# Formula of the Week

Hello Aspirants!

Here’s some formulas to ace your prep this Arithmetic week:
• When the interest is compounded Annually:
Amount= P (1 + R/100) n
• When the interest is compounded Half-yearly:
Amount = P (1 + (R/2)/100)2n
• When the interest is compounded Quarterly:
Amount = P (1 + (R/4)/100)4n

Regards,
CATKing Team

Hello Aspirants!

Here’s some formulas to ace your prep this Arithmetic week:

• When the rates are different for different years, say R1%, R2% and R3% for 1 year, 2 years and 3-year resp. Then, Amount = P (1 + R1/100) (1 + R2/100) (1 + R3/100)

• Present worth of ₹ x due n years hence is given by: Present worth = x/ (1 + R/100)n • If a certain sum becomes “x” times in n years, then the rate of compound interest will be R = 100(x1/n – 1)

• If a sum of money P amounts to A1 after T years at CI and the same sum of money amounts to A2 after (T + 1) years at CI, then R = (A2 – A1)/ A1 x 100

Hope you are enjoying the process of learning.

Regards,
CATKing Team

Hello Aspirants!

Here’s some formulas to ace your prep this Geometry week:

Equations of a lines:
→ General equation of a line Ax + By = C

→ Slope intercept form y = mx + c (c is y intercept)

→ Point-slope form y – y1 = m (x – x1 ) (m is the slope of the line)

→ Intercept form x / a + y / b = 1 (where a and b are x and y intercepts respectively)

→ Two point form: (y−y1) / (y2−y1) = (x−x1) / (x2−x1)

Hope you are enjoying the process of learning.

Regards,
CATKing Team

Dear Aspirants!

Suppose there is a line PQ with P(x1, y1) and Q(x2, y2)
PQ= √((x_2-x_1 )+(y_2-y_1 ) )
Slope of PQ= m= √(((y_2-y_1 ))/((x_2-x_1 ) )) = tan⁡θ
Equation of PQ is as below: or y = mx + c
The product of the slopes of two perpendicular lines is –1.
The slopes of two parallel lines are always equal. If m1 and m2 are slopes of two parallel lines, then m1=m2.
The distance between the points (x1, y1) and (x2, y2) is

Enjoy the process of learning

Regards,
CATking

Dear Aspirants!

Here is the Formula for the Week.

(a – b)² = (a² + b² – 2ab)
(a + b)² = (a² + b² + 2ab)
(a + b)(a – b) = (a² – b²)
(a + b)² = (a² + b² + 2ab)

Enjoy the process of learning

Regards,
CATking

Dear Aspirants!

Here is the Formula for the Week.

(a³ – b³) = (a – b)(a² + ab + b²)
(a³ + b³) = (a + b)(a² – ab + b²)
(a³ + b³ + c³ – 3abc) = (a + b + c)(a² + b² + c² – ab – bc – ac)
When a + b + c = 0, then a³ + b³ + c³ = 3abc

Enjoy the process of learning

Regards,
CATking

Hello Aspirants!

• HCF * LCM of two numbers = Product of two numbers
• The greatest number dividing a, b and c leaving remainders of x1, x2 and x3 is the HCF of (a-x1), (b-x2) and (c-x3).
• The greatest number dividing a, b and c (a<b<c) leaving the same remainder each time is the HCF of (c-b), (c-a), (b-a)
• If a number N, is divisible by X and Y and HCF (X, Y) =1. Then, N is divisible by X*Y.

Regards,
CATKing Team