𝗠𝗔𝗧𝗛 𝐏𝐎𝐋𝐋 𝐂𝐇𝐀𝐍𝐍𝐄𝐋😊:
*Topics to Master for an A*

1️⃣ Fractions, Decimals & Percentages
2️⃣Number Bases
3️⃣Limits of Accuracy
4️⃣ Factorization
5️⃣ Plane Shapes
6️⃣ Quadratic Expressions
7️⃣ Equations
8️⃣ Simulatenous Equation
9️⃣ Quadratic formula
🔟 Solving Triangles - Pythagoras, CHASHOTAO, SINE rule, Cosine Rule, Surds
1️⃣1️⃣ Functions
1️⃣2️⃣ Scale
1️⃣3️⃣Locus & Construction
1️⃣4️⃣ Statistics
1️⃣5️⃣ Functional Graphs
1️⃣6️⃣ Inequalities & Linear Programming
1️⃣7️⃣ Conversions
1️⃣8️⃣ Standard Form
1️⃣9️⃣ Number patterns
2️⃣0️⃣ Travel Graphs
2️⃣1️⃣ Consumer Arithmetic
2️⃣2️⃣ General Arithmetic
2️⃣3️⃣ Algebra
2️⃣4️⃣ Variation
2️⃣5️⃣ Transformation
2️⃣6️⃣ Time ⌚
2️⃣7️⃣ Lines of symmetry & Order of Rotational Symmetry
2️⃣8️⃣ Probability
2️⃣9️⃣ Similarity & Congruency
3️⃣0️⃣ Subject of Formula
3️⃣1️⃣ Decimal Places & Significant figures
3️⃣2️⃣ Matrices
3️⃣3️⃣ Sets
3️⃣4️⃣ Completing the square
3️⃣5️⃣ Matrices
3️⃣6️⃣ Indices & Logarithms
3️⃣7️⃣ HCF & LCM
3️⃣8️⃣ Circle Geometry
3️⃣9️⃣ Mensuration of plane & solid shapes
4️⃣0️⃣ Directed Numbers
Bearing
Polygons
🔢🔢 🔢🔢🔢🔢🔢🔢

Graphs

Algebraic graphs
Function
Velocity time gragh

Statistics
Ungrouped data
Line gragh
Bar gragh
Pie chart
Pictograph

Grouped data
Histogram
Cumulative/ogive
Frequency polygon

Transformation

Vector

Menstruation of plan and solid shapes

Solving triangles and Bearing

Consumer arithmetic
Construction

Construction with bearing

All the best

*☑️ बीजगणित के सूत्र:*

*(a+b)² =* a²+2ab+b²

*(a-b)² =* a²-2ab+b²

*(a-b)² =* (a+b)²-4ab

*(a+b)² + (a-b)² =* 2(a²+b²)

*(a+b)² – (a-b)² =* 4ab(a+b)³ = a³+3a²b+3ab²+b³

*(a+b)² – (a-b)² =* a³+b³+3ab(a+b)

*(a-b)³ =* a³-3a²b+3ab²-b³

*(a-b)³ =* a³+b³+3ab(a+b)

*(a+b)³ + (a-b)³ =* 2(a³+3ab²)

*(a+b)³ + (a-b)³ =* 2a(a²+3b²)

*(a+b)³ – (a-b)³ =* 3a²b+2b³

*(a+b)³ – (a-b)³ =* 2b(3a²+b²)

*a²-b² =* (a-b)(a+b)

*a³+b³ =* (a+b)(a²-ab+b²)

*a³-b³ =* (a-b)(a²+ab+b²)

*a³-b³ =* (a-b)³ + 3ab(a-b)

*(a+b+c)² =* a²+b²+c²+2(ab+bc+ca)

*(a+b+c)³ =* a³+b³+c³+3(a+b)(b+c)(c+a)

*a³+b³+c³ =* (a+b+c)³ – 3(a+b)(b+c)(c+a)

*(a+b+c+d)² =* a²+b²+c²+d²+2(ab+ac+ad+bc+bd+cd)

*a³+b³+c³-3abc =* (a+b+c)(a²+b²+c²-ab-bc-ca)।


*🫠 बस 1 𝐋𝐢𝐤𝐞 ❤️ चाहिए*

*1. A water tank can hold 2400 litres of water. If 1200 litres of water are already in the tank, what percentage of the tank is still empty?*

A) 25%🙏
B) 33.33%👍
C) 50%😢
D) 66.67%❤️

*2. What is the value of x in the equation 2x + 5 = 11?*

A) 2👍
B) 3🙏
C) 4😢
D) 5❤️

*3. A shop has a 15% discount on all items. If a shirt originally costs $20, how much will it cost after the discount?*

A) $15😢
B) $16❤️
C) $17🙏
D) $18👍

*4. If a bakery sells 250 loaves of bread at $2 each, how much money does the bakery make in total?*

A) $450😢
B) $500❤️
C) $550🙏
D) $600👍

🔺 **Formulas of percentage* :-✍️
*
Profit = Selling price – Buying price

Loss = Buying price – Selling price

Profit % = Profit Buying price × 100

Loss % = Loss Buying price × 100

Selling price = Buying price + Profit

Selling price = Buying price – Loss

Selling price = Selling price – Profit

Selling price = Selling price + Loss

Profit = (Profit%/(100 + Profit)) × Selling price

Loss = (Loss%/(100-Loss)) × Selling price

🔺 *Formula of sphere..* ✍️

Curved surface area of sphere = 4πr2
Volume of sphere = 4/3 πr3
*Volume of spherical* shell = 4/3 π (R3 – r3)
Area of the entire surface of spherical shell = 4/3 π(R2- r2 )
Volume of the largest sphere in the cube = 1/6 a3
Surface area of the largest sphere in the cube = πr 2
One side of the largest cube in the sphere = 2R / √3
Curved surface area of a hemisphere = 2 πr2
Entire surface area of a hemisphere = 3 πr2
Volume of a hemisphere = 2/3 πr3

🔺 *Formula of Cone-* ✍️

Volume of cone = 1/3 πr2h
Slant height of a right circular cone = √ ( h2 + r2 )
Height of the cone = √ (l2 – r2 )
Base radius of the cone = √ (l2 – h2 )
Curved surface area of the cone = πrl
Entire surface area of a right circular cone = πr ( l + r )

Area of the base of a cone = πr2

🔺 Cylinder formula... ✍️

Volume of cylinder = πr2h
Height of cylinder = Volume / πr2
Radius of right circular cylinder = √ (Volume / πh)
Volume of metal in a hollow cylinder = πh (R2 – r2 )
Curved surface area of cylinder = 2πrh
Entire surface area of cylinder = 2πr ( h + r )
Height of right circular cylinder = (Entire surface area of cylinder / 2πr) – r
Base area of right circular cylinder = πr2

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✍ IMPORTANT MATHS FORMULA

01. Work = force × distance
कार्य = बल × दूरी

02. Energy = force × distance
ऊर्जा = बल × दूरी

03. Speed = distance / time
गति = दूरी / समय

04. Velocity= displacement / time
वेग = विस्थापन / समय

05. Electric field = electrical force/charge
विद्युत क्षेत्र= वैद्युत बल/आवेश

06. Force = force/area
प्रतिबल=बल/क्षेत्रफल

07. Volume = length × width × height
आयतन = लंबाई × चौड़ाई × ऊंचाई

08. Mass density = mass/volume
द्रव्यमान घनत्व =द्रव्यमान/आयतन

09. Acceleration =velocity / time
त्वरण = वेग / समय

10. Power = work / time
शक्ति = कार्य / समय

11. Pressure = force / area
दाब =बल/क्षेत्रफल

11. Momentum = mass × velocity
संवेग = द्रव्यमान × वेग

13. Area (A) = Length × Width
क्षेत्रफल ( A ) = लम्बाई × चौड़ाई

14. Force (F) = Mass × Acceleration
बल ( F ) = द्रव्यमान × त्वरण

15. Pressure Energy = Pressure × Volume
दाब ऊर्जा = दाब × आयतन

16. Impulse = force × time
आवेग = बल × समय

17. Linear momentum = mass × velocity
रैखिक संवेग = द्रव्यमान × वेग

18. Kinetic energy = 1/2 mv²
गतिज ऊर्जा = 1/2 mv²

19. Mechanical energy = kinetic energy + potential energy
यांत्रिक ऊर्जा = गतिज ऊर्जा + स्थितिज ऊर्जा

20. Angular momentum = Inertial × Angular velocity
कोणीय संवेग = जड़त्वाघूर्ण × कोणीय वेग
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