🌸 • Module 4 : Percentages, Formulas and 3D Geometry

Question 1

How do you calculate the percentage increase of an amount?

Answer 1

Increase/Original amount x 100

Example : If the price increases from 50 to 60, the increase is (60-50)/50 x 100=20%.

Question 2

How do you calculate the percentage decrease of an amount?

Answer 2

Decrease/Original amount x 100

Example : If the price decreases from 80 to 60, the decrease is (80-60)/80 x 100=25%.

Question 3

How do you calculate a percentage of an amount using a calculator?

Answer 3

Multiply the amount by the percentage (as a decimal).

Example : 20% of 250= 250 x 0.20=50.

Question 4

How do you find the original price before a percentage increase?

Answer 4

Use reverse percentage :
Final price/1+percentage increase

Example : If the final price is 120 after a 20% increase : 120/1.20 =100.

Question 5

How do you find the original price before a percentage decrease?

Answer 5

Use reverse percentage :
Final price/1-percentage decrease

Example : If the final price is 80 after a 20% decrease : 80/0.80 =100.

Question 6

What is standard form?

Answer 6

Standard form is a way to write very big or very small numbers easily. It’s written as a number between 1 and 10, multiplied by a power of 10.

Example : 4500 = 4.5 x 10³

Question 7

How do you write small numbers in standard form?

Answer 7

Use negative powers of 10.

Example : 0.0045 = 4.5 x 10⁻³

Question 8

How do you multiply numbers in standard form?

Answer 8

Multiply the decimal numbers and add the powers of 10.

Example : (3x10²) x (2x10³)=6x10⁵.

Question 9

What is the formula for the volume of a cuboid?

Answer 9

Volume = length x width x height.

Example : If length = 3, width = 4, and height = 5, then volume = 3x4x5=60.

Question 10

What is the formula for the volume of a cylinder?

Answer 10

Volume= πr²h
Where r is the radius and h is the height.

Example : For a cylinder with r = 3, and h = 5, volume = π x 3² x 5 = 45π.

Question 11

What is the formula for the surface area of a cylinder?

Answer 11

Surface area = 2πr² + 2πrh
Where r is radius and h is height.

Question 12

How do you find the volume of a cone?

Answer 12

⅓ πr²h
Where r is radius and h is height.

Question 13

What is the formula for the volume of a pyramid?

Answer 13

⅓ x Base Area x h
Where h is the height and the base area is the area of the shape at the bottom of the pyramid.

Question 14

What is a net of a solid?

Answer 14

a 2D shapes that can be folded to form the 3D shape.

Example : A net for a cube is made of 6 square faces.

Question 15

What is the formula for the surface area of a triangular prism?

Answer 15

Surface Area = Base Area + Area of Rectangular Faces

Where the base area is the area of the triangle and the rectangular faces are the sides of the prism.

Question 16

What is the difference between independent and mutually exclusive events?

Answer 16

Independent events : The outcome of one does not affect the other.

Mutually exclusive events : Both events cannot happen at the same time.

Question 17

What is the formula for the volume of a sphere?

Answer 17

4/3 πr³
Where r is the radius of the sphere.

Question 18

How do you rearrange a simple formula?

Answer 18

Rearrange by isolating the desired variable.

Example : If A = B + C, then rearrange to find B = A - C.

Question 19

What is the OR rule in probability for mutually exclusive events?

Answer 19

If events A and B are mutually exclusive, P(A or B) = P(A) + P(B).

Question 20

What is the formula for the surface area of a cuboid?

Answer 20

Surface Area = 2(lw + lh + wh),
Where l = length, w = width, h = height.