Category: ICSE

ML Aggarwal Class 7 Solutions Chapter 17 Data Handling Ex 17.4 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 17 Data Handling Ex 17.4

Question 1.
Tell whether the following is certain to happen, impossible to happen, can happen but not certain:
(i) You are older today than yesterday.
(ii) Two hundred people can sit in a Maruti car.
(iii) A tossed coin will land heads up.
(iv) A die when tossed shall land up with 8 on top.
(v) India will win the next test series.
(vi) Tomorrow will be a cloudy day.
(vii) The next traffic light seen will be green.
Solution:

Question 2.
A coin is flipped to decide which team starts the game. What is the probability that your team will start the game?
Solution:

Question 3.
There are 6 marbles in a box with numbers 1 to 6 marked on them.
(i) What is the probability of drawing a marble with number 5?
(ii) What is the probability of drawing a marble with number 2?
Solution:

Question 4.
A die is tossed once. Find the probability of getting
(i) a number less than 3
(ii) a prime number
(iii) a number greater than 2
Solution:

Question 5.
A box contains 3 defective mangoes and 21 good mangoes. One mango is drawn from the box at random. Find the probability of getting
(i) a defective mango
(ii) a good mango
Solution:

Question 6.
A card is drawn from a well-shuffled pack of 52 playing cards. Find the probability of getting
(i) a red card
(ii) a king
(iii) a card of spades
Solution:

ML Aggarwal Class 7 Solutions Chapter 15 Visualising Solid Shapes 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 7 Solutions for ICSE Maths Chapter 15 Visualising Solid Shapes Objective Type Questions

Mental Maths

Question 1.
Fill in the blanks:
(i) A solid having no vertex and no edge is a ………..
(ii) A solid that has congruent and parallel polygons as top and bottom faces and all other faces rectangular is known as ………
(iii) A pyramid having 4 equilateral triangles as its faces is known as ………
(iv) A solid having 3 faces (one curved and two circulars), no vertex and two curved edges are known as ……..
(v) A solid having a circular base and one vertex is called a ………
(vi) A triangular prism has ……… faces, ………… edges and ………. vertices.
(vii) A triangular pyramid has ……… faces, ………. edges and ……… vertices.
(viii) A square pyramid has ……… faces, ……….. edges and ……… vertices.
(ix) The base of a triangular pyramid is a ………
(x) Out of ……….. faces of a triangular prism, ……… are rectangle and ……….. are triangles.
(xi) Out of ……….. faces of a square pyramid, ………. are a triangle and ………. is/are squares.
(xii) Out of ………. faces of a rectangular pyramid, ………. are triangles and the base is a ……….
(xiii) A ……….. is a sort of skeleton – outline in 2-D, which on folding results in a 3-D shape.
(xiv) If the sum of numbers on the two dice thrown together is 9, then the sum of the numbers opposite to these faces is ……….
Solution:

Question 2.
State whether the following statements are true (T) or false (F):
(i) The faces of a prism are triangular.
(ii) A cube can be treated as a prism.
(iii) A pyramid has only one vertex.
(iv) All the faces, except the base, of a square pyramid are triangular.
(v) A tetrahedron has 3 rectangular faces and 1 rectangle face.
(vi) A square pyramid has 5 faces and one vertex.
(vii) A cone has one vertex, two faces, and one curved edge.
(viii)The shadow of a 3-D object is a 2-D figure.
(ix) A cube can cast a shadow in the shape of a rectangle.
(x) A cube can cast a shadow in the shape of a hexagon.
(xi) In an isometric sketch, the line segments of different lengths can represent the sides of a cube.
(xii) In an oblique sketch of a cuboid, the size of the opposite faces must be different.
(xiii) The top, front and side views of a sphere are different.
(xiv) The adjoining net is of a hexagonal pyramid.

Solution:

Multiple Choice Questions

Choose the correct answer from the given four options (3 to 11):
Question 3.
A triangular prism has
(a) 4 vertices and 6 edges
(b) 6 vertices and 9 edges
(c) 6 vertices and 6 edges
(d) 9 vertices and 6 edges
Solution:

Question 4.
A square pyramid has
(a) 4 vertices and 4 faces
(b) 4 vertices and 5 faces
(c) 5 vertices and 4 faces
(d) 5 vertices and 5 faces
Solution:

Question 5.
A solid having 4 (plane) faces, 4 vertices and 6 edges is called a
(a) triangular prims
(b) rectangular prism
(c) triangular pyramid
(d) rectangular pyramid
Solution:

Question 6.
The number of cubes in the given structure is
(a) 12
(b) 10
(c) 9
(d) 8

Solution:

Question 7.
An isometric sheet is made up of dots forming
(a) squares
(b) rectangles
(c) right-angled triangles
(d) equilateral triangles
Solution:

Question numbers 8 to 11 are based on the given figure in which unit cubes are put together to form a structure as shown:

Question 8.
The number of unit cubes in the given structure is
(a) 13
(b) 20
(c) 21
(d) 22
Solution:

Question 9.
The number of unit cubes to be added to make a cuboid of dimensions 4 unit × 4 unit × 2 unit is
(a) 11
(b) 12
(c) 13
(d) 14
Solution:

Question 10.
If the structure is painted on the surface everywhere, then the number of unit cubes having no face painted is
(a) 0
(b) 1
(c) 2
(d) 11
Solution:

Question 11.
The side view of the given structure is

Solution:

ML Aggarwal Class 7 Solutions Chapter 17 Data Handling Ex 17.3 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 17 Data Handling Ex 17.3

Question 1.
Find the median of the following data:
(i) 3, 1, 5, 6, 3, 4, 5
(ii) 3, 1, 5, 6, 3, 4, 5, 6
Solution:

Question 2.
Find the mode of the following data:
(i) 3, 1, 5, 6, 3, 4, 5, 3
(ii)

Solution:

Question 3.
Find the median and the mode of the data:
13, 16, 12, 14, 19, 12, 14, 13, 14
Solution:

Question 4.
The scores in mathematics test (out of 25) of 15 students is as follows:
19, 25, 23, 20, 9, 20, 15, 10, 5, 16, 25, 20, 24, 12, 20
Find the mode and median of this data. Are they same?
Solution:

Question 5.
The weights (in kg) of 15 students of a class are:
38, 42, 35, 37, 45, 50, 32, 43, 43, 40, 36, 38, 43, 38, 47
(i) Find the median and mode of this data.
(ii) Is there more than one mode?
Solution:

Question 6.
The runs scored in a cricket match by 11 players is as follows:
6, 15, 120, 50, 100, 80, 10, 15, 8, 10, 15
Find the mean, mode and median of this data. Are the three same?
Solution:

Question 7.
Find the mode of the following data:
12, 14, 12, 15, 16, 13, 14, 18, 19, 12, 14, 15, 16, 15, 16, 16, 15, 17, 13, 16, 16, 15, 15, 13, 15, 17, 15, 14, 15, 13, 15, 14.
Solution:

ML Aggarwal Class 7 Solutions Chapter 15 Visualising Solid Shapes Ex 15.3 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 15 Visualising Solid Shapes Ex 15.3

Question 1.
Count the number of cubes in the following structures:

Solution:

Question 2.
What cross-section is made in the following
(i) vertical cut (ii) horizontal cut?
(a) A brick
(b) A round apple
(c) A die
(d) A circular pipe
(e) An ice cream cone
(f) A square pyramid
Solution:

Question 3.
For each solid given below, the three views (1), (2) and (3) are given. Identify for each solid the corresponding top, front and side views:


Solution:

Question 4.
For the solids given below sketch the front, side and top view:

Solution:

ML Aggarwal Class 7 Solutions Chapter 17 Data Handling Ex 17.1 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 17 Data Handling Ex 17.1

Question 1.
The number of rooms in 25 houses of a locality is as given below:
4, 3, 2, 6, 4, 3, 2, 1, 5, 3, 2, 3, 4, 3, 5, 1, 6, 1, 3, 4, 2, 3, 4, 3, 5
(i) Arrange the above data in ascending order.
(ii) Find the range of the data.
(iii) Construct a frequency distribution table for the above data.
(iv) Find the number of houses which have 4 or more than 4 rooms.
(v) Drawbar graph to represent the above data.
Solution:

Question 2.
The given bar graph shows the number of books sold by a bookstore for five consecutive years. Read the bar graph and answer the following questions:
(i) About how many books were sold in 2008, 2009 and 2011 years?
(ii) In which years were about 475 books and 225 books sold?

Solution:

Question 3.
Two hundred students of 6th and 7th class were asked to name their favorite colour so as to decide upon what should be the colour of their school building. The results are shown in the following table:

Represent the given data on a bar graph.
Answer the following questions with the help of the bar graph:
(i) Which is the most preferred colour?
(ii) Which is the least preferred colour?
(iii) How many colors are there in all? What are they?
Solution:

Question 4.
Sale of English and Hindi books in four consecutive years is given below:

Draw a double bar graph to represent the above data and answer the following questions:
(i) In which year was the difference in the sale of two language books least?
(ii) Can you say that the demand for English books rose faster? Justify your answer.
Solution:

Question 5.
Consider the following data collected from a survey of a colony:

Draw a double bar graph choosing an appropriate scale.
Answer the following questions using the bar graph:
(i) Which sports is most popular?
(ii) Which is more preferred, watching or participating in sports?
Solution:

ML Aggarwal Class 7 Solutions Chapter 16 Perimeter and Area 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 7 Solutions for ICSE Maths Chapter 16 Perimeter and Area Check Your Progress

Question 1.
A 3 m wide path runs outside and around a rectangular park of length 125 m and breadth 65 m. Find the area of the path.
Solution:

Question 2.
In the given figure, all adjacent line segments are at right angles. Find:
(i) the area of the shaded region
(ii) the area of the unshaded region.

Solution:

Question 3.
Find the area of a triangle whose:
(i) base = 2 m, height = 1.5 m
(ii) base = 3.4 m and height = 90 cm
Solution:

Question 4.
In the given figure, PQRS is a parallelogram. QM is the height from Q to SR and QN is the height from Q to PS. If SR = 12 cm, PS = 8 cm and QM = 7.6 cm, find:
(i) the area of the parallelogram PQRS
(ii) the length of QN.

Solution:

Question 5.
From the given figure, find
(i) the area of ΔABC
(ii) length of BC
(iii) the length of altitude from A to BC.

Solution:

Question 6.
In the given figure, the area of the right-angled triangle is 54 cm². If one of its legs is 12 cm long, find its perimeter.

Solution:

Question 7.
If the area of a circle is 78.5 cm², find its circumference. (Take π = 3.14)
Solution:

Question 8.
Find the circumference of the circle whose area is 16 times the area of the circle with diameter 7 cm.
Solution:

Question 9.
From square cardboard, a circle of the biggest area was cut out. If the area of the circle is 154 cm², calculate the original area of the cardboard.
Solution:

Question 10.
A road 3.5 m wide surrounds a circular park whose circumference is 88 m. Find the cost of paving the road at the rate of ₹ 60 per square meter.
Solution:

Question 11.
In the given figure, ABCD is a square of side 14 cm. Find the area of the shaded region.
Take π = \(\frac { 22 }{ 7 }\)

Solution:

Question 12.
The boundary of a shaded region in the given figure consists of three semicircles, the smaller being equal. If the diameter of the larger one is 28 cm, find
(i) the length of the boundary
(ii) the area of the shaded region.

Solution:

ML Aggarwal Class 7 Solutions Chapter 15 Visualising Solid Shapes Ex 15.2 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 15 Visualising Solid Shapes Ex 15.2

Question 1.
The dimensions of a cuboid are 5 cm, 3 cm, and 2 cm. Draw three different isometric sketches of this cuboid with height
(i) 2 cm
(ii) 3 cm
(iii) 5 cm
Solution:

Question 2.
Give (i) an oblique sketch (ii) an isometric sketch for each of the following:
(a) A cube is with an edge 4 cm long.
(b) A cuboid of length 6 cm, breadth 4 cm, and height 3 cm.
Solution:

Question 3.
The adjoining figure shows an isometric sketch of a 3-D shape. Draw an oblique sketch that matches this sketch.

Solution:

Question 4.
Draw an isometric sketch of each of the following oblique shapes:

Solution:

ML Aggarwal Class 7 Solutions Chapter 14 Symmetry 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 7 Solutions for ICSE Maths Chapter 14 Symmetry Check Your Progress

Question 1.
Draw the line (or lines) of symmetry, if any of the following shapes and count their number.

Solution:

Question 2.
For each of the given shape in Question 1, find the order of the rotational symmetry (If any).
Solution:

Question 3.
Give the order of rotational symmetry of each of the following figures:

Solution:

ML Aggarwal Class 7 Solutions Chapter 16 Perimeter and Area Ex 16.3 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 16 Perimeter and Area Ex 16.3

Take π = \(\frac { 22 }{ 7 }\), unless stated otherwise.
Question 1.
Find the circumference of the circles with the following radius:
(i) 7 cm
(ii) 21 cm
(iii) 28 mm
(iv) 3.5 cm
Solution:

Question 2.
Find the area of the circles, given that:
(i) radius = 14 mm
(ii) diameter = 49 m
(iii) diameter = 9.8 m
(iv) radius = 5 cm
Solution:

Question 3.
Find the circumference and area of a circle of radius 20 cm. (use π = 3.14)
Solution:

Question 4.
The minute hand of a tower clock is 1.4 m long. How far does the tip of the hand move in 1 hour?
Solution:

Question 5.
A gardener wants to fence a circular garden of diameter 21 m. Find the length of the rope he needs to purchase if he makes 2 rounds of the fence. Also find the cost of the rope, if it costs ₹ 4 per metre.
Solution:

Question 6.
If the circumference of a circle exceeds its diameter by 30 cm, find the radius of the circle.
Solution:

Question 7.
Find the length of the diameter of a circle whose circumference is 44 cm.
Solution:

Question 8.
The circumference of a circle is 31.4 cm. Find the radius and the area of the circle. (Take π = 3.14)
Solution:

Question 9.
Find the radius and the circumference of a circle whose area is 144π cm².
Solution:

Question 10.
How many times will the wheel of a car rotate in a journey of 88 km, given that the diameter of the wheel is 56 cm?
Solution:

Question 11.
From square cardboard of side 21 cm, a circle of the maximum area is cut out. Find the area of the cardboard left.
Solution:

Question 12.
A piece of wire is bent in the shape of an equilateral triangle of side 4.4 cm. If this wire is rebent to form of a circle, find the radius and the area of the circle.
Solution:

Question 13.
A wire is in the form of a square of side 27.5 cm. It is straightened and bent into the shape of a circle. Find the area of the circle.
Solution:

Question 14.
A wire is in the form of a rectangle 18.7 cm long and 14.3 cm wide. If this wire is reshaped and bent in the form of the circle, find the radius and the area of the circle so formed.
Solution:

Question 15.
The diameter of a circular park is 84 m. On its outside, there a 3.5 m wide road. Find the cost of constructing the road at ₹ 240 per m².
Solution:

Question 16.
A circular pond is surrounded by a 2 m wide circular path. If the outer circumference of the circular path is 44 m, find the inner circumference of the circular path. Also, find the area of the path.
Solution:

Question 17.
In the given figure, the area enclosed between the concentric circles is 770 cm². If the radius of the outer circle is 21 cm, calculate the radius of the inner circle.

Solution:

Question 18.
From a circular card sheet of radius 14 cm, two circles of radius 3.5 cm and a rectangle of length 3 cm and breadth 1 cm are removed (as shown in the given figure). Find the area of the remaining sheet.

Solution:

Question 19.
Calculate the length of the boundary and the area of the shaded region in the following diagrams. All measurements are in centimetres.
(i) The unshaded part is a semicircle.

(ii) Four semicircles on a square.

Solution:

Question 20.
Find the perimeter and the area of the shaded region in the following figures. All measurements are in centimetres.

Solution:

ML Aggarwal Class 7 Solutions Chapter 14 Symmetry 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 7 Solutions for ICSE Maths Chapter 14 Symmetry Objective Type Questions

Mental Maths

Question 1.
Fill in the blanks:
(i) The hands of a clock rotate only in ………. direction.
(ii) While opening the cap of a bottle, the direction of rotation is ……….
(iii) The number of lines of symmetry of an isosceles right-angled triangle is …………
(iv) A figure has ……….. symmetry if it is its own image under a reflection.
(v) The centre of rotation of an equilateral triangle is the point of intersection of its ………..
(vi) The centre of rotation of a rhombus is the point ……….
(vii) A regular polygon of n-sides has ……….. the number of lines of symmetry.
(viii) The angle of rotational symmetry in an equilateral triangle is ……….
(ix) The angle of rotational symmetry in a regular pentagon is ……..
(x) If after a rotation of 45° about a fixed point the figure looks exactly the same, then the order of rotational symmetry is ……….
Solution:

Question 2.
State whether the following statements are true (T) or false (F):
(i) The letter A has line symmetry but no rotational symmetry.
(ii) A rhombus is also a parallelogram and hence it does not have line symmetry.
(iii) A parallelogram has two lines of symmetry.
(iv) The order of rotational symmetry of a rhombus is four.
(v) A circle has exactly four lines of symmetry.
(vi) In a regular pentagon, the perpendicular bisector of the sides are the only lines of symmetry.
(vii) In a regular hexagon, the perpendicular bisector of the sides are the only lines of symmetry.
(viii) In a rectangle, the angle of rotational symmetry is 90°.
(ix) A semicircle has rotational symmetry of order 2.
(x) An isosceles triangle has neither a line symmetry nor a rotational symmetry.
(xi) If a figure possesses a rotational symmetry, then it must look exactly the same atleast once up to a rotation of 180°.
(xii) The angle of rotation of a figure is obtained by dividing 360° by the order of rotational symmetry.
(xiii) A regular triangle has 3 lines of symmetry and rotational symmetry of order 3.
(xiv) A regular pentagon has 5 lines of symmetry and rotational symmetry of order 5.
Solution:

Multiple Choice Questions

Choose the correct answer from the given four options (3 to 14):
Question 3.
A quadrilateral having four lines of symmetry is a
(a) parallelogram
(b) rectangle
(c) rhombus
(d) square
Solution:

Question 4.
The letter Z has
(a) one horizontal line of symmetry
(b) one vertical line of symmetry
(c) two lines of symmetry
(d) no line of symmetry
Solution:

Question 5.
A figure that does not have any rotational symmetry is
(a) circle
(b) parallelogram
(c) kite
(d) regular pentagon
Solution:

Question 6.
The number of lines of symmetry in the given figure is
(a) 1
(b) 3
(c) 6
(d) infinitely many

Solution:

Question 7.
Rotating a figure by 60° anticlockwise is equivalent to a clockwise rotation of
(a) 60°
(b) 120°
(c) 240°
(d) 300°
Solution:

Question 8.
A figure having 1 line of symmetry and whose order of rotational symmetry is also 1 is
(a) rhombus
(b) parallelogram
(c) kite
(d) scalene triangle
Solution:

Question 9.
The order of rotational symmetry of a line segment is
(a) 1
(b) 2
(c) 3
(d) 4
Solution:

Question 10.
The order of the rotational symmetry in the given figure is
(a) 1
(b) 2
(c) 4
(d) infinitely many

Solution:

Question 11.
A possible angle of rotation of a figure having rotational symmetry of order greater than 1 is
(a) 36°
(b) 144°
(c) 150°
(d) 360°
Solution:

Question 12.
The figure which does not have both reflection and rotational symmetry is

Solution:

Question 13.
In the word ’MATHS’ which of the following pairs of letters have rotational symmetry?
(a) M and T
(b) A and S
(c) T and S
(d) H and S
Solution:

Question 14.
The letter which has both reflection and rotational symmetry is
(a) H
(b) M
(c) S
(d) Y
Solution:

ML Aggarwal Class 7 Solutions Chapter 14 Symmetry Ex 14.2 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 14 Symmetry Ex 14.2

Question 1.
Which of the following figures have rotational symmetry? In the case of rotational symmetry, find the order of rotational symmetry.

Solution:

Question 2.
Which of the following figures have rotational symmetry of order greater than 1?

Solution:

Question 3.
Name any two figures that have both lines of symmetry and rotational symmetry.
Solution:

Question 4.
Name the quadrilaterals which have both line and rotational symmetry of order more than 1.
Solution:

Question 5.
Draw a rough sketch of:
(i) a triangle with both line and rotational symmetries of order more than 1.
(ii) a triangle with only one line of symmetry and no rotational symmetry of order more than 1.
(iii) a triangle with no line symmetry but rotational symmetry of order 1.
(iv) a quadrilateral with no line symmetry but rotational symmetry of order more than 1.
(v) a quadrilateral with line symmetry but not rotational symmetry of order more than 1.
Solution:

Question 6.
If a figure has two or more than two lines of symmetry, can it have rotational symmetry of order more than one?
Solution:

Question 7.
A figure looks exactly the same as its original figure after rotation of 60°. At what other angles will this figure appear the same?
What can you say if the angle of rotation is
(i) 72°
(ii) 45°
(iii) 50°?
Solution:

Question 8.
Can a figure possessing rotational symmetry have an angle of rotation of measure
(i) 180°
(ii) 120°
(iii) 90°
(iv) 30°
(v) 15°
(vi) 17°?
Solution: