ICSE

ML Aggarwal Class 6 Solutions Chapter 9 Algebra 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 9 Algebra Check Your Progress

Question 1.
Look at the following matchstick pattern of polygons. Complete the table. Also write the general rule that gives the number of matchsticks.

Solution:

Question 2.
Write an algebraic expression for each of the following:
(i) If 1 metre cloth costs ₹ x, then what is cost of 6 metre cloth?
(ii) If the cost of a notebook is ₹ x and the cost of a book is ₹ y, then what is the cost of 5 notebooks and 2 books?
(iii) The score of Ragni in Mathematics is 23 more than two-third of her score in English. If she scores x marks in English, what is her score in Mathematics?
(iv) If the length of a side of a regular pentagon is x cm, then what is the perimeter of the pentagon?
Solution:

Question 3.
When x = 4 and y = 2, find the value of:
(i) x + y
(ii) x – y
(iii) x² + 2
(iv) x² – 2xy + y²
Solution:

Question 4.
When a = 3 and b = -1, find the value of 2a³ – b⁴ + 3a²b³.
Solution:

Question 5.
When a = 3, b = 0, c = -2, find the values of:
(i) ab + 2bc + 3ca + 4abc
(ii) a³ + b³ + c³ – 3abc
Solution:

Question 6.
Solve the following linear equations:
(i) 2x – \(1 \frac{1}{2}=4 \frac{1}{2}\)
(ii) 3(y – 1) = 2(y + 1)
(ii) n – 3 = 5n + 21
(iv) \(\frac{1}{3}(7 x-1)=\frac{1}{4}\)
Solution:

ML Aggarwal Class 6 Solutions Chapter 12 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 6 Solutions for ICSE Maths Chapter 12 Symmetry Objective Type Questions

Mental Maths
Question 1.
Fill in the blanks:
(i) The subtraction symbol – has …….. lines of symmetry.
(ii) The addition symbol + has …….. lines of …….. symmetry.
(iii) Line of symmetry is also known …….. line or …….. of symmetry.
(iv) A kite has …….. line(s) of symmetry:
(v) A parallelogram has …….. line(s) of symmetry.
(vii) A rectangle is symmetrical about the lines joining the …….. of the opposite sides.
(viii)The number of capital letters of the English alphabet having only vertical line of symmetry is ……..
(ix) The number of capital letters of the English alphabet having only horizontal line of symmetry is ……..
(x) The number of capital letters of the English alphabet having both horizontal and vertical lines of symmetry is ……..
(xi) The digits having two lines of symmetry are …….. and ……..
Solution:

Question 2.
State whether the following statements are true (T) or false (F):
(i) The letter N has one line of symmetry.
(ii) Every hexagon has six lines of symmetry.
(iii) All right-angled triangles have one line of symmetry.
(iv) A triangle with more than one line of symmetry must be an equilateral triangle.
(v) A line of symmetry divides a figure into two identical parts.
(vi) A circle has only 8 lines of symmetry.
(vii) A regular octagon has 10 lines of symmetry.
(viii) A square and a rectangle have the same number of lines of symmetry.
(ix) A right-angled triangle can have at most one line of symmetry.
(x) If an isosceles triangle has more than one line of symmetry, then it must be rn equilateral triangle.
(xi) If a rectangle has more than two lines of symmetry, then it must be a square.
Solution:

Multiple Choice Questions
Choose the correct answer from the given four options (3 to 15):
Question 3.
The number of lines of symmetry of a scalene triangle is
(a) 0
(b) 1
(c) 2
(d) 3
Solution:

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

Question 5.
The number of lines of symmetry of a rectangle is
(a) 0
(b) 1
(c) 2
(d) 4
Solution:

Question 6.
A rhombus is symmetrical about
(a) each of its two diagonals
(b) each of its two lines joining the mid-points of opposite sides
(c) each of the perpendicular bisector of its sides
(d) none of these.
Solution:

Question 7.
The number of lines of symmetry of a circle is
(a) 4
(b) 8
(c) 16
(d) unlimited
Solution:

Question 8.
Which of the following letters does not have any line of symmetry?
(a) B
(b) T
(c) Z
(d) Y
Solution:
Z (c)

Question 9.
Which of the following letters does not have the vertical line of symmetry?
(a) A
(b) H
(c) M
(d) E
Solution:

Question 10.
Which figure from the following figures is not symmetrical with respect to any line?

Solution:

Question 11.
In which of the given figures is the dotted line of symmetry?

Solution:

Question 12.
Amongst the given figures, the one having a maximum number of lines of symmetry is:

Solution:

Question 13.
The angle between the mirror line l and the line segment joining a point and its reflection (image) is:
(a) 0°
(b) 45°
(c) 60°
(d) 90°
Solution:
90° (d)

Question 14.
Which of two figures are image of each other (mirror line shown dotted)?

Solution:

Question 15.
Which of the two figures are mirror images of each other (mirror line showed dotted)?

Solution:

ML Aggarwal Class 6 Solutions Chapter 12 Symmetry Ex 12.2 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 12 Symmetry Ex 12.2

Question 1.
Copy the following figures on a squared paper. Complete each of them such that the dotted line is the line of symmetry:

Solution:

Question 2.
Copy the following figures on a squared paper. Complete each of them such that the resultant figure has two dotted lines as the lines of symmetry:

Solution:

Question 3.
In the given figure, l is the line of symmetry. Complete the diagram to make it symmetrical.

Solution:

Question 4.
In the given figure, l is the line of symmetry. Draw the image of the parallelogram and complete the diagram so that it becomes symmetrical.

Solution:

Question 5.
Copy the following figures on a squared paper and find their reflections in the mirror line l.

Solution:

ML Aggarwal Class 6 Solutions Chapter 12 Symmetry Ex 12.1 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 12 Symmetry Ex 12.1

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

Solution:

Question 2.
Draw the line (or lines) of symmetry, if any, of the following pictures (of objects) and count their number:

Solution:

Question 3.
Draw the line (or lines) of symmetry, if any, of the following road signs and count their number:

Solution:

Question 4.
Draw the line (or lines) of symmetry, if any, of the following numerals and count their number:

Solution:

Question 5.
Copy the following figures on a squared paper and draw the lines of symmetry (if any) and count their number:

Solution:

Question 6.
Write the letters of words ‘JUST LOOK’ which have no line of symmetry.
Solution:

Question 7.
Can you draw a triangle which has
(i) exactly one line of symmetry?
(ii) exactly two lines of symmetry?
(iii) exactly three lines of symmetry?
(iv) no lines of symmetry?
Sketch a rough figure in each case and name the triangle.
Solution:

ML Aggarwal Class 6 Solutions Chapter 11 Understanding Symmetrical Shapes 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 11 Understanding Symmetrical Shapes Check Your Progress

Question 1.
In the given figure, identify the longest and shortest line segments by measuring their lengths.

Solution:

Question 2.
Where will the hour hand of a clock stop if it starts from 10 and turns through 3 right angles?
Solution:
7

Question 3.
Classify the angles whose measures are given below:
(i) 56°
(ii) 125°
(iii) 90°
(iv) 180°
(v) 215°
(vi) 328°
Solution:

Question 4.
Name the types of the following triangles:
(i) ∆ABC with AB = 8 cm, AC = 7 cm and BC = 5.5 cm.
(ii) ∆PQR with PQ = PR = 5 cm and QR = 7.3 cm.
(iii) ∆DEF with D = ∠90°.
(iv) ∆XYZ with ∠Y = 90° and XY = YZ.
(v) ∆LMN with ∠L = 30°, ∠M = 70° and ∠N = 80°.
Solution:

Question 5.
Name each of the following triangles in two different ways (you may use ruler and protractor):

Solution:

Question 6.
State whether the following statements are true or false:
(i) A rectangle is a regular quadrilateral.
(ii) A rhombus is a regular quadrilateral.
(iii) Every parallelogram is a rhombus.
(iv) The diagonals of a rhombus intersect at right angles.
(v) A polygon having 6 sides is called an octagon.
(vi) A road roller has two plane circular faces and one curved face.
(vii) A rectangular pyramid has 5 rectangular faces.
Solution:

Question 7.
Draw a rough sketch of a regular octagon and draw a square by joining exactly four of its vertices.
Solution: