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CBSE Class 10 Core Formulas and Concepts

24 flashcards to revise the key facts for the CBSE Class 10. Study material written for practice, not the official exam.

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Fundamental Theorem of Arithmetic
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1
Fundamental Theorem of Arithmetic
Every composite number can be uniquely expressed (factorized) as a product of prime numbers, apart from the order in which the prime factors occur.
2
Quadratic Formula and Nature of Roots
x = (-b +/- sqrt(b^2 - 4ac)) / (2a); Discriminant D = b^2 - 4ac: D > 0 gives two distinct real roots, D = 0 gives two equal real roots, D < 0 gives no real roots.
3
Arithmetic Progression: nth Term and Sum of n Terms
nth term: a_n = a + (n - 1)d; Sum: S_n = n/2 [2a + (n - 1)d] = n/2 [a + l], where a is the first term, d is the common difference, and l is the last term.
4
Basic Proportionality Theorem (Thales's Theorem)
If a line is drawn parallel to one side of a triangle intersecting the other two sides in distinct points, then the other two sides are divided in the same ratio.
5
Coordinate Geometry: Section Formula (Internal Division)
The coordinates of point P(x, y) dividing the line segment joining A(x1, y1) and B(x2, y2) internally in ratio m1:m2 are ((m1x2 + m2x1)/(m1 + m2), (m1y2 + m2y1)/(m1 + m2)).
6
Three Fundamental Trigonometric Identities
1) sin^2(theta) + cos^2(theta) = 1; 2) 1 + tan^2(theta) = sec^2(theta); 3) 1 + cot^2(theta) = cosec^2(theta).
7
Circle Tangent Theorem
The tangent at any point of a circle is perpendicular to the radius through the point of contact, and the lengths of tangents drawn from an external point to a circle are equal.
8
Volume and Curved Surface Area of a Right Circular Cone
Volume = 1/3 pi r^2 h; Curved Surface Area (CSA) = pi r * l, where slant height l = sqrt(r^2 + h^2).
9
Empirical Relationship Between Mean, Median, and Mode
Mode = 3 Median - 2 Mean (valid for moderately asymmetrical frequency distributions).
10
Chemical Reaction of Rusting of Iron
4Fe + 3O2 + 2x H2O -> 2Fe2O3 . xH2O (hydrated iron(III) oxide), requiring both oxygen and moisture.
11
Chlor-Alkali Process Products and Reactions
Electrolysis of aqueous NaCl (brine) produces sodium hydroxide at cathode, chlorine gas at anode, and hydrogen gas at cathode: 2NaCl + 2H2O -> 2NaOH + Cl2 + H2.
12
Chemical Formula of Plaster of Paris and Gypsum
Plaster of Paris: CaSO4 . 1/2 H2O (calcium sulphate hemihydrate); Gypsum: CaSO4 . 2H2O (calcium sulphate dihydrate).
13
Reactivity Series of Metals (Decreasing Order)
K > Na > Ca > Mg > Al > Zn > Fe > Pb > [H] > Cu > Hg > Ag > Au; elements above hydrogen displace it from dilute acids.
14
Homologous Series of Alkanes, Alkenes, and Alkynes
Alkanes: C_n H_(2n+2); Alkenes: C_n H_(2n); Alkynes: C_n H_(2n-2), where successive members differ by a -CH2- unit (14 unified mass units).
15
Saponification Reaction
Ester + Sodium hydroxide -> Soap (sodium carboxylate salt) + Alcohol (glycerol): CH3COOC2H5 + NaOH -> CH3COONa + C2H5OH.
16
Role of Hydrochloric Acid and Pepsin in Gastric Digestion
Gastric glands secrete HCl which creates an acidic medium (pH 1.5-2.5) that activates inactive pepsinogen into pepsin, which digests dietary proteins into peptones.
17
Xylem vs Phloem Transport Mechanisms
Xylem conducts water and dissolved minerals unidirectionally from roots via transpirational pull; Phloem translocates soluble photosynthetic assimilates (sucrose) bidirectionally using ATP energy.
18
Mendelian Monohybrid Cross Phenotypic and Genotypic Ratios
F2 Phenotypic ratio = 3 : 1 (Dominant : Recessive); F2 Genotypic ratio = 1 : 2 : 1 (Homozygous dominant : Heterozygous : Homozygous recessive).
19
Spherical Mirror Formula and Sign Convention
1/f = 1/v + 1/u, and Magnification m = -v/u = h_i / h_o; focal length f is negative for concave mirrors and positive for convex mirrors.
20
Thin Lens Formula and Optical Power
1/f = 1/v - 1/u; Magnification m = v/u; Power P = 1 / f (in meters), measured in Dioptres (D); converging lens has positive power, diverging lens has negative power.
21
Ohm's Law and Electrical Resistivity Equation
V = I R; Resistance R = rho (l / A), where rho is electrical resistivity (ohm-meter), l is conductor length, and A is cross-sectional area.
22
Joule's Law of Heating and Electrical Energy Consumption
Heat H = I^2 R t = V I t; 1 commercial unit of electrical energy (1 kWh) = 3.6 x 10^6 Joules.
23
Fleming's Left-Hand Rule (Electric Motors)
Stretch thumb, forefinger, and central finger mutually perpendicular: Forefinger represents Magnetic Field, Central finger represents Current, Thumb represents Direction of Force (Motion).
24
Trophic Levels and Lindeman's 10% Ecological Law
Only approximately 10% of the energy available at a given trophic level is transferred to the next higher trophic level; 90% is lost as metabolic heat and life functions.

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