top part is smaller than the bottom
part and the middle part has the least area. Hence, rate of increase of water
level will be fastest in the middle part. Rate of rise of water level in the top
part will be slower than the middle part and the rate of rise of water level is
slowest in the bottom part.
Hence, when the container is filled, slope of the graph of height of water level
increases in the middle part and decreases in the top part.
Answer: (b)
1.2 Line B isperpendicular to line A 
Hence, slope of line B =
1
m
Hence, slope of line B and m have opposite signs.
Answer: (d) 
1.3 Diameter of the vessel = 12 cm
Hence, radius of the vessel = 12 2 = 6 cm
Diameter of the ball = 6 cm
Hence, radius of the ball = 3 cm 
Let the rise in surface of water = h cm
Volume of the ball = volume of water displaced
4 33 62 h3
h4 33 1 1 cm 3 62
Answer: (b) 
1.4 Let the natural number = n
This number is 80% of the next natural number
Hence,
n80 n 1100
n
80 n 80
100 100
n
80 n 80
100 100
20 n 80
100 100
n 4
Answer: (b) 
1.5 Total number of persons = 16 (Peter and his 15 friends)
Bill amount = $114.40
Hence, share of 1 person =
$114.40 $7.1516
Peter paid for the share of 6 persons (himself and 5 of his friends) Hence,
amount paid by Peter = $7.15 6 = $42.90
Answer: (c)
1.6 The man takes 3 steps in one second
Hence, time taken to take 150 steps =
150 seconds = 50 seconds 3
Hence, he walks 120 meters in 50 seconds 
Hence, his speed = 120 meter per second = 2.4 meter per second 50
Answer: (b) 
1.7 Total distance traveled by the train 
= 3x2 xy 2y2 x y x y 2x2 xy 3y2 km
= 3x3 x2y 2xy2 3x2y xy2 2y3 2x3 x2y 3xy2 2x2y xy2 3y3 = 5x3 3x2y 5xy2 y3
Answer: (d)
1.8 In all isosceles right-angled triangle, angels are 90 , 45 and 45 . Hence,
they are all similar 
Answer: (c)
1.9 a = 180 140 = 40
(Supplementary angles) x
y = 80 + a = 80 + 40 = 120
(External angle of the triangle)
x = 20 + y = 20 + 120 = 140
80 14020 y a 
(External angle of the triangle)
Answer: (c)
1.10 Three-seventh of 84 students were selected
Hence, number of selected students =
3 84 367
Selected students were divided equally into six teams
Hence, number of students in each team = 36 6 = 6
Answer: (b)
1.11 In ABC,A
AB2 AC2 92 122 81 144 225 152 BC2
Hence, ABC is a right angled triangle with 9 12 BAC = 90
Hence, area of
ABC = 
1
2AB AC B D 15 C 
Also, area of ABC =1 BC AD2
Hence, 1 BC AD1 AB AC2 2
15 AD 9 12
9 12 7.2 unitsAD15
Answer: (d) 
1.12 20 men complete the work working 12 hours a day for 60 days
Hence, 20 men complete the work working = 12 60 hours = 720 hours 
8 hours a day for 90 days = 8 90 hours = 720 hours
Hence, number of hours is the same.
Hence, 20 men will complete the work working 8 hours a day for 90 days
Answer: (c)
2.1 Let the slant height of the cone = L ft
By Pythagorus theorem, 
L2 122 92 144 81 225 152
Hence, L = 15 ft
Radius of the tent = r = 9 ft 12 
Hence, curved surface area of the tent
9
= rL
= 22 9 15 sq. ft7
Cost of 1 sq. ft of canvas cloth = $7 
Hence, cost of cloth = $22 9 15 7 $29707
Answer: $2970.
2.2 AE2 BD2
AC2 CE2 CB2 CD2 (By Pythagorus theorem) 2 CB2 CE2 CD2AC
AB
2 CB2 AC2 2 2 (By Pythagorus theorem)(D and E are midpoints)
AB
2 CB2 AC2 4
AB
2 AB2
4 (By Pythagorus theorem)
4
2 42 4 16 4 20 sq. units Answer: 20 sq. units. 
2.3 Quantity of alcohol in 10 liter mixture =
5
5 3 105 1025 liter 8 4
Quantity of alcohol in 5 liter mixture = 7 535 liter7 5 12
Hence, total quantity of alcohol in the third vessel
= 25 35 25 3 35 110 55liter 4 12 12 12 6
Quantity of mixture in the third vessel = 10 + 5 liters = 15 liters.
Hence, percentage of alcohol in the third vessel = 55 1 100%550% 611%6 15 9 9
Answer: 611%9
2.4 Distance covered by the tip of the 7 cm long minute hand in 15 minutes =
one-fourth of the circumference of the circle of radius 7 cm
= 1 222 7 cm 4 7
= 11 cm 
Answer: 11 cm.
2.5 
y 
B A
C
x
Answers:
(a) Line BC has the greatest positive slope. (b) Line AC has the greatest y-
intercept. (c) Line AC has the greatest x-intercept?
3.1 (a) P = 1.25n + 3.75p + 2.25m
When n increases by 1, P increases by $1.25. Answer: $1.25 is the night fees
per person.
3.1 (b) When p increases by 1, P increases by 3.75 Answer: $3.75 is the cost
of 1 pizza.
3.1 (c) When m increases by 1, P increases by 2.25 Answer: $2.25 is the cost
of 1 ice cream. 
3.1 (d) Before 11:00 pm, there is no night fees. 
There is discount of 25% after 11:00 pm
Cost of 1 pizza after 11:00 pm = $3.75, which is 75% of the price before
11:00 pm
Hence, cost of 1 pizza before 11:00 pm = $
100 3.75 = $575
Cost of 1 ice cream after 11:00 pm = $2.25, which is 75% of the price before
11:00 pm
Hence, cost of 1 ice cream before 11:00 pm = $100 2.25 = $375
Hence, formula of P before 11:00 pm is
P = 5p + 3m
Answer: P = 5p + 3m
3.1 (e) If John eats 1 pizza and 1 ice cream before 11:00 pm, he will have to
pay = $5 + $3 = $8 
If John eats 1 pizza and 1 ice cream after 11:00 pm, he will have to pay =
$1.25 + $3.75 + $2.25 = $7.75 
$7.75 is less than $8 
Answer: John should eat after 11:00 pm.
3.2 (a) Diagonals of a rhombus are perpendicular and they bisect each other. 
x 
3 cm
4 cm
3.2 (b) Let length of the side = x
By Pythagorus theorem, x2 32 42 9 16 25 52 Hence, x = 5 cm
Answer: 5 cm
3.2 (c) Hence, perimeter of rhombus = 4 5 = 20 cm 
Answer: 20 cm 
3.2 (d) Area of rhombus = 1 Product of diagonals =1 8 6 24 sq. cm 2 2
3.3 (a) ADC = 180 - x (SupplementaryC angles) 
Answer: ADC = 180 - x
3.3 (b) Since AD = DC, 
hence DAC = DCAx
DAC + DCA + ADC = 180 A D B (Angles of a triangle)
Hence, 2 DAC + 180 - x = 180
xDAC2
Answer:
DAC
x
2
3.3 (c) Since DB = DC, 
hence DCB = DBC
DCB + DBC + BDC = 180 (Angles of a triangle) Hence, 2 DBC + x = 180
xDBC 902
Answer:
DBC
90
x 2
3.3 (d) ACB = ACD + DCB = DAC + DBC = x 90x 90 . 2 2
Answer: ACB = 90 . Hence, ACB does not depend on x.
GRADE 9 ASSESSMENT OF MATHEMATICS
Multiple-Choice Items
Test Paper No. 6 
PREPARED BY:
Sanjiva Dayal (sanjivadayal@yahoo.com)
Six liters sugar solution contains 8% sugar and rest is water. One liter of water evaporated. What is the
percentage of sugar in the remaining solution?
The radius and height of a cylinder are both equal to the radius of a sphere. What is the ratio of the
volume of the sphere to the volume of the cylinder?
8% sugar solution 
(a) 24%5
(b) 81%5
(c) 93%5
(d) 63%5
(a) 1:2
(b) 3:2
(c) 4:3
(d) 3:1
4. 
John buys 30 chairs, all at the same price. He sells
20 of them at a profit of 16% and has to sell the remaining 10 at a loss of 4%. What is his profit
percentage in the deal?
2. 
Peter and Paul enter into a partnership business with capital $15,000 and $21,000 respectively. The
profit from the business is to be divided in the proportion of their capitals. Peter received $3040 from
the profit. How much did Paul receive from the profit?
(a) 12% (b) 14% (c)
62%3
(d) 91%3
(a) $4180
(b) $4256
(c) $4378
(d) $4398
Due to global warming, Gangotri glacier in India is shrinking at the rate of 30 meters annually. What is
the average shrink in one second?
A wet cloth was put in the drying machine. The weight of the cloth changes with time as shown in the
graph.
1.7
1.65
1.6
1.55
1.5 012 3 45 Time (minutes)
What was the weight of the water present in the cloth before drying?
(a) 5.7 105m (b) 2.3 105m (c) 3.5 104m (d) 9.5 107m
(a) 50 grams (b) 100 grams (c) 125 grams (d) 150 grams
6. 
The sum of the ages of father and son is 50 years. When the son will attain the father’s present age, then
the sum of their ages will be 102 years. What is the present age of the son?
8. 
The length, width and height of a rectangular prism are each decreased by 10%. What is the percentage
decrease in the volume of the rectangular prism?
(a) 8 years (b) 10 years (c) 12 years (d) 15 years
(a) 30% (b) 28.8% (c) 27.1% (d) 26.9%
9. 
There are a3b2 3 boxes of chocolates. Each box contains a2b3 4 chocolates. These chocolates
are distributed equally among a4b5 2 children. How many chocolate each child gets?
(a) a8b7
(b) a7b6
9b7(c) a
(d) a9b8
Sides of an equilateral triangle are (x + 2) cm,
(2 x – 3) cm and (2x – 3) cm. What is the perimeter of the triangle?
In an isosceles triangle of fixed perimeter, the length of the equal sides is y cm and the length of the
third side is x cm.
y y
(a) 15 cm (b) 18 cm (c) 21 cm (d) 24 cm
11.
Which of the following pair of lines cannot be parallel?
(a) Two sides of a quadrilateral (b) Two sides of a pentagon (c) Two chords of a circle (d) Two
diameters of a circle
x 
The variation of y withx is shown in the graph.
30
25
20
15
10
5
0
0 5 10 15 20 25
x (cm)
What is the perimeter of the isosceles triangle?
(a) 30 cm (b) 40 cm (c) 50 cm (d) 60 cm
13.
A cow is given rich diet and gains 15% in weight. The cow is then put on a poor diet and looses 20% in
weight. What is the overall change in weight of the cow?
A regular polygon has fixed number of sides. If its side length is changed, its perimeter changes as
shown in the graph.
There are 3x2 x 2 words in a book. How
(a) Looses 5% weight (b) Looses 8% weight (c) Looses 10% weight (d) Gains 6% weight
many words are there in 2x 3 copies of the book? 
25
20
15
10 5 0 0123 Side length (cm)
What is the number of sides of the polygon?
(a) 7 
(b) 8 
(c) 9 
(d) 10
15.
Figure ABCD is a parallelogram and L is a point on the side CD such that CL = 2DL.
A B
D L C 
What is the ratio of the area of the triangle ABL to the area of the parallelogram ABCD?
(a) 6x3 7x2 7x 6 (b) 6x3 11x2 7x 6 (c) 6x3 7x2 x 6 (d) 3x3 11x2 7x 6
17.
Diameter of the wheels of a car is d, in meters. When the wheels of the car are rotating at the rate of n
revolutions per second, the speed of the car v, in meters per second, is given by the formula
v dn
The variation of speed v with n is shown in the graph.
35
30
25
20
15
10
5
0
(a) 1:2
(b) 1:3
(c) 1:4
(d) 2:3
01 23 n (revolutions per second)
What is the diameter of the wheels?
(a) 2 m
(b) 2.5 m (c) 3 m
(d) 3.5 m John met with an accident and was brought to the hospital. 100 ml of glucose was
immediately injected into him and the next 100 ml was drip injected slowly over the period of 30
minutes as shown in the graph.
Peter is a taxi driver. Fuel tank of his taxi has capacity of 50 liters of fuel. As soon as the fuel in the
tank drops to 10 liters, Peter fills the tank to the full capacity. Which of the following graph correctly
shows the quantity of fuel in the tank against the distance traveled?
200
(a) 
150
100
50
0 0 5 10 15 20 25 30 Time (minutes)
50 40 30 20 10 0
John’s condition stabilized after consuming 160 ml of glucose. After how much time John’s condition
stabilized? 
(b)
(a) 12 minutes (b) 14 minutes (c) 16 minutes (d) 18 minutes
19.
Surface area of a sphere is S sq. units and its volume is V cubic cm. What is the relationship between S
and V?
0 500 1000 1500 2000 Distance (km)
50
40
30
20
10
0
0 500 1000 1500 2000 Distance (km)
(c)
(a) S2 36 V (b) V3 36 S2
(c) S3 36 V3
(d) S3 36 V2
50
40
30
20
10
0
0 500 1000 1500 2000 Distance (km)
(d)
50
40
30
20
10
0
0 500 1000 1500 2000 Distance (km)
Peter is an engineer and he is doing calculations for designing a bridge. 
5
0 01 23 45 Diameter (cm)
He has to simplify the following expression:
4 x2 xy9 y2 2 x3 y9 4 3 2
What is the value of this expression?
(a) 
8 x3 xy2 27 y3
27 8
(b) 
8 x3 x2 y27 y3
27 8
(c)
8x3 27y3
27 8
(d) 
8x3 2x2y 3xy2 27y3 27 3 2 8
Which of the following graph correctly shows the relationship between the circumference of a circle
and its diameter?
(a)
15
10
(b)
15
13
11
9
7
5
3
1
-1 01 23 45 Diameter (cm)
(c)
15
13
11
9
7
5
3
1
-1 01 23 45 Diameter (cm)
(d) The interior angles of a polygon are in the ratio 2:4:5:6:6:7. What is the greatest angle? Peter is
participating in 20 km marathon walk. Distance moved by Peter with the number of steps he walks is
shown in the graph below.
15
13
11
9
7
5
3
1
-1 01 23 45 Diameter (cm)
(a) 144
(b) 156
(c) 168
(d) 172
200
150
24.
In an adult, resting heart rate is normally about 70 beats per minute. However, the heart can beat up
faster when a person is exercising vigorously. The maximum heart rate M, in beats per minute, of a
person of age N, in years, is shown in the graph.
0 012345 Number of steps
200
190
180
170
160
150
How many steps did Peter take during the Marathon walk?
(a) 500 steps (b) 5000 steps (c) 5500 steps (d) 50,000 steps
20 25 30 35 40 45 50 55 60 N (years)
26.
Look at the coordinate plane given below. What is the formula of H in terms of N?
(a) H = 200 + N (b) H = 220 + N (c) H = 200 N (d) H = 220 N
100
50
y 
(4,7)
(2,3) (6,x) 0 x What is the value of x
?
(a) 4 
(b) 5 
(c) 6 
(d) 7 
A quadrilateral is drawn on the coordinate plane.
y
Jennifer has $5000. She invested some of his money at 6% per annum and the rest amount at 9% per
annum interest. In one year she received interest of $390. How much money she invested at 6%
interest?
0 x
How many sides of this quadrilateral has positive slope?
(a) 1 
(b) 2 
(c) 3 
(d) 4
28.
The ticket of a circus is $2 for children and $3 for adults. On Monday, 320 persons watched the circus
and the total collection was $830. What was the number of children who watched the circus on
Monday?
(a) $2000 (b) $2100 (c) $2300 (d) $2700
30.
A tank is being filled with water at a constant rate.
4 of the tank is filled in 1 hour. In how much time9
the rest of the tank will be filled?
(a) 110
(b) 130
(c) 150
(d) 190
(a) 135 minutes (b) 1 hour 
(c) 75 minutes (d) 90 minutes
31.
In the following figure AB = AC. A 
x 2x
40 50 D B C E
What is the measure of BAC?
(a) 50
(b) 60
(c) 70
(d) 80
32.
The minute hand of a clock rotates through angle A in time T. What is the formula of A, in degrees, in
terms of T, in minutes?
1112 1 10 2 9 3 
8 4 7 6 5 
(a)
A 6T (b) A 60T (c)
A
T
6 (d) 
A
T 60
ANSWERS
1. 6 liters of solution contains 8% sugar and rest is water.
Hence, quantity of sugar = 6
8 12 liter100 25
1 liter of water evaporated, hence quantity of remaining solution = 6 liters – 1 liter = 5 liters Hence,
percentage of sugar in the remaining
solution =
12 1 100%48% 93%25 5 5 5
Answer: (c) 
2. Ratio of share of Peter to share of Paul = 
15000:21000 = 5:7
Share of Peter = $3040
Hence, share of Paul =
7
3040 $42565
Answer: (b)
3. Let radius of cylinder = height of cylinder = 
radius of sphere = r units
Hence, ratio of volume of sphere to volume of
cylinder =4 r3 : r2r = 4:33
Answer: (c) 
4. Let the cost price of each chair = x units
20 chairs are sold at the profit of 16%.
Hence, sale price of these 20 chairs =
20x16 20x20 116 x116x units100 100 5
10 chairs are sold at a loss of 4%.
Hence, sale price of these 10 chairs = 
10x4 10x48 x units100 5
Hence, total sale price = 
116x 48x 164x units5 5 5
Total cost price = 30x units
Hence, profit percentage 
164x 30x5 100%30x
164 150100%30 5
14 2%3
91%3
Answer: (d)
5. 1 year has 365 days. 1 day has 24 hours, 1 
hour has 60 minutes and 1 minute has 60
seconds.
Hence,1 year = 365 24 60 60 seconds 
Glacier shrinks 30 meters in 1 year.
Hence, average shrink in 1 second
= 30 m 9.5 10 7 m365 24 60 60
Answer: (d)
6. Let the present age of the son = x years Hence, present age of father = (50 – x) years Son will attain
father’s present age after (50 – 2x) years
Father’s age after (50 – 2x) years will be = (50 – x) years + (50 – 2x) years = (100 – 3x) years
Sum of their ages is 102.
Hence, (50 – x) + (100 – 3x) = 102
150 – 4 x = 102
4x = 150 – 102
4x = 48
x = 12
Answer: (c)
7. Weight of wet cloth before drying = 1.7 kg. During drying, the weight of the cloth decreases due to
loss of water. When the cloth is completely dry, the weight becomes constant and the graph becomes
horizontal. Weight of dry cloth = 1.55 kg
Hence, weight of water in the wet cloth = 1.7 1.55 kg
= 0.15 kg
= 0.15 1000 grams 
= 150 grams
Answer: (d)
8. Let the length, width and height of the rectangular prism be L, W and H respectively. Hence,
volume = L W H 
After decrease in dimensions by 10%, length = L – 0.1L = 0.9L
width = W – 0.1W = 0.9W
height = H – 0.1H = 0.9H
Hence, volume after decrease in dimensions = 0.9L 0.9W 0.9H = 0.729 L W H Hence, percentage
decrease in volume = L W H 0.729 L W H100%L W H
= 1 0.729 100% 27.1%
Answer: (c)
9. There are a3b2 3 boxes of chocolates.
Each box contains a2b3 4 chocolates. Hence, total number of chocolates
= a3b2 3 a2b3 4
These chocolates are distributed equally
2 children.a4b5among 
Hence, number of chocolates each child gets 3 a2b3 4
= a3b2
a4b5 2
= 
a3 3b2 3a2 4b3 4 a4 2b5 2
= 
a9b6a8b12 8b10a
a
9 8b6 12
= a8b10
= 
a17b18
a8b10
= a17