Prasanna

ML Aggarwal Class 6 Solutions Chapter 1 Knowing Our Numbers Ex 1.1 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 1 Knowing Our Numbers Ex 1.1

Question 1.
Write the smallest natural number. Can you write the largest natural number?
Solution:

Question 2.
Fill in the blanks:
(i) 1 lakh = … ten thousand
(ii) 1 million = … hundred thousand
(iii) 1 crore = … ten lakh
(iv) 1 billion =… hundred million.
Solution:

Question 3.
Insert commas suitably and write each of the following numbers in words in the Indian system and the International system of numeration.
(i) 506723
(ii) 180018018
Solution:

Question 4.
Write the following numbers in expanded form:
(i) 750687
(ii) 5032109
Solution:

Question 5.
Write the following number in figures:
(i) Seven lakh three thousand four hundred twenty.
(ii) Eighty crore twenty three thousand ninety three.
Also write the above numbers in the place value chart.
Solution:

Question 6.
Write each of the following numbers in numeral form and place commas correctly:
(i) Seventy three lakh seventy thousand four hundred seven.
(ii) Nine crore five lakh forty one.
(iii) Fifty eight million four hundred twenty three thousand two hundred two.
Solution:

Question 7.
Write the face value and place value of the digit 6 in the number 756032.
Solution:

Question 8.
Find the difference between the place value and the face value of the digit 9 in the number 229301.
Solution:

Question 9.
Determine the difference of the place value of two 7’s in 37014472 and write it in words in International system.
Solution:

Question 10.
Determine the product of place value and the face value of the digit 4 in the number 5437.
Solution:

Question 11.
Find the difference between the number 895 and that obtained on reversing its digits.
Solution:

ML Aggarwal Class 6 Solutions Chapter 3 Integers Ex 3.4 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 3 Integers Ex 3.4

Question 1.
Find the value of:
(i) 6 – 9 + 4
(ii) -5 – (-3) + 2
(iii) 7 + (-5) + (-6)
(iv) 6 – 3 – (-5)
Solution:

Question 2.
Evaluate the following:
(i) -77 + (-84) + 318
(ii) 54 + (-218) – (-76)
(iii) -121 – (-78) + (-193) + 576
(iv) -65 + (-76) – (-28) + 32
Solution:

Question 3.
Find the value of:
(i) 8 – 6 + (-2) – (-3) + 1
(ii) 31 + (-23) – 35 + 18 – 4 – (-3)
Solution:
(i) 8 – 6 + (-2) – (-3) + 1
= 8 – 6 – 2 + 3 + 1
=-6 – 2 + 8 + 3 + 1
= -6 – 2 + 12
=-8 + 12 = 4

(ii) 31 + (-23) – 35 + 18 – 4 – (-3)
= 31 – 23 – 35 + 18 – 4 + 3
= -23 – 35 – 4 + 31 + 18 + 3
= -23 – 35 – 4 + 52
= -62 + 52 = -10

Question 4.
Rashmi deposited ₹ 4370 in her account on Monday and then withdrew ₹ 2875 on Tuesday. Next day she deposited ₹ 1550. What was her balance on Thursday?
Solution:
Rashmi deposited in her account on Monday = ₹ 4370
Less withdrawal on Tuesday = ₹ 2875
So the Balance on Tuesday
= ₹ 4370 – ₹ 2875
= ₹ 1495
Again she deposited on Wednesday = ₹ 1550
Balance on Thursday
= ₹ 1495 + ₹ 1550 = ₹ 3045

ML Aggarwal Class 6 Solutions Chapter 3 Integers Ex 3.3 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 3 Integers Ex 3.3

Question 1.
Evaluate the following, using the number line:
(i) 4 – (-2)
(ii) -4 – (-2)
(iii) 3 – 6
(iv) -3 – (-5)
Solution:

Question 2.
Subtract :
(i) -6 from 9
(ii) 6 from -9
(iii) -6 from -9
(iv) -725 from -63
(v) -376 from 10
(vi) 92 from -620
Solution:

Question 3.
Evaluate the following:
(i) -237 – (+ 1884)
(ii) -346 – (- 1275)
(iii) -190 – (-3512)
(iv) -2718 – (+ 6827)
Solution:

Question 4.
The sum of two integers is 17. If one of them is -35, find the other.
Solution:

Question 5.
What must be added to -23 to get -9?
Solution:

Question 6.
Find the predecessor of 0.
Solution:

Question 7.
Find the successor and the predecessor of the following integers:
(i) -31
(ii) -735
(iii) -240
Solution:

ML Aggarwal Class 6 Solutions Chapter 3 Integers Ex 3.2 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 3 Integers Ex 3.2

Question 1.
Evaluate the following, using the numbers line
(i) 4 + (-5)
(ii) (-4) + 5
(iii) 7 + (-3)
(iv) -6 + (-2)
Solution:

Question 2.
Evaluate the following :
(i) (-8) + (-14)
(ii) -35 + (-47)
(iii) 91 + (-48)
(iv) (-203) + 501
(v) (-36) + 29
(vi) (-131) + 97.
Solution:

Question 3.
Evaluate the following :
(i) -1083 + (-3974)
(ii) 706 + (-394)
(iii) 1309 + (-2811)
Solution:

Question 4.
Fill in the following blanks :
(i) -(-5) = ……..
(ii) -(-30) = …….
(iii) -(-539) = ………
Solution:

Question 5.
Write down the additive inverses of:
(i) 9
(ii) -11
(iii) -237
(iv) 567
Solution:

ML Aggarwal Class 7 Solutions for ICSE Maths Model Question Paper 6 acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 ICSE Maths Model Question Paper 6

(Based on Chapters 10 to 17)
Time allowed: 2\(\frac { 1 }{ 2 }\) Hours
Maximum Marks: 90

General Instructions

• All questions are compulsory.
• The question paper consists of 29 questions divided into four sections A, B, C, and D.
• Section A comprises of 8 questions of 1 mark each.
• Section B comprises of 6 questions of 2 marks each.
• Section C comparises of 10 questions of 4 marks each.
• Section D comprises of 5 questions of 6 marks each.
• Question numbers 1 to 8 in Section A is multiple choice questions where you are to select one correct option out of the given four.

Section – A

Question numbers 1 to 8 is of 1 mark each.
Question 1.
In the given figure, if ∠AOC and ∠COB form a linear pair, then the value of x
(a) 60
(b) 55
(c) 50
(d) 45

Solution:

Question 2.
An exterior angle of a triangle is 118°. If one of the two interior opposite angle is 54°, then the other interior opposite angle is
(a) 62°
(b) 54°
(c) 64°
(d) 59°
Solution:

Question 3.
In a right-angled triangle, the lengths of two legs are 8 cm and 15 cm. The length of the hypotenuse is
(a) 23 cm
(b) 20 cm
(c) 17 cm
(d) 17 m
Solution:

Question 4.
If ΔABC = ΔPRQ, the the correct statement is
(a) AB = PQ
(b) ∠B = ∠Q
(c) ∠C = ∠R
(d) AC = PQ
Solution:

Question 5.
The number of lines that can be drawn parallel to a given line l through a point outside the line l is
(a) 0
(b) 1
(c) 2
(d) infinitely many
Solution:

Question 6.
If the area of a circle is numerically equal to its circumference, then the diameter of the circle is
(a) 2 units
(b) 4 units
(c) 6 units
(d) 8 units
Solution:

Question 7.
A quadrilateral having exactly two lines of symmetry and rotational symmetry of order 2 is a
(a) square
(b) parallelogram
(c) rhombus
(d) kite
Solution:

Question 8.
A mode is the observation of the data
(a) whose position is in the middle
(b) having maximum value
(c) occurring a maximum number of times
(d) occurring a minimum number of times
Solution:

Section – B

Question numbers 9 to 14 are of 2 marks each.
Question 9.
An angle is 30° more than one-half of its complement. Find the angle.
Solution:

Question 10.
In the given figure, find the value of x.

Solution:

Question 11.
A die is thrown once. Find the probability of getting
(i) a prime number
(ii) a composite number
Solution:

Question 12.
You want to show that ΔDEF = ΔPQR by SAS congruence rule.
It is given that ∠E = ∠Q, you need to have
(i) EF = …….
(ii) PQ = ………

Solution:

Question 13.
In the given figure, two adjacent sides of a parallelogram are 15 cm and 10 cm. If the distance between the longer sides is 8 cm, find the
(i) area of parallelogram
(ii) the distance between the shorter sides.

Solution:

Question 14.
Find the mean age of six students whose ages (in years) are:
15, 13, 16, 13, 14, 16.
Solution:

Section – C

Question numbers 15 to 24 are of 4 marks each.
Question 15.
In the given figure, lines l and m are parallel. Find the values of x, y, and z.

Solution:

Question 16.
In the given figure, BC = AC. Find the value of x.

Solution:

Question 17.
If the lengths of the two sides of a triangle are 6 cm and 8.5 cm, then what can be the length of the third side?
Solution:

Question 18.
In the given figure, AD is perpendicular bisector of \(\bar { BC }\).
(i) State three pairs of equal parts in ∆ABD and ∆ACD.
(ii) Is ∆ABD = ∆ACD? Give reasons.
(iii) Is ABC an isosceles triangle? Give reasons.

Solution:

Question 19.
Draw a line, say AB, take a point P outside line AB. Through P, draw a line parallel to line AB using ruler and compasses only.
Solution:

Question 20.
In the given figure, ABCD is a rectangle with AB = 20 cm and BC = 14 cm. Two semicircles are cut from each of two breadths as diameters. Find
(i) the area of the shaded region
(ii) the perimeter of the shaded region.
Take π = \(\frac { 22 }{ 7 }\).

Solution:

Question 21.
Draw the reflection of the letter E in the given mirror line shown dotted.

Solution:

Question 22.
Three cubes each with edge 2 units are placed side by side to form a cuboid. Find the dimensions of the cuboid so formed and draw an isometric sketch of this cuboid.
Solution:

Question 23.
Draw two nets of a regular tetrahedron.
Solution:

Question 24.
A boy scored the following marks in various class tests during a year, each test is marked out of 20:
15, 17, 16, 7, 9, 12, 14, 16, 3, 19, 12, 16
(i) Arrange the marks in ascending order.
(ii) What are his modal marks?
(iii) What are his median marks?
(iv) What are his mean marks?
Solution:

Section – D

Question numbers 25 to 29 are of 6 marks each.
Question 25.
In the given figure, all measurements are in centimeters. If AD is perpendicular to BC, find the length of B.

Solution:

Question 26.
In the adjoining figure, show that ΔABC = ΔDBC. Hence, find the values of x and y.

Solution:

Question 27.
By using ruler and compasses only, construct a triangle ABC with BC = 7.5 cm, ∠B = 60° and ∠A = 90°.
Solution:

Question 28.
Anjali took a wire of length 88 cm and bent it into the shape of a circle. Find the area enclosed by that circle. If the same wire is bent in the shape of a square, then find the area enclosed by that square. Which shape encloses more area and by how much?
Take π = \(\frac { 22 }{ 7 }\)
Solution:

Question 29.
Given below is the data of school going students (boys and girls):

Draw a double bar graph to represent the above data and hence answer the following questions:
(i) Which mode of transport is used by more students?
(ii) Which mode of transport is used by more number of girls that the number of boys?
What values are being promoted by using a bicycle as a mode of transport?
Solution:

ML Aggarwal Class 6 Solutions Chapter 3 Integers Ex 3.1 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 3 Integers Ex 3.1

Question 1.
Write the opposite of the following:
(i) Loss of ₹ 5000
(ii) 30 km East of Delhi
(iii) 200 m above sea level
(iv) 325 BC
(v) Spending ₹ 2700
(vi) 25°C above freezing point.
Solution:

Question 2.
Write each of the following using appropriate sign ‘+’ or ‘-‘:
(i) Gain of 3 kg Weight
(ii) Earning ₹ 1340
(iii) 20°C below freezing point
(iv) Loss of ₹ 470
(v) Depositing ₹ 2500 in a bank
(vi) 240 m below sea level
(vii) A jet plane flying at a height of 9320 m.
(viii) 6 m down in the basement of a building.
Solution:

Question 3.
In each of the following pairs, which number is to the right of the other on the number line?
(i) 3, 5
(ii) 0, -2
(iii) -3, -5
(iv) 2, -7
Solution:

Question 4.
In each of the following pairs, which number is to the left of the other on the number line?
(i) -3, 0
(ii) 2, -5
(iii) -4, -7
(iv) -10,-16
Solution:

Question 5.
Draw a number line and answer the following questions:
(i) Which integers lie between -9 and -2?
(ii) which is the largest among them?
(iii) Which is the smallest among them?
Solution:

Question 6.
Write four consecutive integers just greater than -9.
Solution:

Question 7.
Write four consecutive integers just before -2.
Solution:

Question 8.
Draw a number line and answerthe following questions:
(i) Which number will we reach if we move 6 units to the right of-1?
(ii) Which number will we reach if we move 7 units to the left of 2?
(iii) In which direction should we move to reach 3 from -3?
(iv) In which direction should we move to reach -8 from -3?
Solution:

Question 9.
Using the number line, write the integer which is:
(i) 5 more than -1
(ii) 5 less than -1
(iii) 7 less than 2
(iv) 3 more than -7
Solution:

Question 10.
Evaluate the following.

Solution:

Question 11.
Use the appropriate symbol < or > to fill in the following blanks:
(i) -3 ………… 7
(ii) 0 ………….. -2
(iii) -10 ………… -11
(iv) -6 …………….. -2
(v) -5 ………….. -13
(vi) -30 …………… -19
Solution:

Question 12.
Arrange the following integers in ascending order:
(i) -5, 3, 0, -9, 2
(ii) -28, -33, 9, -4, -31, -2, 35
Solution:

Question 13.
Arrange the following integers in descending order:
(i) -31,25,-37, 43, 0,-5
(ii) -101, 95, -3, -8, 36, -7, -84
Solution:

Question 14.
State whether the following statements are true (T) or false (F):
(i) 0 is the smallest positive integer.
(ii) Every negative integer is less than every natural number.
(iii) -7 is to the right of-6 on the number line,
(iv) The absolute value of an integer is always greater than the integer.
Solution:

ML Aggarwal Class 7 Solutions for ICSE Maths Model Question Paper 5 acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 ICSE Maths Model Question Paper 5

(Based on Chapters 13 to 16)
Time allowed: 1 Hour
Maximum Marks: 25
General Instructions

• Questions 1-2 carry 1 mark each.
• Questions 3-5 carry 2 marks each.
• Questions 6-8 cany 3 marks each
• Questions 9-10 carry 4 marks each.

Choose the correct answer from the given four options (1-2):
Question 1.
If the area of a triangle is 48 cm2 and the length of its base is 12 cm, then its height is
(a) 4 cm
(b) 8 cm
(c) 12 cm
(d) 16 cm
Solution:

Question 2.
The letter which has both line and rotational symmetry is
(a) W
(b) N
(c) X
(d) E
Solution:

Question 3.
If the circumference of a circular sheet is 44 cm, then find its area.
Take π = \(\frac { 22 }{ 7 }\).
Solution:

Question 4.
Copy the given figure and draw all lines of symmetry.

Solution:

Question 5.
The given figure shows a net of a die; the numbers inserted in each square indicate the number of dots on that face. Insert suitable numbers in the blank squares, remembering that the number of dots on opposite faces of a die should be 7.

Solution:

Question 6.
A figure looks exactly the same at its original figure after a rotation of 72°. At what other angles will this figure appear the same? What can you say if the angle of rotation is (i) 60° (ii) 75°?
Solution:

Question 7.
In the given figure, a circle is inscribed in a semicircle of radius 7 cm. Find the area of the region.
Take π = \(\frac { 22 }{ 7 }\).

Solution:

Question 8.
Draw an isometric sketch of a cuboid of length 5 units, breadth 4 units and height 3 units.
Solution:

Question 9.
In the given figure, ABCD is a parallelogram with AB = 6 cm and AD = 5 cm. If DM is perpendicular to AB and the area of parallelogram ABCD is 24 cm², find the length of AM.

Solution:

Question 10.
By using ruler and compass, construct a triangle ABC with BC = 6.5 cm, AC = 5 cm and ∠C = 60°.
Solution:

ML Aggarwal Class 6 Solutions Chapter 2 Whole Numbers Check Your Progress for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 2 Whole Numbers Check Your Progress

Question 1.
Write next three consecutive whole numbers of the number 9998.
Solution:

Question 2.
Write three consecutive whole numbers occurring just before 567890.
Solution:

Question 3.
Find the product of the successor and the predecessor of the smallest number of 3-digits.
Solution:

Question 4.
Find the number of whole numbers between the smallest and the greatest numbers of 2-digits.
Solution:

Question 5.
Find the following sum by suitable arrangements:
(i) 678 + 1319 + 322 + 5681
(ii) 777 + 546 + 1463 + 223 + 537
Solution:

Question 6.
Determine the following products by suitable arrangements:
(i) 625 × 437 × 16
(ii) 309 × 25 × 7 × 8
Solution:

Question 7.
Find the value of the following by using suitable properties:
(i) 236 × 414 + 236 × 563 + 236 × 23
(ii) 370 × 1587 – 37 × 10 × 587
Solution:

Question 8.
Divide 6528 by 29 and check the result by division algorithm.
Solution:

Question 9.
Find the greatest 4-digit number which is exactly divisible by 357.
Solution:

Question 10.
Find the smallest 5-digit number which is exactly divisible by 279.
Solution:

ML Aggarwal Class 7 Solutions for ICSE Maths Model Question Paper 4 acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 ICSE Maths Model Question Paper 4

(Based on Chapters 10 to 12)
Time allowed: 1 Hour
Maximum Marks: 25

General Instructions

• Questions 1-2 carry 1 mark each.
• Questions 3-5 carry 2 marks each.
• Questions 6-8 cany 3 marks each
• Questions 9-10 carry 4 marks each.

Choose the correct answer from the given four options (1-2):
Question 1.
In the given figure, if l || m then the value of x is
(a) 65°
(b) 105°
(c) 115°
(d) 125°

Solution:

Question 2.
A triangle whose two angles measure 40° and 100° is
(a) scalene
(b) isosceles
(c) equilateral
(d) right-angled
Solution:

Question 3.
In the given figure, lines l and m intersect at O. If ∠1 + ∠3 = 222°, then find the measure of ∠2.

Solution:

Question 4.
In the given figure, AB = AC. Find the value of x.

Solution:

Question 5.
If ∆PQR = ∆EFD, write the parts of ∆EFD that correspond to:
(i) ∠Q
(ii) \(\bar { PR }\)
(iii) ∠P
(iv) \(\bar { QR }\)
Solution:

Question 6.
In the given figure, l || m and p || q. Find the value of x, y, and z.

Solution:

Question 7.
In the given figure, AB = AC. Find the values of x and y.

Solution:

Question 8.
If the lengths of two sides of a triangle are 5 cm and 7.5 cm then what can be the length of the third?
Solution:

Question 9.
An apple orchard is in the shape of a rectangle. If its length is 60 m and the length of one diagonal is 75 m, then find:
(i) the breadth of the orchard.
(ii) the perimeter of the orchard.
Solution:

Question 10.
In the given figure, measures of some parts are given.
(i) State the three pairs of equal parts in ∆ABD and ∆ACD.
(ii) Is ∆ABD = ∆ACD? Give reason.
(iii) Is D mid-point of BC? Why?

Solution:

ML Aggarwal Class 6 Solutions Chapter 2 Whole Numbers Objective Type Questions for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 2 Whole Numbers Objective Type Questions

Mental Maths
Question 1.
Fill in the blanks:
(i) A whole number is less than all those whole numbers that lie to its on the number line.
(ii) One more than a given whole is called its
(iii) There is atleast one whole number between two whole numbers.
(iv) 738 × 335 = 738 x (300 + 30 + ……..)
(v) If a is a non-zero whole number and a × a = a, then a = ……..
(vi) …….. is the only whole number which is not a natural number.
(vii) The additive identity in whole numbers is …….
Solution:

Question 2.
State whether the following statements are true (T) or false (F):
(i) The predecessor of a 3-digit number is always a 3-digit number.
(ii) The successor of a 3-digit number is always a 3-digit number.
(iii) If a is any whole number, then a + a = 1.
(iv) If a is any non-zero whole number, then 0 ÷ a = 0.
(v) On adding two different whole numbers, we always get a natural number.
(vi) Between two whole numbers there is a whole number.
(vii) There is a natural number which when added to a natural number, gives that number.
(viii) If the product of two whole numbers is zero, then atleast one of them is zero.
Solution:

Multiple Choice Questions
Choose the correct answer from the given four options (3 to 16):
Question 3.
The whole number which does not have a predecessor in whole number system is
(a) 0
(b) 1
(c) 2
(d) none of these
Solution:

Question 4.
The predecessor of the smallest 4-digit number is
(a) 99
(b) 999
(c) 1000
(d) 1001
Solution:

Question 5.
The predecessor of 1 million is
(a) 9999
(b) 99999
(c) 999999
(d) 1000001
Solution:

Question 6.
The product of the predecessor and the successor of the greatest 2-digit number is
(a) 9900
(b) 9800
(c) 9700
(d) none of these
Solution:

Question 7.
The sum of the successor of the greatest 3-digit number and the predecessor of the smallest 3-digit number is
(a) 1000
(b) 1100
(c) 1101
(d) 1099
Solution:

Question 8.
The number of whole numbers between 22 and 54 is
(a) 30
(b) 31
(c) 32
(d) 42
Solution:

Question 9.
The number of whole numbers between the smallest whole number and the greatest 2-digit number is
(a) 100
(b) 99
(b) 98
(d) 88
Solution:

Question 10.
If a is a whole number such that a + a = a, then a is equal to
(a) 0
(b) 1
(c) 2
(d) none of these
Solution:

Question 11.
The value of (93 × 63 + 93 × 37) is
(a) 930
(b) 9300
(c) 93000
(d) none of these
Solution:

Question 12.
Which of the following is not equal to zero?
(a) 0 × 5
(b) 0 = 5
(c) (10 – 10) + 5
(d) (5 – 0) + 5
Solution:

Question 13.
Which of the following statement is true?
(a) 21 – (13 – 5) = (21 – 13) – 5
(b) 21 – 13 is not a whole number
(c) 21 × 1 = 21 × 0
(d) 13 – 21 is not a whole number
Solution:

Question 14.
Which of the following statement is not true?
(a) Zero is the identity for multiplication of whole numbers.
(b) Addition and multiplication both are commutative for whole numbers.
(c) Addition and multiplication both are associative for whole numbers.
(d) Multiplication is distributive over addition for whole numbers.
Solution:

Question 15.
On dividing a number by 9 we get 47 as quotient and 5 as remainder. The number is
(a) 418
(b) 428
(c) 429
(d) none of these
Solution:

Question 16.
By using dot (•) pattern, which of the following numbers can be arranged in two ways namely a triangle and a rectangle?
(a) 12
(b) 11
(c) 10
(d) 9
Solution:

Higher Order Thinking Skills (HOTS)
Question 1.
The height of a slippery pole is 10 m and an insect is trying to climb the pole. The insect climbs 5 m in one minute and then slips down by 4 m. In how much time will insect reach the top?
Solution:

Question 2.
Which is greater, the sum of first twenty whole numbers or the product of first twenty whole numbers?
Solution:

Question 3.
If a whole number is divisible by 2 and 4, is it divisible by 8 also?
Solution: