List of top Mathematics Questions asked in CBSE Class VII

Draw, wherever possible, a rough sketch of 

1.  a triangle with both line and rotational symmetries of order more than 1. 
2.  a triangle with only line symmetry and no rotational symmetry of order more than 1. 
3.  a quadrilateral with a rotational symmetry of order more than 1 but not a line symmetry. 
4.  a quadrilateral with line symmetry but not a rotational symmetry of order more than 1.

Give the order of rotational symmetry for each figure:

Which of the following figures have rotational symmetry of order more than 1:

Shade: (i) \(\frac{1}{2}\) of the circles in box (a)
(ii) \(\frac{2}{3}\) of the triangles in box (b)
(iii) \(\frac{3}{5}\) of the squares in box (c).

Find:
(a) \(\frac{1}{2}\) of (i) 24 (ii) 46
(b) \(\frac{2}{3}\) of (i) 18 (ii) 27
(c) \(\frac{3}{4}\) of (i) 16 (ii) 36
(d) \(\frac{4}{5}\) of (i) 20 (ii) 35

Multiply and reduce to the lowest form and convert into a mixed fraction:
(i) 7 × \(\frac{3}{5}\)
(ii) 4 × \(\frac{1}{3}\)
(iii) 2 × \(\frac{6}{7}\)
(iv) 5 ×\(\frac{2}{9}\)
(v) \(\frac{2}{3}\)× 4
(vi) \(\frac{5}{2}\) × 6
(vii) 11 × \(\frac{4}{7}\)
(viii) 20 × \(\frac{4}{5}\)
(ix) 13 × \(\frac{1}{3}\)
(x) 15 × \(\frac{3}{5}\)

Can we have a rotational symmetry of order more than 1 whose angle of rotation is 

1. 45°? 
2.  17°?

Name any two figures that have both line symmetry and rotational symmetry.

Give three examples of shapes with no line of symmetry.

Some pictures (a) to (c) are given below. Tell which of them show:
\((a)\)

\((b)\)

\((c)\)

(i) 3 × \(\frac{1}{5}\) =\(\frac{3}{5}\)
(ii) 2 × \(\frac{1}{3}\) =\(\frac{2}{3}\)
(iii) 3 × \(\frac{3}{4}\) = \(\frac{21}{4}\)

An elevator descends into a mine shaft at the rate of 6 m/min. If the descent starts from 10 m above the ground level, how long will it take to reach – 350 m.

State the number of lines of symmetry for the following figures: 

1. An equilateral triangle 
2.  An isosceles triangle 
3.  A scalene triangle 
4.  A square 
5.  A rectangle 
6.  A rhombus 
7.  A parallelogram 
8.  A quadrilateral 
9.  A regular hexagon 
10.  A circle

Copy the diagram and complete each shape to be symmetric about the mirror line(s):

Copy the figure given here. 

Take any one diagonal as a line of symmetry and shade a few more squares to make the figure symmetric about a diagonal. Is there more than one way to do that? Will the figure be symmetric about both the diagonals?

The following figures have more than one line of symmetry. Such figures are said to have multiple lines of symmetry. 

Identify multiple lines of symmetry, if any, in each of the following figures:

 

Write five pairs of integers (a, b) such that a ÷ b = –3. One such pair is (6, –2) because 6 ÷ (–2) = (–3).

In the following figures, the mirror line (i.e., the line of symmetry) is given as a dotted line. Complete each figure performing reflection in the dotted (mirror) line. (You might perhaps place a mirror along the dotted line and look into the mirror for the image). Are you able to recall the name of the figure you complete?

Copy the figures with punched holes and find the axes of symmetry for the following:

Verify that a ÷ (b + c) ≠ (a ÷ b) + (a ÷ c) for each of the following values of a, b and c. (a) a = 12, b = – 4, c = 2 (b) a = (–10), b = 1, c = 1

Shazli took a wire of length 44 cm and bent it into the shape of a circle. Find the radius of that circle. Also find its area. If the same wire is bent into the shape of a square, what will be the length of each of its sides? Which figure encloses more area, the circle or the square? (Take \(\pi\) = \(\frac{22}{ 7}\) )

Find the perimeter of the adjoining figure, which is a semicircle including its diameter.

Saima wants to put a lace on the edge of a circular table cover of diameter 1.5 m. Find the length of the lace required and also find its cost if one meter of the lace costs Rs 15. (Take \(\pi\) = 3.14)

From a circular sheet of radius 4 cm, a circle of radius 3 cm is removed. Find the area of the remaining sheet. (Take \(\pi\) = 3.14)

A gardener wants to fence a circular garden of diameter 21m. Find the length of the rope he needs to purchase, if he makes 2 rounds of fence. Also find the cost of the rope, if it costs RS 4 per meter. (Take \(\pi\) = \(\frac{22}{7}\) )