## ML Aggarwal Class 6 Solutions for ICSE Maths Model Question Paper 6

**Questions 1 to 8 are of 1 mark each.**

**Choose the correct answer from the given four options (1 to 8):**

Question 1.

The value of the expression \(\frac{5}{3}\)x^{2} – 1 when x = -2 is

Solution.

Question 2.

By joining any two points of a circle, we obtain its

(a) radius

(b) circumference

(c) diameter

(d) chord

Solution:

chord (d)

Question 3.

Which of the following statement is true?

(a) Every closed curve is a polygon

(b) Every closed simple curve is a polygon

(c) Every simple curve made up entirely of line segment is a polygon

(d) Every simple closed curve made up entirely of line segments is a polygon.

Solution:

Question 4.

The median of the numbers 3, 1,0, 6, 5, 3, 4, 1, 2, 2 is

(a) 2

(b) 2.5

(c) 3

(d) none of these

Solution:

Question 5.

If the perimeter of a regular octagon is 72 cm, then its side is

(a) 6 cm

(b) 8 cm

(c) 9 cm

(d) 12 cm

Solution:

Question 6.

If Anandi’s present age is x years and her father’s age is 3 years less than 4 times her age, then her father’s present age is

(a) (4x – 3) years

(b) (3x – 4) years

(c) 4(x – 3) years

(d) (4x + 3) years

Solution:

Question 7.

The number of lines of symmetry which a quadrilateral cannot have is

(a) 1

(b) 2

(c) 3

(d) 4

Solution:

Question 8.

The number of bisectors that can be drawn of a given angle is

(a) 1

(b) 2

(c) 4

(d) infinitely many

Solution:

1 (a)

**Section-B**

**Questions 9 to 14 are of 2 marks each.**

Question 9.

A cuboidal box has height h cm. Its length is 4 times the height and the breadth is 7 cm less than the length. Express the length and the breadth of the box in terms of its height.

Solution:

Question 10.

In the given figure, name the point(s)

(i) in the interior of ∠EOD.

(ii) in the exterior of ∠FOE.

Solution:

Question 11.

Write the following statement in mathematical form using literals, numbers and the signs of basic operations:

“Three times a number x is equal to 12 less than twice the number y.”

Solution:

Question 12.

If the area of a rectangular plot is 240 sq. m and its breadth is 12 m, then find the perimeter of the plot.

Solution:

Question 13.

On a squared paper, sketch a hexagon with exactly one line of symmetry.

Solution:

Question 14.

Find the area of the region enclosed by the given polygon.

Solution:

**Section-C**

**Questions 15 to 24 are of 4 marks each.**

Question 15.

In the given figure, count the number of segments and name them.

Solution:

Question 16.

In the given figure, state which of the angles marked with small letters are acute, obtuse, reflex or right angle (you may judge the nature of angle by observation).

Solution:

Question 17.

There are 40 employees in a Government Office. They were asked how many children they have. The result was:

1, 2, 3, 1, 0, 2, 0, 1, 2, 2, 1, 3, 5, 2, 0, 0, 2. 4, 1, 1

2, 2, 0, 3, 0, 0, 2, 1, 3, 6, 0, 2, 1, 0, 3, 2, 2, 2, 1, 4

(i) Arrange the above data in ascending order.

(ii) Construct frequency distribution table for the given data.

Solution:

Question 18.

A survey was carried out on 32 students of class VI in a school. Data about different modes of transport used by them to travel to school was displayed in a pictograph as under:

Observe the pictograph and answer the following questions:

Observe the pictograph and answer the following questions:

(i) Which is the most popular mode of transport?

(ii) What is the number of students who travel either by cycle or walking?

(iii) What are the advantages of using a school bus as a mode of transport?

(iv) What mode of transport would you suggest and why?

Solution:

Question 19.

If p = 4, q = 3 and r = -2, then find the value of the algebraic expression \(\frac{p^{2}+q^{2}-r^{2}}{p q+q r-p r}\).

Solution:

Question 20.

A room is 5 m long and 3 m 50 cm wide. How many square metres of carpet is needed to cover the floor of the room completely?

Solution:

Question 21.

Solve the linear equation

3(2x – 1) = 5 – (3x – 2).

Solution:

Question 22.

Copy the given figure on a squared paper and complete the figure such that the resultant figure is symmetrical about the dotted line.

Solution:

Question 23.

Draw a net of a square pyramid.

Solution:

Question 24.

Draw a line segment of length 7.5 cm and construct its axis of symmetry.

Solution:

**Section-D**

**Questions 25 to 29 are of 6 marks each.**

Question 25.

A survey was carried out on 150 families of a colony about the consumption of milk per day. The result was recorded as:

Represent the above data by a vertical bar graph, choosing scale: 1 unit height = 6 families. What are the advantages of taking milk every day?

Solution:

Question 26.

Draw a rough sketch of a regular hexagon. Connecting three of its vertices, draw

(i) an isosceles triangle

(ii) an equilateral triangle

(iii) a right-angled triangle.

Solution:

Question 27.

The cost of cultivating a rectangular field at the rate of ₹5 per square metre is ₹2880. If the length of the field is 32 m, find the cost of fencing the field at the rate of ₹11.25 per metre.

Solution:

Question 28.

By using a ruler and compass, construct an angle of 45° and bisect it. Measure any one part.

Solution:

Question 29.

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

Solution: