## 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:

(d) Every simple closed curve made up

entirely of line segments is a polygon. (d)

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:

Arrange the numbers in ascending order

0, 1, 1, 2, 2, 3, 3, 4, 5, 6

Total terms = 10

Median = \(\frac{5^{\text { th }} \text { term }+6^{\text { th }} \text { term }}{2}\)

= \(\frac{2+3}{2}=\frac{5}{2}=2.5\) (b)

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:

Side of octagon = 8 sides

Perimeter = 72 cm

∴ Its side = \(\frac{72}{8}\) = 9 cm (c)

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:

Let age of Anandi = x years

and father’s age = (4x – 3) years (a)

Question 7.

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

(a) 1

(b) 2

(c) 3

(d) 4

Solution:

3 (c)

Because quadrilateral has 4 lines of symmetry.

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

**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:

According to question,

Length = (4 × Height) cm

Breadth = Length – 7 cm = (4 height – 7 cm)

Question 10.

In the given figure, name the point(s)

(i) in the interior of ∠EOD.

(ii) in the exterior of ∠FOE.

Solution:

(i) P

(ii) D, P, Q

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:

The Mathematical form using literals,

numbers and the signs of basic operations of three times

a number x is equal to 12 less than twice the number y is 3x = 12y – 12.

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:

Area of plot = 240 sq. m

Length (l) = ?

Breadth (b) = 12 m

We know that,

Area = l × b

⇒ l = \(\frac{240}{12}\)

⇒ l = 20

∴ Length = 20

Now, Perimeter = 2(l + b) = 2(20 + 12) = 2(32) = 64 m

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:

Construction: Extent the point F and point D and meet them at G.

Now, we have two rectangles

i.e. ABCG with length = 20 cm and breadth = 10 m

and rectangle DEFG with length = 8 m and breadth = 6 m

Area of the region enclosed by the given polygon

= (20 × 10) m – (8 × 6) m

= 200 m – 48 m

= 152 m

**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:

Number of segments = 7

Name — \(\overline{\mathrm{AB}}, \overline{\mathrm{BC}}, \overline{\mathrm{CD}}, \overline{\mathrm{DA}}, \overline{\mathrm{BE}}, \overline{\mathrm{BD}}, \overline{\mathrm{ED}}\)

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:

∠x is acute; m

∠y, ∠p, ∠q are obtuse,

∠r is reflex

and ∠c is a right angle.

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:

(i) 0, 0, 0, 0, 0, 0, 0, 0, 0,

1, 1, 1, 1, 1, 1, 1, 1, 1,

2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,

3, 3, 3, 3, 3,

4, 4,

5,

6

(ii)

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 school bus as mode of transport?

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

Solution:

(i) The most popular mode of transport is school bus.

(ii) The number of students travel by cycle = 3

The number of students travel by walking = 7

Hence, total number of students who travel

either by cycle or walking = 3 + 7=10 students

(iii) Reach school in time, saves energy (diesel/petrol), more safe.

(iv) School Bus [reason (iii)] because it is the most safest mode to travel.

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:

Length = 5 m

Breadth = 3.5 m

Carpet needed to cover floor of room

= Length × Breadth

= 5 × 3.5

= 17.5 sq. m

Question 21.

Solve the linear equation

3(2x – 1) = 5 – (3x – 2).

Solution:

3(2x – 1) = 5 – (3x – 2)

⇒ 6x – 3 = 5 – 3x + 2

⇒ 9x = 10

⇒ x = \(\frac{10}{9}\)

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:

The following steps to draw a line segment of length 7.5 cm

and construct its axis of symmetry.

(i) Draw a line segment AB of 7.5 cm.

(ii) Taking A as centre, draw a circle by using compasses.

The radius of circle should be more than half the length of AB.

(iii) With the same radius as before,

draw another circle using compasses

while taking point B as centre.

Let it cut the previous circle at C and D.

(iv) Join CD. CD is the axis of symmetry.

**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:

Milk is good for the bones because it offers a rich source of calcium,

a mineral essential for healthy bones and teeth.

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:

Total cost of cultivating the rectangular = ₹2880

Rate of cultivating = ₹5 per sq. m

∴ Area of field = \(\frac{2880}{5}\) = 576 m^{2}

Now, length of the field (l) = 32 m

∴ Breadth = \(\frac{\text { Area }}{\text { Length }}=\frac{576}{32}\) = 18 cm

Now, circumference of the field = 2(l + b) = 2(32 + 18) = 100 m

Rate of fencing = ₹11.25 per m

∴ Total cost = ₹11.25 × 100 = ₹1125

Question 28.

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

Solution:

Steps of construction:

- Draw a straight line BC.
- With B as a centre and any suitable radius,

draw an arc to meet BC at E. - With E as centre and same radius

draw an arc to meet previous arc at G. - With G and F as centre and same radius

draw another arc to meet the first arc at H. - With H and E as centre draw two arcs of equal radius less than \(\frac{1}{2}\) GE.
- Cutting each other at J joined BJ and produce it to D.
- With L and E as centre draw two arcs of equal radius less than \(\frac{1}{2}\) LE.
- Cutting each other at K joined BK and produce it to I.
- Measuring angle ∠IBC = 22.5°

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: