Maths Chapter-11: Algebra

Exercise 1

Question 1

Let the side of an equilateral triangle be m. Show the perimeter of the triangle with the help of m.

Answer

Perimeter = sum of three sides

= m+m+m

= 3m

 

Question 2

Let the side of a regular hexagon be denoted by m. Show the perimeter of the hexagon with the help of m.

(All sides are equal in regular hexagon)

Answer

Side of regular hexagon = m

Perimeter = sum of all sides

= 6m

 

Question 3

In the given figure a cube, 3 – D cube is shown. It has six identical squares as all the sides are equal so same six faces. Let the length of a side of cube be given by m. Find formula for total length of the cube.

Answer

Length of an edge = m

Number of edges = 12

Total length of the edges = total number of edges × Length of each edge

= 12m

 

Question 4

Diameter of a circle is a line which passes through the centre and joins two points of circle. (In the given figure XY is a diameter of circle; c is centre.) Express the diameter of the circle (d) in form of its radius(r).

Answer

d = twice the radius

= 2r

 

 

Exercise 2

Question 1

Make as many expressions with no. as you can from three numbers 2, 6 and 9. Each no. should be used only once. Use only addition, multiplication and subtraction.

Answer

We can make many expressions using 2, 6 and 9 as given below.

9+ (6 – 2)

9 + (6 × 2)

(6 – 2) + 9

(6 + 2) × 9

(2 + 9) – 6

(2 × 9) × 6

 

Question 2

Which of these expressions are formed with numbers only?

  1. y + 6
  2. (8 × 10) – 6p
  3. 9 (15 – 7) + 6 × 4
  4. 9n
  5. 11
  6. 7 – 7m
  7. (2 × 40) – (4 × 20) – 25 + q

Answer

From above expressions given, it can be observed that option (c) and (e) are formed by using numbers only.

 

Question 3

Identify the operations and tell how the expressions have been formed.

  1. a + 2, a – 2, b + 13, b – 13
  2. 7t, t/7, 15t
  3. 4x + 13, 4x – 13
  4. 8c, -8c + 2, -8m – 2

Answer

1. Addition: 2 is added to a

Subtraction: 2 is subtracted from a

Addition: 13 is added to b

Subtraction: 13 is subtracted from b

2. Multiplication: t is multiplied with 7

Division: t is divided by 7

Multiplication: t is multiplied with 15

3.Multiplication and addition: 4 is multiplied with x and result is added to 13.

Multiplication and subtraction: 4 is multiplied with x and 13 is subtracted from the result.

4. Multiplication: 8 is multiplied with c

Multiplication and addition: -8 is multiplied by c and add 2 to the result.

Multiplication and subtraction: c is multiplied with -8 and 2 is subtracted from the result.

 

Question 4

Give expressions for the below:

  1. 3 added to m
  2. 3 subtracted from m
  3. m multiplied by 8
  4. n divided by 8
  5. 9 subtracted from –n
  6. –m multiplied by 6
  7. –n divided by 6
  8. n multiplied by -9

Answer

  1. m + 3
  2. m – 3
  3. 8m
  4. n/8
  5. –n – 9
  6. -6m
  7. –n/6
  8. -9n

 

Question 5

Give expressions for the following cases

  1. 15 added to 3p
  2. 15 subtracted from 3p
  3. 7 times x to which 6 is added
  4. 7 times x from which 6 is subtracted
  5. z is multiplied by -9
  6. z is multiplied by -5 and then 3 is added to the result
  7. q is multiplied by 8 and the result is subtracted from 12
  8. q is multiplied by -8 and the result is added to 12

Answer

  1. 3p + 15
  2. 3p – 15
  3. 7x + 6
  4. 7x – 6
  5. -9z
  6. -5z + 3
  7. 12 – 8q
  8. -8q + 12

 

Question 6

(a) Form expressions with s and 5. Use only one operation in the expressions. Every expression should have s in it.

(b) Form expressions with t, 3 and 8. Every expression should have t. Use only two operations. These two operations should be different.

Answer

(a) s + 5

s – 5

5s

\(\frac{s}{5}\) \(\frac{5}{s}\)

5 – s

(b) 3t + 8

3t – 8

8t + 3

8t – 3 etc..