Important Formulas for CAT 2023 Preparation - CAT Exam Revision Tips

Important Formulas for CAT Preparation : Formulas play a vital role in CAT exam readiness. Let's explore the importance of CAT formulas and dive into the essential formulas you need for the CAT 2023 Quantitative Aptitude (QA) sectio n. Mastering these formulas and their application is key to solving CAT questions swiftly and accurately.

List of Important formulas for CAT 2023 preparation:

Probability:

• PE=n(E)/n(S), where n(E) = favorable outcomes, and n(S) = total outcomes.

Profit, Loss, and Discount

• Profit Percentage = (Profit/Cost Price) x 100
• Loss Percentage = (Loss/Cost Price) x 100
• Selling Price = Cost Price + Profit
• Selling Price = Cost Price - Loss
• Cost Price = Selling Price - Profit
• Cost Price = Selling Price + Loss
• Profit = Selling Price - Cost Price
• Loss = Cost Price - Selling Price
• Discount = Marked Price - Selling Price
• Discount Percentage = (Discount/Marked Price) x 100
• Marked Price = Selling Price/(1 - Discount Percentage/100)
• Marked Price = Cost Price/(1 - Profit Percentage/100)

LCM and HCF

• HCF × LCM = Product of the two numbers.
• LCM of co-prime numbers = Product of the numbers.
• HCF of co-prime numbers = 1.
• HCF of two numbers a and b = HCF of (a-b, b).
• LCM of two numbers a and b = (a x b) / HCF(a, b).
• HCF of three numbers a, b, and c = HCF of (HCF(a, b), c).
• LCM of three numbers a, b, and c = LCM of (LCM(a, b), c).

Time and Work

• Work Done = Time Taken × Rate of Work
• Rate of Work = 1 / Time Taken
• Time Taken = 1 / Rate of Work
• If a piece of work is done by A in n days, then A's 1 day's work = 1/n
• If A's 1 day's work = 1/n, then A can finish the work in n days
• If A can do a piece of work in x days and B can do the same work in y days, then the work done by both A and B in one day = 1/x + 1/y
• If A can do a piece of work in x days and B can do the same work in y days, then the time taken by both A and B to complete the work together = (xy) / (x + y)

Averages

• Average = (Sum of observations) / (Number of observations)
• If the average of n numbers is A, then the sum of the n numbers is nA.
• If the average of n numbers is A and m more numbers are added to the list, then the new average becomes (nA + mB) / (n + m), where B is the average of the m numbers.
• If the average of n numbers is A and each number is increased by x, then the new average becomes (nA + nx) / n.
• If the average of n numbers is A and each number is decreased by x, then the new average becomes (nA - nx) / n.

Logarithm

• Definition of a logarithm: If x>0 and b is a constant (b≠1), then y=logbx if and only if x=by.
• Logarithmic identities:
  • logb(xy) = logbx + logby
  • logb(x/y) = logbx - logby
  • logb(x^p) = p logbx
  • logb1 = 0
  • logbb = 1
  • logb(x) = 1 / logx(b)
• Change of base formula: logb(x) = loga(x) / loga(b)
• Common logarithm: log10(x) = log(x)
• Natural logarithm: loge(x) = ln(x)

Surds and Indices

• Product rule: a^m × a^n = a^(m+n)
• Quotient rule: a^m / a^n = a^(m-n)
• Power rule: (a^m)^n = a^(m×n)
• Negative exponent rule: a^(-m) = 1 / a^m
• Rational exponent rule: a^(m/n) = nth root of a^m
• Fractional exponent rule: a^(p/q) = qth root of a^p
• Surds multiplication rule: √a × √b = √(ab)
• Surds division rule: √a / √b = √(a/b)
• Surds addition rule: √a + √b ≠ √(a+b)
• Surds subtraction rule: √a - √b ≠ √(a-b)

Set Theory & Function

• De Morgan's Law: (A ∩ B)' = A' U B' and (A U B)' = A' ∩ B'
• Cardinality of a set: The number of elements in a set is called its cardinality.
• Union of sets: A U B = {x: x ∈ A or x ∈ B}
• Intersection of sets: A ∩ B = {x: x ∈ A and x ∈ B}
• Complement of a set: A' = {x: x ∉ A}
• Difference of sets: A - B = {x: x ∈ A and x ∉ B}
• Cartesian product of sets: A × B = {(a, b): a ∈ A and b ∈ B}

Trigonometry

• Sine = Opposite/Hypotenuse
• Cosine = Adjacent/Hypotenuse
• Tangent = Opposite/Adjacent
• Secant = Hypotenuse/Adjacent
• Cosecant = Hypotenuse/Opposite
• Cotangent = Adjacent/Opposite
• Sum and Difference Formulas:
  • sin(u + v) = sin(u)cos(v) + cos(u)sin(v)
  • cos(u + v) = cos(u)cos(v) – sin(u)sin(v)
  • sin(u – v) = sin(u)cos(v) – cos(u)sin(v)
  • cos(u – v) = cos(u)cos(v) + sin(u)sin(v)
• Reciprocal Identities:
  • cosec θ = 1/sin θ
  • sec θ = 1/ cos θ
  • cot θ = 1/tan θ
  • sin θ = 1/cosec θ
  • cos θ = 1/sec θ
  • tan θ = 1/cot θ

Coordinate Geometry

• Distance Formula: The distance between two points P(x1, y1) and Q(x2, y2) is given by √[(x2 - x1)^2 + (y2 - y1)^2].
• Slope Formula: The slope of a line passing through two points P(x1, y1) and Q(x2, y2) is given by (y2 - y1) / (x2 - x1).
• Equation of a Line: The equation of a line passing through a point (x1, y1) with slope m is given by y - y1 = m(x - x1) or y = mx + (y1 - mx1).
• Midpoint Formula: The midpoint of a line segment joining two points P(x1, y1) and Q(x2, y2) is given by [(x1 + x2) / 2, (y1 + y2) / 2].
• Section Formula: If a point R(x, y) divides the line segment joining two points P(x1, y1) and Q(x2, y2) in the ratio m:n, then x = [(nx2) + (mx1)] / (m + n) and y = [(ny2) + (my1)] / (m + n).
• Slope of a Parallel Line: The slope of a line parallel to a line with slope m is also m.
• Slope of a Perpendicular Line: The slope of a line perpendicular to a line with slope m is -1/m.

Mensuration

• Area of a triangle = 1/2 × base × height
• Area of a rectangle = length × breadth
• Area of a square = side × side
• Area of a parallelogram = base × height
• Area of a trapezium = 1/2 × (sum of parallel sides) × height
• Circumference of a circle = 2πr
• Area of a circle = πr^2
• Volume of a cube = side^3
• Surface area of a cube = 6 × side^2
• Volume of a cuboid = length × breadth × height
• Surface area of a cuboid = 2(lb + bh + hl)
• Volume of a cylinder = πr^2h
• Surface area of a cylinder = 2πrh + 2πr^2
• Volume of a sphere = 4/3 × πr^3
• Surface area of a sphere = 4πr^2

Number Systems

• Sum of first n natural numbers = n(n+1)/2
• Sum of squares of first n natural numbers = n(n+1)(2n+1)/6
• Sum of cubes of first n natural numbers = [n(n+1)/2]^2
• Sum of first n odd numbers = n^2
• Dividend = (Divisor x Quotient) + Remainder

Sum of Series

• 1 + 2 + 3 + ... + n = n(n + 1)/2, and more.

Geometry

• Area of sector, Cube Volume, Surface Area, Diagonal, Volume of cuboid, and more.

How to Memorize the Important Formulas for CAT 2023?

1. Get the Idea : First, understand why the formula works. When you know the logic behind it, it sticks in your memory better. So, try to grasp the reasoning and practice it regularly.
2. Practice a Lot : Regular practice is key. Keep using these formulas by solving problems with them. This helps you really understand and remember them for a long time.
3. Flashcards Are Handy : Make flashcards with the formulas and look at them regularly. Flashcards are like quick reminders that help you remember the formulas faster.
4. Use Memory Tricks : Try using memory tricks or mnemonics. These are like little shortcuts that make it simpler to recall the formulas.
5. Keep Going Over Them : Regular revision is super important. It reinforces your memory and makes sure you don't forget the formulas over time.
6. Mock Tests Help : Do practice tests often. They not only test what you know but also show you where you might need more practice.

Effective Memorization Techniques for Learning Important Formulas for CAT 2023

Mnemonic Devices Which Helps to Remember Important Formulas for CAT 2023?

1. SOHCAHTOA : Use this one for trigonometry – Sine = Opposite / Hypotenuse, Cosine = Adjacent / Hypotenuse, and Tangent = Opposite / Adjacent.
2. C. HOPKiN’S Ca Mg : Remember the essential macronutrients – Carbon, Hydrogen, Oxygen, Phosphorus, Potassium, Nitrogen, Sulfur, Calcium, and Magnesium.
3. Queen Elizabeth Second's Navy Commands, Controls, Communicates : For organic chemistry, recall the order of o,p-directing groups – Alkyl, Halogen, Alkoxyl, Amino, Hydroxyl, Amide, Phenyl, (R), (X), (OR), (-NH2 |-NHR |-NR2), (OH), (NHCOR), (C6H5).
4. FOClN BrIS CHP : When it comes to the reactivity of halogens, think Fluorine, Chlorine, Bromine, Iodine.
5. C (see) Hopkins CaFe, Mighty-good Man, Cu (see your) Money, hope they are Closed or out of Business : Remember the reactivity series of metals – Copper, Silver, Gold, Platinum, Mercury, Lead, Iron, Tin, Hydrogen, Copper, Zinc, Magnesium, Calcium, Sodium, Potassium.

CAT Exam Revision Tips

1. Know the Exam : First things first, understand the CAT exam pattern and what's in the syllabus. This sets the foundation for your preparation.
2. Plan It Out : Make a study plan that covers all the topics and concepts you need to tackle before the exam. It keeps you organized.
3. Regular Revision : Don't forget to regularly go over what you've learned. This refreshes your memory and helps you recall things faster during the exam.
4. Mock Tests Matter : Practice mock tests frequently. They're like practice rounds that show you where you're strong and where you need more work.
5. Tackle Weak Spots : Focus extra effort on the areas where you feel less confident. More practice and revisiting concepts can make a big difference.
6. Break Time : Take breaks during your study sessions. It helps you avoid getting burnt out and keeps your motivation up.
7. Stay Confident : Believe in yourself. Confidence can reduce stress and boost your performance.