ICSE

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 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 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 7 Solutions for ICSE Maths Model Question Paper 3 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 3

(Based on Chapters 1 to 9)
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 comprises of 10 questions of 4 marks each and
• 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 are of 1 mark each.
Question 1.
The number of integers between -16 and 5 is
(a) 19
(b) 20
(c) 21
(d) 22
Solution:

Question 2.
50 m 5 cm is the same as
(a) 50.5 m
(b) 50.05 m
(c) 50.005 m
(d) 5.05 m
Solution:

Question 3.

Solution:

Question 4.
The number 5,540,000,000,000 in the scientific notation can be written as:
(a) 554 × 10¹⁰
(b) 55.4 × 10¹¹
(c) 5.54 × 10¹²
(d) 5.54 × 10¹¹
Solution:

Question 5.
The number of unlike terms in the expression 5x²y – 2xy² – 2yx² + 3y(xy + y²) + 7 is
(a) 3
(b) 4
(c) 5
(d) 6
Solution:

Question 6.
x = -2 is a solution of the equation
(a) 2x + 5 = 9
(b) 3x – 1 = 5
(c) 4x + 3 = 1
(d) 5x + 12 = 2
Solution:

Question 7.
The ratio of the number of girls to the number of boys in a class is 5 : 4. If there are 16 boys in the class, then the number of students in the class is
(a) 20
(b) 32
(c) 36
(d) 45
Solution:

Question 8.
If 12% of a number is 9, then the number is
(a) 36
(b) 48
(c) 60
(d) 75
Solution:

Section – B

Question numbers 9 to 14 are of 2 marks each.
Question 9.
Using suitable properties, evaluate:
238 × (-44) + (-238) × 56.
Solution:

Question 10.
State whether each of the following statement is true or false for the sets P and Q where P = {letters of TITLE} and Q = {letters of LITTLE}
(i) P ↔ Q
(ii) P = Q
Solution:

Question 11.
Evaluate: -3\(\frac { 3 }{ 8 }\) – (-2\(\frac { 1 }{ 6 }\))
Solution:

Question 12.
Simplify and express in the exponential form: (4³ × 3⁶) ÷ (16 × 9²).
Solution:

Question 13.
If I earn ₹ 75000 per month and spend ₹ 40000 per year for helping poor students then find the ratio of the money spent on helping poor students and the annual income.
Solution:

Question 14.
If ₹ 4000 amounts to ₹ 5000 in 2 years, find the rate of simple interest per annum.
Solution:

Section – C

Question numbers 15 to 24 are of 4 marks each.
Question 15.
Simplify:

Solution:

Question 16.
Vikram’s monthly salary is ₹ 12750. He spends \(\frac { 1 }{ 5 }\) of his salary on food and out of the remaining, he spends \(\frac { 1 }{ 4 }\) on rent and \(\frac { 1 }{ 6 }\) on the education of children. Find
(i) how much he spends on each item?
(ii) how much money is still left with him?
Solution:

Question 17.
Insert five rational numbers between \(\frac { -2 }{ 5 }\) and \(\frac { -1 }{ 3 }\)
Solution:

Question 18.
Afzal can walks 5\(\frac { 3 }{ 4 }\) km in one hour. How much distance will he cover in 2 hours 40 minutes? What are the health advantages of having a brisk walk?
Solution:

Question 19.
If a vehicle covers a distance of 57.72 km in 3.7 litres of petrol. How much distance will it cover in one litre of petrol?
Solution:

Question 20.
The perimeter of a triangle is 5 – 3x + 7x² and two of its sides are 2x² + 3x – 2 and 3x² – x + 3. Find the third side of the triangle.
Solution:

Question 21.

Solution:

Question 22.
Solve the equation: 3(2x – 1) – 2(2 – 5x) = 1
Solution:

Question 23.
If 74% of the population of a village is illiterate and the number of literate people is 2158, then find the population of the village.
Solution:

Question 24.
Simplify:

Solution:

Section – D

Question numbers 25 to 29 are of 6 marks each.
Question 25.
If we represent the distance above the ground by a positive rational number and that below the ground by a negative rational number, then answer the following question:
An elevator descends into a mine shaft at the rate of 4\(\frac { 3 }{ 4 }\) metre per minute. If it begins to descend from 7\(\frac { 1 }{ 2 }\) metre above the ground, what will be its position after 18 minutes from the ground?
Solution:

Question 26.
In a competition, the question paper consists of 25 questions. 4 marks are awarded for every correct answer, 2 marks are deducted for every incorrect answer and no marks for not attempting a question. If Vaishali scored 58 marks and got 17 correct answers, how many questions she attempted incorrectly? How many questions she did not attempt?
Solution:

Question 27.
Divide ₹ 216000 into two parts such that one-fourth of one part is equal to one-fifth of the other part. Find the two parts.
Solution:

Question 28.
If a table is sold for ₹ 437 at a loss of 8%, find its cost price. At what price must it be sold to gain 10%?
Solution:

Question 29.
Solve the inequality:
3 – 2x ≥ x – 10, x ∈ N.
Also, represent its solution set on the number line.
Solution:

ML Aggarwal Class 7 Solutions for ICSE Maths Model Question Paper 2 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 2

(Based on Chapters 4 to 7)
Time allowed: 1 Hour
Maximum Marks: 25

Instructions

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

Choose the correct answer from the given four options (1-2):
Question 1.
The expression \(\left( \frac { 1 }{ 3 } \right) ^{ 9 }\) × (3⁴)² is equal to
(a) 3⁹
(b) 3
(c) \(\left( \frac { 1 }{ 3 } \right) ^{ 2 }\)
(d) \(\frac { 1 }{ 3 }\)
Solution:

Question 2.
On selling an article for ₹ 100, Renu gains ₹ 20. Her gain percentage is
(a) 25%
(b) 20%
(c) 16\(\frac { 2 }{ 3 }\) %
(d) 15%
Solution:

Question 3.
Ravi donated ₹ 3⁶ to a blind school and Rashmi donated ₹ 6³ to an orphanage. Who donated more money?
Solution:

Question 4.
Find the cardinal number of the set A where A = {x | x is a two-digit number, the sum of whose digits is 11}.
Solution:

Question 5.
Find the fourth proportional to 8, 24, 25.
Solution:

Question 6.

Solution:

Question 7.
18% of the apples in a basket go bad. If there are 123 good apples in the basket, find the total number of apples in the basket.
Solution:

Question 8.
A natural number has been divided into two parts in the ratio 8 : 5. If the difference of two parts is 24, find the number and the two parts.
Solution:

Question 9.
If 2.5 kg of apples cost ₹ 187.5, then how much quantity of apples can be bought for ₹ 330?
Solution:

Question 10.
What sum of money will amount to ₹ 2875 in 3 years at 5% per annum simple interest?
Solution: