Math Revision - 2

The width of each of six continuous classes in a frequency distribution is 4, and the lower class limit of the lowest class is 8. What is the upper-class limit of the highest class?

• 36
• 24
• 32

• 28

Answer explanation

• The first class will be 8–12, as the width is 4.

• The next five classes will follow the same width:

  • 12–16

  • 16–20

  • 20–24

  • 24–28

  • 28–32

• The upper-class limit of the highest class is 32.

A frequency distribution has 5 classes, each with a width of 6. If the lower limit of the first class is 12, what is the upper-class limit of the last class?

• 24

• 42

• 30

• 36

Answer explanation

• First class: 12–18
  (The upper-class limit is found by adding the width, 12+6=1812 + 6 = 1812+6=18).

• The next classes are:

  • Second class: 18–24

  • Third class: 24–30

  • Fourth class: 30–36

  • Fifth class: 36–42

• The upper-class limit of the last class is 42.

A lampshade is shaped like a cone with a radius of 7 cm. If the curved surface area of the lampshade is 176 cm², find the slant height of the lampshade.

• 6 cm
• 10 cm
• 12 cm
• 8 cm

The height of a conical vessel is 3.5 cm. If its capacity is 3.3 litres of milk. Find the diameter of its base.

• 28.0 cm
• 40.0 cm
• 25.0 cm
• 60.0 cm

Answer explanation

Height of a conical vessel = 3.5 cm and

The capacity of the conical vessel is 3.3 litres or 3300 cm³

Now,

We know, the volume of a cone = 1/3 πr²h

3300 = 1/3 x 22/7 x r² x 3.5

r = 30

So, the radius of the cone is 30 cm

Hence, the diameter of its base = 60 cm.

A hemispherical bowl made of brass has an inner diameter 10.5 cm. Find the cost of tin plating it on the inside at the rate of Rs.4 per 100 cm².

• Rs. 5.25
• Rs. 8.90
• Rs. 15.75
• Rs. 6.93

Answer explanation

The inner diameter of the hemispherical bowl = 10.5 cm

So, radius = 5.25 cm

Now, the surface area of the hemispherical bowl = 2πr²

= 2 × 3.14 × (5.25)²

= 173.25

So, the surface area of the hemispherical bowl is 173.25 cm²

Find the cost:

Cost of tin plating 173.25cm² area = Rs. 4×173.25100 = Rs. 6.93

Therefore, the cost of tin plating the inner side of the hemispherical bowl is Rs. 6.93.

Two angles of a triangle are equal and the third angle is greater than each of those angles by 30⁰. Determine all the angles of the triangle.

• 50, 50, 80
• 70, 70, 40
• 40, 40, 100
• 60, 60, 60

Answer explanation

Let x, x, x + 30⁰ be the angles of a triangle.

Sum of all angles in a triangle = 180⁰

x + x + x + 30⁰ = 180⁰

3x + 30⁰ = 180⁰

3x = 150⁰

or x = 50⁰

And x + 30⁰ = 50⁰ + 30⁰ = 80⁰

Answer: Three angles are 50⁰, 50⁰ and 80⁰.

In a Δ ABC, if ∠A = 120° and AB = AC. Find ∠B and ∠C.

• ∠B = 60°, ∠C = 60°
• ∠B = 45°, ∠C = 75°
• ∠B = 90°, ∠C = 30°
• ∠B = 30°, ∠C = 30°

Simplify:(√5 -2)( √3 – √5)

• √15 - 3√5 + 2√3 - 5
• √5 - 2√3 + √15 - 2
• √3 - 2 + 5 - 2√5
• √15 - 5 + 2√5 - 2√3

The radius of a cylindrical tank is 5 cm and its height is 10 cm. Calculate the volume of the tank in cubic centimeters.

• 300 cm³

• 350 cm³

• 785 cm³

• 250 cm³

Simplify: (2√3 + 4)(√3 - 1)

• 2√3 - 2 + 4√3 - 4

• 2√3 - 4 + 4√3 - 2

• 2√3 - 4 + 4√3 + 2

• 2√3 - 4 + 4√3 - 2√3