This document contains a summary of the key chapters and concepts covered in the Term 1 Complete Maths course, including: 1. Real numbers, polynomials, pairs of linear equations in two variables, triangles, coordinate geometry, trigonometry, areas related to circles, and probability. 2. The chapters describe important formulas, definitions, theorems, examples and questions. Concepts covered include HCF, LCM, quadratic equations, similarity, Pythagoras theorem, trigonometric ratios, and probability calculations. 3. Key formulas introduced are for distance, midpoint, section, centroid, area of circle/sector/segment, trig ratios, and probability. Examples are provided to demonstrate solving pairs of linear

1. Class- 10
Term -1 COMPLETE MATHS
IN ONE SHOT REVISION

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3. CHAPTER - 1 REALNUMBERS
FORMULAS---
HCF(a,b) XLCM(a,b) =ax b
2n x 5m in adenominatorno
other number then it is
terminating

4. CHAPTER - 1 REALNUMBERS
Q1. Given that HCF(306,657)=9, findLCM (306,657).

5. CHAPTER - 1 REALNUMBERS
Findwhich is terminating or non-terminating :

6. CHAPTER - 1 REALNUMBERS

7. CHAPTER - 2 POLYNOMIALS
GRAPH ANALYSIS FORPARABOLAS:
 If parabola is “U” shapethen a>0but
if parabola is “∩” then a<0.
 Y-axis intersection always gives ‘C’ if
“ +ve” then Cis also “+ve” and if ‘-ve’
then Cis also ‘-ve’.
 Wherethe X-axis intersect that are
the roots of that equation.
y=x^{2} -3x-4
General Quadratic equation =
ax2+bx+c

8. CHAPTER–2POLYNOMIALS
General Quadratic equation = ax2+bx+c
Relationshipbetween roots and coefficient of
quadratic equation---
α +β = -b/a
α .β =c/a
Formation of
Quadraticequation
when the
roots/zeroes are
given ---
X2–(a-b)x +a.b =0

9. CHAPTER–2POLYNOMIALS
Relationship between roots and coefficient of
cubic equation ---
α +β +γ =-b/a
αβ+ βγ +γα=c/a
αβγ =-d/a
General Cubic equation ---
ax3 + bx2 + cx + d = 0

10. CHAPTER–2POLYNOMIALS
Findthe number of zeroes of p(x) .

11. CHAPTER–2POLYNOMIALS
Q22.If 5is a zero of the quadraticpolynomial, x2 –kx –15,
then the valueof k is
(a) 2
(b)-2
(c)4
(d) –4

12. CHAPTER– 3PAIR OF LINEAR
EQUATION IN TWO VARIABLE
General equation --
a1 x + b1 y + c1= 0,and
A2 x + b2 y +c2=0

13. CHAPTER– 3PAIR OF LINEAR
EQUATION IN TWO VARIABLE

14. CHAPTER– 3PAIR OF LINEAR
EQUATION IN TWO VARIABLE
Algebraic methods ---
1. Substitution method
2. Cross multiplicationmethod
3. Elimination method

15. CHAPTER– 3PAIR OF LINEAR
EQUATION IN TWO VARIABLE
Examples--- how tosolvebyelimination
and bysubstitution methods:
1. 2x+ 3y =8
4x +3y=7

16. CHAPTER– 3PAIR OF LINEAR
EQUATION IN TWO VARIABLE

17. CHAPTER – 6 TRIANGLES
Twotriangles are similarif :
1. Theircorrespondingangles are equal and
2. Theircorrespondingsides are in the same
ration (orproportion).
Similarity criterion intriangles 
1. AAA/ AA
2. SAS
3. SSS

18. CHAPTER – 6 TRIANGLES
Thales theorem :
Statement : ifa lineis drawn parallel to
one side of a triangle to intersect the
other two sides in distinct points, the
other two sides are divided in the same
ratio.

19. CHAPTER – 6 TRIANGLES
Pythagoras Theorem
If triangle is right angled triangle , then :
(hypotenuse)2= (base)2 + (perpendicular)2

20. CHAPTER – 6 TRIANGLES
Important results:
In right angled triangle , if we make a
perpendicular on the hypotenuse from
the opposite vertex , then all three
triangles are similar.

21. CHAPTER – 7 COORDINATE GEOMETRY
SIGN CONVERSIONS:

22. CHAPTER – 7 COORDINATE GEOMETRY
Distance formula :

23. CHAPTER – 7 COORDINATE GEOMETRY
Find the distance betweenthepoints
(-2,1)and(3,2)

24. CHAPTER – 7 COORDINATE GEOMETRY
If we want to find the distancefrom
the origin (0,0), then :

25. CHAPTER – 7 COORDINATE GEOMETRY
Find thedistance between the
points : (0,0)and (3,3)

26. CHAPTER – 7 COORDINATE GEOMETRY
Mid point formula :

27. CHAPTER – 7 COORDINATE GEOMETRY
Findthe mid point of this line
whose point are(1,1)and ( 2,4).

28. CHAPTER – 7 COORDINATE GEOMETRY
Section formula :

29. CHAPTER – 7 COORDINATE GEOMETRY
Centroid formula
Thepoint of intersection of the medians
of the triangle.
Here ,Centroid is point M

30. CHAPTER–8TRIGONOMETRY
Sine (sin)
Cosine(cos)
Tangent (tan)
Cosecant(cosec)
Secant (sec)
Cotangent (cot)
Opposite side / Hypotenuse
Adjacent side / Hypotenuse
Opposite side / Adjacent side
Hypotenuse / Opposite side
Hypotenuse / Adjacent side
Adjacent side / Opposite side
TRIGNOMETRYRATIOS

31. CHAPTER–8TRIGONOMETRY
TRIGNOMETRYRATIOSTRICK
TOMEMORISE
PANDIT (P) BADRI (B) PRASAAD (P)
HAR (H) HAR (H) BOLE (B)

32. CHAPTER–8TRIGONOMETRY
Changing trigonometryratios

33. CHAPTER–8TRIGONOMETRY
Trigonometry ratiosComplementary angles
sin (90 –θ) =cos θ
cos(90–θ) =sinθ
tan( 90 –θ) = cot θ
cot( 90 –θ) = tan θ
sec(90–θ) =cosecθ
cosec(90–θ) =secθ

34. CHAPTER–8TRIGONOMETRY

35. CHAPTER–8TRIGONOMETRY

36. CHAPTER– 12AREASRELATEDTO CIRCLES
BASICFORMULASOFCIRCLE
Area of circle = ∏r2
Circumference of circle = 2∏r
Circumference of semi-circle= ∏r
NEWFORMULASOFCIRCLE
Area of sector = θ/360 x ∏r2
Length of the arc= θ/360x 2∏r
Area of segment =area of sector –
area of ∆AOB
= θ/360 x ∏r2 - ½ sin θxr2
Area of equilateral ∆=

37. CHAPTER –15 PROBABILITY
PRPBABILITYmainFORMULA
P(E)=number of favorable outcomes to E
Total possibleoutcomes
Complementary events P(C):
P(E)+P(C) =1

38. CHAPTER–15PROBABILITY
Important terms
Prime numbers = 2,3,5,7,11…….etc.
Composite numbers =
4,6,8,9,12,….etc.
Tossingacoin =head or tail (total
outcomes =2 =21)
Tossingtwo coins=(total outcome =
4 =22)
Tossing three coins =( totaloutcomes
=8 =23)
Formula tofind total
outcome of dice =(6)n
;where ‘n’ isthe no. of
times thedice thrown

39. CHAPTER–15PROBABILITY

40. TERM –1MATHS समाप्त
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