Haryana CET 2025 Math Revision Notes

Exam Pattern (Maths Section):

• Number of Questions: Typically 10-15 questions for Maths.
• Weightage: 10-15 Marks out of 100 total marks.
• Question Type: Multiple Choice Questions (MCQs).
• Negative Marking: No negative marking. (However, for Group C, some sources suggest a deduction for unattempted questions - it's crucial to confirm this in the official 2025 notification).
• Language: Bilingual (English and Hindi).

Key Topics and Concepts to Revise:

I. Number System

Types of Numbers:

• Natural Numbers (N): $\{1,2,3,\dots\}$
• Whole Numbers (W): $\{0,1,2,3,\dots\}$
• Integers (Z): $\{\dots,−2,−1,0,1,2,\dots\}$
• Rational Numbers (Q): Numbers of the form $p/q$ where $p,q$ are integers and $q \neq 0$. Includes terminating and repeating decimals.
• Irrational Numbers: Non-terminating, non-repeating decimals (e.g., $\sqrt{2}, \pi$).
• Real Numbers (R): All rational and irrational numbers.
• Prime Numbers: Only factors are 1 and itself (e.g., 2, 3, 5, 7, 11).
• Composite Numbers: Numbers with more than two factors (e.g., 4, 6, 8, 9).
• Even/Odd Numbers: Divisibility by 2.
• Co-prime Numbers: Two numbers with HCF 1 (e.g., 7 and 10).

Place Value and Face Value:

• Understanding the value of digits based on their position (e.g., in 785, place value of 7 is 700, face value is 7).

Divisibility Rules:

• By 2: Last digit is even.
• By 3: Sum of digits is divisible by 3.
• By 4: Last two digits are divisible by 4.
• By 5: Last digit is 0 or 5.
• By 6: Divisible by both 2 and 3.
• By 8: Last three digits are divisible by 8.
• By 9: Sum of digits is divisible by 9.
• By 10: Last digit is 0.
• By 11: Difference between sum of digits at odd places and sum of digits at even places is 0 or divisible by 11.

II. HCF and LCM

• HCF (Highest Common Factor) / GCD (Greatest Common Divisor): The largest number that divides two or more numbers without leaving a remainder.
  • Methods: Prime factorization, long division.
• LCM (Least Common Multiple): The smallest number that is a multiple of two or more numbers.
  • Method: Prime factorization.
• Relation: For two numbers $a,b$: $a \times b = HCF(a,b) \times LCM(a,b)$.
• Problems: Finding the smallest/largest number that is divisible by/divides a set of numbers, alarm/bell problems, traffic light problems.

III. Simplification / BODMAS

BODMAS Rule (Order of Operations):

1. Brackets (Parentheses) - ( ) { } [ ]
2. Orders (Exponents/Powers, Square Roots)
3. Division and Multiplication (from left to right)
4. Addition and Subtraction (from left to right)

• Basic Operations: Efficient calculation of addition, subtraction, multiplication, and division.
• Surds and Indices: Basic rules of exponents and roots.
  • $a^m \times a^n = a^{m+n}$
  • $a^m / a^n = a^{m-n}$
  • $(a^m)^n = a^{mn}$
  • $a^0 = 1$
  • $a^{-n} = 1/a^n$
  • $\sqrt{a} = a^{1/2}$

IV. Fractions and Decimals

• Types of Fractions: Proper, Improper, Mixed, Equivalent.
• Operations on Fractions: Addition, Subtraction, Multiplication, Division.
• Conversion: Converting fractions to decimals and vice-versa.
• Comparison: Comparing fractions and decimals.

V. Percentage

• Definition: Part per hundred. (e.g., $10\% = 10/100 = 0.1$).
• Calculations: Finding a percentage of a number, converting decimals/fractions to percentages and vice-versa.
• Percentage Increase/Decrease: $$ \text{Percentage Change} = \left(\frac{\text{Change}}{\text{Original Value}}\right) \times 100 $$
• Successive Percentage Change: For two successive changes of $x\%$ and $y\%$, effective change is $x+y+\frac{xy}{100}\%$.
• Word Problems: Population growth/decline, salary changes, marks, etc.

VI. Profit and Loss

• Cost Price (CP): Price at which an item is bought.
• Selling Price (SP): Price at which an item is sold.
• Profit (P): $SP - CP$ (if $SP > CP$)
• Loss (L): $CP - SP$ (if $CP > SP$)
• Profit %: $\left(\frac{\text{Profit}}{\text{CP}}\right) \times 100$
• Loss %: $\left(\frac{\text{Loss}}{\text{CP}}\right) \times 100$
• Marked Price (MP): Price displayed on the item.
• Discount (D): $MP - SP$
• Discount %: $\left(\frac{\text{Discount}}{\text{MP}}\right) \times 100$
• Formulas:
  • $SP = CP \times \frac{(100 \pm \text{Profit/Loss}\%)}{100}$
  • $MP = CP \times \left(\frac{100 + \text{Profit}\%}{100 - \text{Discount}\%}\right)$
• Successive Discounts: Calculating equivalent single discount for multiple discounts.

VII. Average

• Definition: $\frac{\text{Sum of all observations}}{\text{Number of observations}}$.
• Properties of Average: If each number is increased/decreased by a constant, the average also increases/decreases by that constant.
• Weighted Average: Used when different observations have different weights.
• Average Speed: $\frac{\text{Total distance}}{\text{Total time}}$.
• Problems: Age-related, batting average, average of numbers in a series.

VIII. Ratio and Proportion

• Ratio: Comparison of two quantities (e.g., $a:b$ or $a/b$).
• Proportion: Equality of two ratios (e.g., $a:b::c:d \Rightarrow a/b = c/d$).
• Product of Extremes = Product of Means: $ad=bc$.
• Types of Proportion: Direct Proportion, Inverse Proportion.
• Problems: Distribution of money/items in a ratio, age ratios, mixture problems (allegation and mixture).

IX. Simple and Compound Interest

• Principal (P): The initial amount of money.
• Rate (R): Interest rate per annum.
• Time (T): Time period (in years).

Simple Interest (SI):

• $SI = \frac{(P \times R \times T)}{100}$
• Amount $= P + SI$

Compound Interest (CI):

• Interest calculated on the principal amount and also on the accumulated interest of previous periods.
• Amount$(A) = P\left(1+\frac{R}{100}\right)^T$ (compounded annually)
• $CI = A - P$
• For half-yearly compounding: R becomes $R/2$, T becomes $2T$.
• For quarterly compounding: R becomes $R/4$, T becomes $4T$.
• Difference between SI and CI: For 2 years: Difference$=P\left(\frac{R}{100}\right)^2$.

X. Time and Work

• Basic Concept: If a person can do a piece of work in $n$ days, then their 1-day work is $1/n$.
• Work = Efficiency $\times$ Time.
• Problems: Individual work rates, combined work rates, pipes and cisterns (inlet/outlet pipes).
• MDH Formula: $\frac{M_1 D_1 H_1}{W_1} = \frac{M_2 D_2 H_2}{W_2}$ (M=Men, D=Days, H=Hours, W=Work).

XI. Time, Speed and Distance

• Formula: Speed = $\frac{\text{Distance}}{\text{Time}}$.
• Units Conversion:
  • km/hr to m/s: multiply by $5/18$.
  • m/s to km/hr: multiply by $18/5$.
• Problems:
  • Trains: Relative speed when moving in same/opposite directions. Time to cross a pole, platform, or another train.
  • Boats and Streams: Upstream speed (Boat Speed - Stream Speed), Downstream speed (Boat Speed + Stream Speed).
  • Average Speed: $\frac{\text{Total Distance}}{\text{Total Time}}$.
  • Relation between speed, distance, time when one is constant.

XII. Mensuration (2D and 3D)

2D Shapes (Area and Perimeter):

• Square: Area = $s^2$, Perimeter = $4s$.
• Rectangle: Area = $l \times b$, Perimeter = $2(l+b)$.
• Triangle: Area = $\frac{1}{2} \times \text{base} \times \text{height}$. For equilateral triangle: Area = $\frac{\sqrt{3}}{4} \times s^2$.
• Circle: Area = $\pi r^2$, Circumference = $2\pi r$.
• Parallelogram: Area = base $\times$ height.
• Rhombus: Area = $\frac{1}{2} \times d_1 \times d_2$.
• Trapezium: Area = $\frac{1}{2} \times (a+b) \times h$.

3D Shapes (Volume and Surface Area - Lateral/Total):

• Cube: Volume = $s^3$, Lateral Surface Area (LSA) = $4s^2$, Total Surface Area (TSA) = $6s^2$.
• Cuboid: Volume = $l \times b \times h$, LSA = $2h(l+b)$, TSA = $2(lb+bh+hl)$.
• Cylinder: Volume = $\pi r^2 h$, LSA = $2\pi rh$, TSA = $2\pi r(r+h)$.
• Cone: Volume = $\frac{1}{3}\pi r^2 h$, LSA = $\pi rl$, TSA = $\pi r(r+l)$ (where $l=\sqrt{r^2+h^2}$).
• Sphere: Volume = $\frac{4}{3}\pi r^3$, Surface Area = $4\pi r^2$.
• Hemisphere: Volume = $\frac{2}{3}\pi r^3$, Curved Surface Area (CSA) = $2\pi r^2$, TSA = $3\pi r^2$.
• Problems: Combining shapes, capacity, cost of painting/fencing.

XIII. Algebra (Basic)

• Linear Equations in One Variable: Solving simple equations (e.g., $3x+5=17$).
• Word Problems: Translating word problems into algebraic equations.
• Basic Identities: $(a+b)^2$, $(a-b)^2$, $(a+b)(a-b)$.