AP ICET 2026 Important Formulas: Complete Quant Formula Sheet for Quick Revision

Why AP ICET 2026 Quantitative Aptitude Formulas Are Important for Scoring High

Without knowing the importance of formulas in AP ICET, you will not develop an interest to learn these. So, first, you need to understand why Quant Formulas are important. The Quantitative Aptitude section in AP ICET tests speed, accuracy, and conceptual clarity. Mugging the formulas without knowing their applications and importance is not going to help. Along with memorising, you must understand the concept behind it and applying the right AP ICET Quantitative Aptitude Formulas will help you in certain ways as discussed below:

• Save time by minimising the calculations

• Direct application of formulas will help to avoid long approaches to solving the questions

• Reduces the chances of making errors (Improves accuracy)

• Work as a confidence booster

• Reduce complexity

Important Tip:

Revise formulas regularly and keep practising questions on these formulas for effective AP ICET 2026 Maths Preparation.

AP ICET Arithmetic Formulas for Quick Revision

Arithmetic consists of topics like percentage, profit and loss, time and work, TSD, etc which form a major portion of AP ICET Mathematical Ability Formulas.

Percentages:

Example 1:
A number is increased by 25% and then decreased by 20%. Find the net percentage change.
Net change $= 25 - 20 + \frac{25 \times (-20)}{100} = 0%$
So, there is no net change.

Example 2:
A’s salary is 20% more than B’s salary. By what percentage is B’s salary less than A’s?
Required % $= \frac{20}{120} \times 100 = 16.67%$

Example 3:
The population of a town increases by 10% every year. Find the total percentage increase in 2 years.
Population after 2 years $= 100(1.1)^2 = 121$
Increase $= 21%$

Profit and Loss

Example 1:
A shopkeeper marks an article 40% above cost price and allows a discount of 20%. Find his profit percentage.
Effective SP $= 1.4 \times 0.8 = 1.12$ of CP
Profit $= 12%$

Example 2:
A person sells two articles at ₹1000 each. On one, he gains 20% and on the other, he loses 20%. Find the overall profit or loss percentage.
Net loss $= \frac{20^2}{100} = 4%$

Example 3:
An article is marked at ₹1200 and sold at a discount of 25%. If the cost price is ₹800, find the profit percentage.
SP $= 1200 \times 0.75 = 900$
Profit $= \frac{100}{800} \times 100 = 12.5%$

Simple Interest (SI) and Compound Interest:

Example 1:
Find the compound interest on ₹2000 at 10% per annum for 2 years.
$A = 2000(1.1)^2 = 2420$
CI $= 2420 - 2000 = 420$

Example 2:
Find the difference between CI and SI on ₹2000 at 10% for 2 years.
Difference $= P(\frac{R}{100})^2 = 2000(0.1)^2 = 20$

Example 3:
At what rate will a sum double itself in 5 years under compound interest?
$2 = (1 + \frac{R}{100})^5$
$R \approx 14.87%$

Ratio and Proportion

1. In the ratio $a:b$, Proportion of $a = \frac{a}{a+b}$, and Proportion of $b = \frac{b}{a+b}$.

2. Duplicate Ratio: The duplicate ratio of $a:b$ is $a^2:b^2$.

3. Triplicate Ratio: The triplicate ratio of $a:b$ is $a^3:b^3$.

4. Sub Duplicate Ratio: The sub duplicate ratio of $a:b$ is $\sqrt{a}: \sqrt{b}$.

6. Sub Triplicate Ratio: The sub triplicate ratio of a:b is ∛a ∶ ∛b.

7. If y varies directly as $x$, then $\frac{ y_1}{ y_2} = \frac{x_1}{x_2}$.

8. If y inversely proportional as x, then $\frac{ y_1}{ y_2} = \frac{x_2}{x_1}$.

9. If A, B, and C are entering into a partnership for a duration, then

$P_A:P_B: P_C=I_A T_A: I_B T_B: I_C T_C$ where P represents share in profit, I represent investment amount and T represents duration of investment.

Example 1:
Divide ₹840 among A, B, and C in the ratio 3 : 5 : 6.
Total ratio $= 14$
Shares $= 180, 300, 360$

Example 2:
If $a : b = 2 : 3$ and $b : c = 4 : 5$, find $a : b : c$.
$= 8 : 12 : 15$

Example 3:
The incomes of A and B are in the ratio 4 : 5 and their expenditures are in the ratio 3 : 4. If both save ₹100, find their incomes.
Incomes = ₹400 and ₹500

Average, Mixture and Alligations

There are several key formulas applied to a sequence of natural numbers that are listed here:

Average:

(i) Average of $n$ observations is given by $\frac{\text{Sum of observations}}{n}$.

(ii) Weighted Average: If average of $n_1$ observations is $A_1$, & average of $n_2$ observations is $A_2$, then Average of $(n_1 + n_2)$ is $\frac{(n_1 A_1+n_2 A_2)}{(n_1+n_2)}$.

If the average of some observations is x and a is added to each observation, then the new average is (x + a).

(iii) If a person travels two equal distances at speeds of $x$ km/h and $y$ km/h, then average speed = $\frac{2xy}{x+y}$ km/h.

Example 1:
The average of 10 numbers is 20. One number is replaced by 40, and the new average becomes 22. Find the replaced number.
Total increase $= 20$
Replaced number = 20

Example 2:
The average age of a class is 60 years. When a teacher aged 70 joins, the average becomes 61. Find the number of students.
Number of students $= 10$

Example 3:
A person travels equal distances at speeds of 30 km/h, 60 km/h, and 90 km/h. Find the average speed.
Average speed $= \frac{3xyz}{xy+yz+zx} = 49.09$ km/h

Mixture and Alligations:

Below is the concept of Mixture and Alligation

When two ingredients with values $X$ and $Y$ are mixed in a particular ratio so that their mean value becomes $M$, then the ratio of mixing of A and B is given by $(M-Y):(X-M)$.

Time and Work

1. If A and B alone can do a work in $x$ and $y$ days respectively, then the time taken $(T)$ by them to complete the work (working together) will be calculated as

$\frac{1}{T}=\frac{1}{x}+\frac{1}{y}$

2. If A and B alone can do a work in $a$ and $b$ days respectively, while C can destroy (negative work) the whole work in $c$ days, then the time taken $(T)$ by them to complete the work (working together) will be calculated as

$\frac{1}{T}=\frac{1}{a}+\frac{1}{b}-\frac{1}{c}$.

This concept is very useful in the questions of pipes and cisterns.

3. $\frac{(M_1 D_1 H_1)}{W_1} = \frac{(M_2 D_2 H_2)}{W_2}$

Where $M$ & $D$ are the number of men or persons of similar kind and the number of days, respectively.

$H$ is the number of working hours per day (Working Rate), and $W$ is the amount of work done.

Example 1:
A can complete a work in 12 days and B in 18 days. Find the time taken if they work together.
$\frac{1}{T} = \frac{1}{12} + \frac{1}{18} = \frac{5}{36}$
$T = 7.2$ days

Example 2:
A can do a work in 10 days and B in 15 days. After working together for 2 days, A leaves. Find total time to complete the work.
Work done $= \frac{1}{3}$
Remaining work = $\frac{2}{3}$
Time taken = 10 days
Total = 12 days

Example 3:
A can complete work in 20 days, B in 30 days, and C can destroy it in 60 days. Find time taken if all work together.
$\frac{1}{T} = \frac{1}{20} + \frac{1}{30} - \frac{1}{60} = \frac{1}{15}$
$T = 15$ days

Time, Speed and Distance

1. Speed = $\frac{\text{Distance}}{\text{Time}}$

2. 1 km/hr = $\frac{5}{18}$ m/s

3. Average Speed = $\frac{\text{Total Distance Covered}}{\text{Total Time Taken}}$

If two equal distances are covered at speeds S1 and S2, then the average speed = $\frac{2S_1S_2}{S_1+S_2}$.

4. Trains:

Example 1:
A train of length 120 m crosses a pole in 6 seconds. Find its speed.
Speed $= 20$ m/s = 72 km/h

Example 2:
Two trains of lengths 100 m and 150 m move in opposite directions at speeds of 36 km/h and 54 km/h. Find the time taken to cross each other.
Time $= 10$ seconds

Example 3:
A man travels the same distance at 5 km/h and returns at 3 km/h. Find the average speed.
Average speed $= 3.75$ km/h

Tip to Remember: When two trains start simultaneously, meet, and then reach their destinations, the ratio of their speeds is the inverse of the ratio of the square roots of the times they take to reach their destinations after the meeting point.

5. Boats:

Example 1:
A boat moves upstream at 8 km/h and downstream at 12 km/h. Find the speed of the stream.
Stream speed $= 2$ km/h

Example 2:
A boat travels 30 km downstream in 2 hours and upstream in 3 hours. Find the speed of the boat in still water.
Boat speed $= 12$ km/h

Example 3:
Find the time taken to travel 24 km upstream if boat speed = 10 km/h and stream speed = 2 km/h.
Upstream speed = 8 km/h
Time = 3 hours

6. Circular Motion: If A and B are moving in a circular track with speeds $u$ and $v$ respectively. Length of circular track is $L$. Taking $u:v$ into it’s reduced form as $a:b$:

AP ICET Algebra Formulas

Algebra questions are frequent in AP ICET. Here are the must-know AP ICET Algebra Formulas:

Important Identities

Polynomials and Equations

1.

2. For any quadratic equation $ax^2+bx+c=0$ where $a, b$ and $c$ are all real and a is not equal to 0.

Discriminant of a quadratic equation:

D = $(b^2 - 4ac)$ is the discriminant of the quadratic equation.

Nature of roots of a quadratic equation:

(a) If D < 0 (i.e. the discriminant is negative) then the equation has no real roots.

(b) If D > 0, (i.e. the discriminant is positive) then the equation has two distinct roots.

(c) If D = 0, then the quadratic equation has equal roots.

3. Nature of Solutions of a Linear Equation:

A system of linear equations

$a_1 x + b_1 y + c_1= 0$,

and $a_2 x + b_2 y + c_2= 0$

If $\frac{a_1}{a_2} \neq \frac{b_1}{b_2}$, solutions are unique.

If $\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}$, solutions do not exist.

If $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$, solutions are infinite.

Logarithms

Example 1 (Using Identities)

If $a + b = 12$ and $ab = 27$, find the value of $a^2 + b^2$.

We know,
$a^2 + b^2 = (a + b)^2 - 2ab$

Substitute values:
$= 12^2 - 2 \times 27 = 144 - 54 = 90$

So, $a^2 + b^2 = 90$

Example 2 (Higher Identity Application)

If $x - \frac{1}{x} = 4$, find the value of $x^2 + \frac{1}{x^2}$.

Using identity:
$x^2 + \frac{1}{x^2} = \left(x - \frac{1}{x}\right)^2 + 2$

Substitute:
$= 4^2 + 2 = 16 + 2 = 18$

Example 3 (Cubic Identity Concept)

If $a + b + c = 0$, find the value of $a^3 + b^3 + c^3$.

Using identity:
$a^3 + b^3 + c^3 = 3abc$

So, answer = $3abc$

Example 4 (Quadratic Roots Concept)

For the equation $x^2 - 7x + 10 = 0$, find the roots.

Factorise:
$x^2 - 7x + 10 = (x - 5)(x - 2)$

Roots = 5, 2

Example 5 (Discriminant-Based Question)

Find the value of $k$ such that the equation $x^2 + kx + 9 = 0$ has equal roots.

Condition for equal roots:
$D = b^2 - 4ac = 0$

So,
$k^2 - 36 = 0$
$k = ±6$

Example 6 (Forming Equation from Roots)

Find the quadratic equation whose roots are 3 and 4.

Sum of roots $= 7$
Product of roots $= 12$

Equation:
$x^2 - 7x + 12 = 0$

Example 7 (Mixed Algebra Concept)

If $a + b = 8$ and $a^2 + b^2 = 40$, find the value of $ab$.

Using:
$a^2 + b^2 = (a + b)^2 - 2ab$

So,
$40 = 64 - 2ab$
$2ab = 24$
$ab = 12$

Example 8 (Advanced Identity Application)

If $x + \frac{1}{x} = 5$, find $x^3 + \frac{1}{x^3}$.

First,
$x^2 + \frac{1}{x^2} = 25 - 2 = 23$

Then,
$x^3 + \frac{1}{x^3} = (x + \frac{1}{x})(x^2 + \frac{1}{x^2} - 1)$
$= 5(23 - 1) = 5 \times 22 = 110$

AP ICET Geometry Formulas

Geometry is a very crucial topic in the mathematical ability section for AP ICET. Revise the following AP ICET Geometry Formulas carefully:

Area and Perimeter or Circumference

Pythagoras Theorem

$a^2+b^2=c^2$ where $a$ and $b$ are the perpendicular sides and $c$ is the hypotenuse.

Mensuration

For 3D figures:

Example 1 (Circle – Percentage Change)

The radius of a circle is increased by 20%. Find the percentage increase in its area.

Area ∝ $r^2$
New area factor $= (1.2)^2 = 1.44$

Increase $= 44%$

Example 2 (Rectangle – Combined Change)

The length of a rectangle is increased by 25%, and the breadth is decreased by 20%. Find the percentage change in area.

New area factor $= 1.25 \times 0.8 = 1$

So, no change in area
Net change $= 0%$

Example 3 (Triangle – Pythagoras Application)

In a right-angled triangle, the base is 9 cm, and the height is 12 cm. Find the hypotenuse.

Using:
$c = \sqrt{9^2 + 12^2} = \sqrt{81 + 144} = \sqrt{225} = 15$

Hypotenuse = 15 cm

Example 4 (Circle – Sector Concept)

Find the area of a sector of a circle of radius 7 cm with central angle $60^\circ$.

Area of sector $= \frac{60}{360} \times \pi r^2$
$= \frac{1}{6} \times \pi \times 49$
$= \frac{49\pi}{6}$

Example 5 (Mensuration – Cylinder)

Find the volume of a cylinder with radius 7 cm and height 10 cm.

Volume $= \pi r^2 h = \pi \times 49 \times 10 = 490\pi$

Example 6 (Sphere – Percentage Change)

The radius of a sphere is increased by 50%. Find the percentage increase in volume.

Volume ∝ $r^3$
New volume factor $= (1.5)^3 = 3.375$

Increase $= 237.5%$

Example 7 (Cube – Dimensional Change)

The side of a cube is doubled. Find the percentage increase in volume.

New volume factor $= 2^3 = 8$

Increase $= 700%$

Example 8 (Combination of Shapes)

A wire of length 44 cm is bent to form a circle. Find the area of the circle.

Circumference $= 44 = 2\pi r$
$r = \frac{44}{2\pi} = 7$

Area $= \pi r^2 = 49\pi$

Example 9 (Rectangle Diagonal Concept)

Find the diagonal of a rectangle with a length of 24 cm and a breadth of 7 cm.

Diagonal $= \sqrt{24^2 + 7^2} = \sqrt{576 + 49} = \sqrt{625} = 25$

Example 10 (Cone – Slant Height Concept)

Find the slant height of a cone with radius 5 cm and height 12 cm.

$l = \sqrt{h^2 + r^2} = \sqrt{144 + 25} = \sqrt{169} = 13$

The above-discussed AP ICET Maths Important Formulas are very crucial during revision.

Ultimate AP ICET: 2026 Mock Test eBook: Detailed Solutions & Comprehensive Resources

This section offers access to the Ultimate AP ICET 2026 Mock Test eBook, featuring a wide range of practice questions with detailed solutions and comprehensive explanations. Designed to simulate the actual AP ICET exam pattern, this resource helps candidates improve speed, accuracy, and problem-solving skills.

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AP ICET 2026 Formula Sheet – A Quick Review:

Why is this formula sheet important?

Yes, for last-minute revision, it plays an important role in certain ways.

Remember:

This compact and well-structured AP ICET 2026 important formulas list is especially useful for:

• Quick revision before mock tests and the final exam

• Strengthening core concepts in Arithmetic, Algebra, and Geometry

• Improving speed and accuracy in problem-solving

• Reducing calculation time using direct formula application

• Boosting confidence during exam preparation

By regularly revising this AP ICET quantitative aptitude formula sheet, candidates can enhance their performance and attempt more questions within the given time.

The main focus is to solve any question in under a minute. This compact AP ICET Quick Revision Formulas list will certainly help you to achieve this feat.

AP ICET 2026: Complete Syllabus, Exam Pattern & Smart Preparation Strategy

This section provides a complete, comprehensive guide to the AP ICET 2026 syllabus, exam pattern and preparation strategy and tips in the PDF format. Candidates can access a detailed breakdown of all topics covered in the exam, understand the latest exam pattern, marking scheme, section-wise weightage and follow a smart preparation plan to maximise scores.

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Tips for AP ICET 2026 Maths Preparation

Using formulas effectively is a skill. Here, we are going to discuss how to use these AP ICET Quant Formulas.

1. Creating a personal AP ICET 2026 formula sheet (Preferably topic-wise).

2. Revise Daily and practice a few questions on each formula. (15 to 20 problems on each formula)

3. Identify weak areas and focus on those.

4. Key topics to focus on: Arithmetic and Algebra.

5. Improve Shortcut Techniques.

Mastering the AP ICET 2026 important formulas is key to scoring well in the Mathematical Ability section. Regular revision, consistent practice, and proper application of formulas will help improve both speed and accuracy. Keep this AP ICET formula sheet handy for quick revision before mock tests and on the final day of the exam.