Kerala Plus One Question Paper 2023 Mathematics (Commerce)

FIRST YEAR

Kerala Board
Question Paper
2023

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Reg. No. : ......................................
Name : ...........................................
FY-451
FIRST YEAR HIGHER SECONDARY EXAMINATION, MARCH 2023

Time : 2 Hours
Part – III Cool-off time : 15 Minutes
MATHEMATICS
Maximum : 60 scores

General Instructions to Candidates :
 There is a ‘Cool-off time’ of 15 minutes in addition to the writing time.
 Use the ‘Cool-off time’ to get familiar with questions and to plan your answers.
 Read questions carefully before answering.
 Read the instructions carefully.
 Calculations, figures and graphs should be shown in the answer sheet itself.
 Malayalam version of the questions is also provided.
 Give equations wherever necessary.
 Electronic devices except non-programmable calculators are not allowed in the
Examination Hall.

 
    15  ‘  ’ .
 ‘  ’    
 .
      .
    .
  , , ,   
.
   .
    .
     
    .

FY-451 1 P.T.O.

Answer any 6 questions from 1 to 8. Each carries 3 scores. (6  3 = 18)

1. (i) Let A = {1, 2, 3, 4}, B = {2, 4, 5} then find A  B. 1

(ii) Write all subsets of P = {a, {b}}. 2

2. (i) If A  B = {(a, x), (a, y), (b, x), (b, y)}, find A and B. 2

(ii) Consider the relation R = {(a, d), (b, e), (c, f)}, write the domain of R. 1

3. (i) The conjugate of 2 + i is _______. 1

(ii) Write the modulus of 3i. 1

(iii) Simplify : i21. 1

4. Solve 5x – 2  3x – 4. Show the graph of solutions on number line. 3

8!
5. (i) Evaluate . 1
6! 2!

(ii) Find the number of permutations of the word ALLAHABAD. 2

6. (i) Write the equation of the directrix of the parabola y2 = 16x. 2

(ii) Find the centre and radius of the circle (x – 5)2 + (y – 3)2 = 25. 1

FY-451 2

1  8    6  .

3  . (6  3 = 18)

1. (i) A = {1, 2, 3, 4}, B = {2, 4, 5}  A  B . 1

(ii) P = {a, {b}}     . 2

2. (i) A  B = {(a, x), (a, y), (b, x), (b, y)}  A, B  . 2

(ii) R = {(a, d), (b, e), (c, f)}   . R- 
. 1

3. (i) 2 + i    _______ . 1

(ii) 3i   . 1

(iii)  : i21. 1

4.   : 5x – 2  3x – 4

   . 3

8!
5. (i)   : 1
6! 2!

(ii) ALLAHABAD     
. 2

6. (i) y2 = 16x     . 2

(ii) (x – 5)2 + (y – 3)2 = 25     . 1

FY-451 3 P.T.O.

x9 – 1
7. Evaluate the limit : lim 4 . 3
x  1 x – 1

8. (i) P() = _______ .

1
(a) 1 (b)
2

1
(c) (d) 0 1
3

(ii) When a die is thrown, find the probability of getting a prime number. 2

Answer any 6 questions from 9 to 16. Each carries 4 scores. (6  4 = 24)

9. (i) If f(x) = 2x – 5 then f(0) = _______ . 1

(ii) The number of elements of the range of a constant function is : 1

(a) 0 (b) 1

(c) 100 (d) 

(iii) If f(x) = x2 and g(x) = 2x + 1, then (f + g) (x) = _______ . 1

1
(iv) The domain of the function f(x) = is 1
x

(a) R (b) R – {0}

1 1 1 
(c)  , , ,........... (d) Q
2 3 4 

FY-451 4

x9 – 1
7.   : lim 4 . 3
x  1 x – 1

8. (i) P() = _______ .

1
(a) 1 (b)
2

1
(c) (d) 0 1
3

(ii)        
 ? 2

9  16    6  .

4  . (6  4 = 24)

9. (i) f(x) = 2x – 5  f(0) = _______ . 1

(ii)      : 1

(a) 0 (b) 1

(c) 100 (d) 

(iii) f(x) = x2, g(x) = 2x + 1   (f + g) (x) = _______ . 1

1
(iv) f(x) =    : 1
x

(a) R (b) R – {0}

1 1 1 
(c)  , , ,........... (d) Q
2 3 4 
FY-451 5 P.T.O.

3
10. (i) If sin x = and x is in the second quadrant, find cos x. 2
5

(ii) Evaluate sin (390). 2

11. (i) If nC2 = nC8 then n = _______ . 1

(ii) What is the number of ways of choosing 4 cards from a pack of 52 playing cards
out of which 2 are spades ? 3

12. Expand (100 + x)4 and hence evaluate 1014. 4

x2 y2
13. Consider the ellipse + =1:
25 9

Find,

(i) foci 2

(ii) the vertices 1

(iii) eccentricity 1

14. (i) Name the octant in which the point (1, – 2, 3) lie. 1

(ii) The z-coordinate of a point on XY plane =

(a) 1 (b) –1

(c) 0 (d)  1

(iii) Find the distance between (2, 0, 1) and (0, 1, 2). 2

FY-451 6

3
10. (i) sin x =  x    cos x- 
5
. 2

(ii)   : sin (390). 2

11. (i) nC2 = nC8  n-  = _______ . 1

(ii) 52     2   

4     ? 3

12. (100 + x)4 –      1014-

. 4

x2 y2
13. + = 1    :
25 9

,

(i)  2

(ii)  1

(iii)    1

14. (i) (1, – 2, 3)     . 1

(ii) XY-   z- =

(a) 1 (b) –1

(c) 0 (d)  1

(iii) (2, 0, 1), (0, 1, 2)    . 2

FY-451 7 P.T.O.

15. (i) Find the derivative of f(x) = x2 w.r.t. x. 1

(ii) Find the derivative of f(x) = sin x from first principle. 3

16. Find the mean deviation about the median for the following data : 4

xi 3 6 9 12 13 15 21 22

fi 3 4 5 2 4 5 4 3

Where xi are the observations and fi are the corresponding frequencies.

Answer any 3 questions from 17 to 20. Each carries 6 scores. (3  6 = 18)

17. (i) Find the fifth term of the sequence with nth term an = 2n + 1. 1

(ii) Find the 8th term of the G.P. 1, 3, 9, …….. 2

(iii) Find the sum to n terms of the sequence 8 + 88 + 888 + ….. 3

18. (i) Write the equation of the straight line through (0, 4), (3, 0) in intercept form. 2

(ii) Identify the slope and y-intercept of the line 2y = 4x + 3. 2

(iii) Find the distance between the point (–1, 1) and the line 2x + 3y + 1 = 0. 2

19. Consider the following data : 6

Classes 0-10 10-20 20-30 30-40 40-50

Frequency 7 8 10 8 7

Determine the mean and standard deviation.

FY-451 8

15. (i) x  f(x) = x2 –  . 1

(ii)    f(x) = sin x-  . 3

16.        : 4

xi 3 6 9 12 13 15 21 22

fi 3 4 5 2 4 5 4 3

 xi   fi   .

17  20    3  .
6  . (3  6 = 18)

17. (i) n-  an = 2n + 1    5-  . 1

(ii) 1, 3, 9, …….  G.P.  8-  . 2

(iii) 8 + 88 + 888 + …..   n   . 3

18. (i) (0, 4), (3, 0)     

  . 2

(ii) 2y = 4x + 3   , y-  . 2

(iii) (–1, 1)   2x + 3y + 1 = 0    

. 2

19.     : 6

 0-10 10-20 20-30 30-40 40-50

 7 8 10 8 7

  ,    .

FY-451 9 P.T.O.

1 1 1
20. Let A and B be two events, P(A) = , P(B) = , P(A  B) = . Then find,
3 2 6

(i) P (A or B) 2

(ii) P (not A) 1

(iii) P (not A and not B) 2

(iv) P (A and not B) 1

_____________

FY-451 10

1 1
20. A, B  2 .  P(A) = , P(B) = , P(A  B) =
3 2
1
6
,

(i) P (A or B) 2

(ii) P (not A) 1

(iii) P (not A and not B) 2

(iv) P (A and not B) 1

 

_____________

FY-451 11 P.T.O.

FY-451 12