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?
y + 6
(8 × 10) – 6p
9 (15 – 7) + 6 × 4
9n
11
7 – 7m
(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.
a + 2, a – 2, b + 13, b – 13
7t, t/7, 15t
4x + 13, 4x – 13
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:
3 added to m
3 subtracted from m
m multiplied by 8
n divided by 8
9 subtracted from –n
–m multiplied by 6
–n divided by 6
n multiplied by -9
Answer
m + 3
m – 3
8m
n/8
–n – 9
-6m
–n/6
-9n
Question 5 : Give expressions for the following cases
15 added to 3p
15 subtracted from 3p
7 times x to which 6 is added
7 times x from which 6 is subtracted
z is multiplied by -9
z is multiplied by -5 and then 3 is added to the result
q is multiplied by 8 and the result is subtracted from 12
q is multiplied by -8 and the result is added to 12
Answer:
3p + 15
3p – 15
7x + 6
7x – 6
-9z
-5z + 3
12 – 8q
-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
s⁄5 5⁄s
5 – s
(b) 3t + 8
3t – 8
8t + 3
8t – 3 etc..