sslc maths one mark

MATHEMATICS
 [1] Write the formula to find the nth term of an arithmetic progression        an = a + (n -1)d
[2] Write the formula to find the sum of natural numbers of an A.P      Sn =
[3] Write the formula to find sum of n
th
term of an A.P     Sn =
𝒏 𝟐
 [ 2a + ( n – 1 ) d  [4] Write the nature of the quadratic equation ax
2
+ bx + c = 0 if    (1) b
2
𝒏 𝒏 −𝟏 𝟐

  − 4ac = 0       (2) b
 −4ac > 0  [1] the roots are equal [2] the roots are real and distinct
 [5]Write the standard form the quadratic equation.    ax
 [6]Write the roots of a quadratic equation.   x = 
  [7]Write the discriminant of the quadratic equation    ∆ = b
−𝒃± 𝒃
𝟐
2
 + bx + c = 0
−𝟒𝒂𝒄 𝟐𝒂
 - 4ac [8]Write the formula to find the lateral surface area of cone  C.S.A = 𝝅rl [9]  The curved surface area of solid sphere   C.S.A =  2𝝅r
2
.
2
[10] If the probability of winning a game is 0.3 . what is gthe probability of losing it .
 P (losing a game ) =1-p( winning )     =1-0.3=0.7 [11] The probability of occurrence of event A is 1/3 . What is the probability of complement of A ?
P ( A') = 1   −  P (A)    =    1 –
𝟏 𝟑
  =   
𝟐 𝟑
 [12]Find the probability of throwing a sum 9 with two dice.
Sum of 9 = {(3, 6), (4, 5), (5, 4) (6,3)} P(sum of 9)   
𝒏(𝑨) 𝒏(𝒔)
  =
𝒏(𝟒) 𝒏(𝟑𝟔)
  =    
𝟏 𝟗
     [12] Write the formula to find the area of sector of a circle with radius ‘r’ and angle with degree measurement x
 
𝜽 𝟑𝟔𝟎
𝟎
 x 𝝅r
2

[13] Length of an arc =   
𝜽 𝟑𝟔𝟎
𝟎
 x 𝝅r
2
0
 [13] Define sector of a circle The region enclosed by the two radii and the corresponding arc. [14]What is tangent of a circle. Tangent is a line that intersects the circle at only one point. [15] Identify the tangent to the circle in the adjoining figure and write its name:  Ans:  AB   [16] What is the value of APB in the given figure  ( AP and BP are tangents to the circle with center O)
 ∆APB = 180
0
 - ∆AOB      = 180
 [17] In the given figure if  ∆PTQ = 55
0
 −  125
0
0
 = 55
 Find ∆POQ  ∆POQ = 180
 - ∆PTQ 180
0
 - 55
0
0
 = 125
0
0
[18] State basic proportionality theorem ( Thales theorem)
If a straight is drawn parallel to one side of triangle, then it divides the other two sides
 divides proportionally  [19] State converse of Thales theorem.
If a straight line divides two sides of a triangle proportionally, then the straight line is parallel to the third side. [20] State “Pythagoras theorem”.
In a right angled triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides.
[21] In the figure DE||BC find the length of AD.
𝑨𝑫 𝑩𝑫
 =
𝑨𝑬 𝑪𝑬
  AD =
𝟐 𝟒
  X  6  =
𝟏𝟐 𝟒
 =  3cm. 

 [22] Find the distance between the point p( 3,4) and the origin d = 𝐱
𝟐
+ 𝐲
𝟐
    =   𝟑
𝟐
+ 𝟒
𝟐
  = 𝟗 + 𝟏𝟔  = 𝟐𝟓  =  5  [23]  Write the section formula .       P =  
𝒎
𝟏
 𝒙
𝒎
𝟐
𝟏
+𝒎
 +  𝒎
𝟐
 𝒙
𝟐
𝟏
 ,
𝒎
  24. Distance formula = 𝒙
𝟐
− 𝒙
𝟏 𝟐
+ (𝒚
𝟐
− 𝒚)
 25. The mid point of the line segment joining the points P( x
  
 𝒙
𝟏
+ 𝒙
𝟐
𝟐
  ,
 𝒚
𝟏
+ 𝒚
𝟐
𝟐

26. Write the prime factors of composite numbers 210 27. Express 1024 as product of prime number 1024 = 2
10
[28]Express 360 as product of prime factors 360 = 2
3
  x  3
2
  x 5   [29]Find the L.CM of 36 and 32 Ans:   36  = 2
2
 x 3
       and   32 = 2
L.C.M = = 2
= 32 X 9 = 288
5
5
 x 3
2
2
 
 [30]  If The HCF of 52  and 182 is 26 , Find the LCM Ans:-   L =
𝐀  𝐗   𝐁 𝐇
 =

𝟓𝟐  𝐗   𝟏𝟖𝟐 𝟐𝟔
   =   2 x 82 = 164
𝟐
𝟏
 𝒚
𝒎
1
𝟐
𝟏
+ 𝒎
 +  𝒎
 , y
1
𝟐
 𝒚
𝟐
𝟏
) and Q ( x
2
 ,y
2
) is   
[31] State the fundamental principle of arithmetic Every composite number can be expressed as product of primes, and this factorisation is unique, apart from the order in which the prime factor occur.
[32] State Euclid division lemma. Let a and b be any two given positive integers, then there exist unique integers q and r such that a =  bq  +  r; 0 ≤  r < b
[33] Is (17 x 5 x 11 x  2 +2) a composite number ?
= 17 x 5 x 11 x 2 + 2 = 2(17 x  5 x 11 + 1) = 2(85 x 11 + 1) = 2(935  + 1)
= 2( 936 )
= 2 x  2
3
 x  3
2
  x 13 = 2
4
 x 3
2
x 13 ∴   It is composite number with  more than 2 prime factors  [34] Find H.C.F of 55 and 210 55 = 5 x 11  210 = 2 x 3 x 5 x 7 
 [36] Find the number of zeroes of the polynomial p(x) from the graph given  Ans: - Number of zeroes =4 [37] Define zero of a polynomial. A polynomial with the value zero (0) is known as zero polynomial. p ( x) = 0 [38]  Write the degree of the polynomial     2x
2
 + 3x
 +15x + 2 Degree = 3
 [39]Express 210 as a product of prime factors.
210 = 2 x  3   x  5 x 7 [40] Find the zeros of the polynomial     x
  − 4 Let   p ( x) = x
2
 − 4 p ( x) = 0
x
x
2
 - 4 = 0
2
= 4 x = ± 𝟒
x = ±2  ∴ The zeros are 2, − 2  
[41] Find the sum of & Product of zeroes of the
  the polynomial  p(x ) = x
2
 – 7x  + 12  Sum ( m + n)  or   (𝜶 + 𝜷 )   = −
𝒃 𝒂
  = −
 = 7 Product  ( mn)  or   (𝜶 𝜷 )   = −
𝒄 𝒂
  = 
 = 12 

𝟏𝟐 𝟏
2
(−𝟕) 𝟏
3