## ML Aggarwal Class 6 Solutions for ICSE Maths Model Question Paper 4

**Choose the correct answer from the given four options (1-2):**

Question 1.

Avanti’s present age is y years and her mother’s age is 4 years less than 3 times her age, then her mother’s present age is

(a) (3y + 4) years

(b) (4y – 3) years

(c) (3y – 4) years

(d) 3(y – 4) years

Solution:

The present age of Avanti = y years

Mother’s age = 4 years less than 3 times

Avanti’s age = (3y – 4) years (c)

Hence, Answer is (c) ⇒ (3y – 4) years

Question 2.

Which of the following statements is false?

(a) Every square is a rhombus.

(b) An equilateral triangle is a regular polygon.

(c) A triangle having all acute angles is scalene.

(d) Every square is a regular polygon.

Solution:

A triangle having all acute angles is scalene. (c)

Question 3.

If = 3, q = -2 and r = -1, find the value of: 2p^{2} + 3q – r^{2} + 2pr – 5pqr.

Solution:

p – 3, q = -2 and r = -1

2p^{2} + 3q – r^{2} + 2pr – 5pqr

Put the value ofp, q, r in the given equation.

= 2(3)^{2} + 3(-2) – (-1)^{2} + 2(3)(-1) – 5(3)(-2)(-1)

= 2(9) – 6 – 1 + 2(-3) – 5(6)

= 18 – 7 – 6 + 30

= 11 – 6 – 30

= 5 – 30 = -25

Question 4.

Fill in the following blanks:

(i) A polygon is a closed simple curve made up of entirely ………….

(ii) A cuboid has 6 rectangular faces, edges and ………. vertices.

Solution:

(i) A polygon is a closed simple curve made up of entire line segment.

(ii) A cuboid has 6 rectangular faces, 12 edges and 8 vertices.

Question 5.

Give reason(s) of using triangular shapes and not polygonal shapes consisting of four or more sides in constructing structures like electric towers and bridges. What value is added in using triangular shapes?

Solution:

Triangular shapes are rigid and cannot be distorted by pressure

while other polygon shapes consisting of four or more sides

are likely to be distorted by pressure.

Structures made up of triangular shapes are sturdy and have a long life,

so these add safety in our life.

Question 6.

Look at the following pattern of squares fonned by matchsticks:

Find the rule that gives the number of matchsticks required in terms of the number of squares formed.

Solution:

In n squares are formed,

then the number of matchsticks required 3n + 1.

Question 7.

Name each of the following triangles in two ways (you may judge by observation or use ruler and protractor):

Solution:

(i) Obtuse angled and scalene.

(ii) Isosceles and right-angled.

Question 8.

Draw a net of a regular tetrahedron.

Solution:

Question 9.

Solve the linear equation:

4 – 3(5x + 2) = 4(7 – 3x).

Also, verify the solution.

Solution:

4 – 3(5x + 2) = 4(7 – 3x)

⇒ 4 – (15x – 6) = 28 – 12x

⇒ -2 – 15x = 28 – 12x

⇒ -15x + 12x = 28 + 2

⇒ -3x = 30

⇒ x = \(-\frac{30}{3}\)

⇒ x = -10

Question 10.

Use the given figure to name:

(i) parallel lines

(ii) concurrent lines

(ii) collinear points

(iv) two opposite rays.

Solution: