Kerala Plus One Question Paper 2023 Mathematics (Science)

FIRST YEAR

Kerala Board
Question Paper
2023

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FY-427
FIRST YEAR HIGHER SECONDARY EXAMINATION, MARCH 2023

Part – III Time : 2 Hours
MATHEMATICS Cool-off time : 15 Minutes
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-427 1 P.T.O.

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

1. (i) If A and B are two sets such that A B, then A B = _____. (1)

(ii) Write the set { x : x is a positive integer and x2 < 40 } in the Roster form. (1)
(iii) Write all the subsets of { 2 }. (1)

2. Solve : 3(1 – x) < 2(x + 4). Also represent the solutions on number line. (3)

3. (i) If (x + 1, y – 4) = (3, 7), then find the values of x and y. (1)

(ii) The Cartesian product A  A has 9 elements among which 2 elements are (–a, 0)
and (0, a). Write A. Also find A  A. (2)

4. Find the number of arrangements of the letters of the word ‘INSTITUTE’. How many
of them begin with N ? (3)

5. If f : R → R defined by

 2 x  3 if x  0
f (x) = 
3( x  1) if x  0
Evaluate lim f (x). (3)
x  0

6. (i) The point (0, 5, 7) lies in (1)
(a) XY-Plane (b) YZ-Plane
(c) XZ-Plane (d) X-axis
(ii) Find the distance between (2, –3, –1) and (–2, 4, 3). (2)

7. If P(A) = 0.35, P(A  B) = 0.25, P(A  B) = 0.6, then find P(B) and P(not – B). (3)

8. Find the centre and radius of the circle x2 + y2 + 8x +10y – 8 = 0. (3)

FY-427 2

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

3  . (6  3 = 18)

1. (i) A  B    . A B  A B = _____. (1)
(ii) { x : x is a positive integer and x2 < 40 }     . (1)
(iii) { 2 }      . (1)

2.   : 3(1 – x) < 2(x + 4).
   . (3)

3. (i) (x + 1, y – 4) = (3, 7)  x-  y-  . (1)
(ii) (–a, 0), (0, a)  9   A  A   
 A   .  A  A . (2)

4. ‘INSTITUTE’      
 ?     N    ? (3)

5. f : R → R- 
 2x  3 if x  0
f (x) = 
3(x  1) if x  0
 lim f (x) . (3)
x  0

6. (i) (0, 5, 7)    . (1)
(a) XY- (b) YZ-
(c) XZ- (d) X-axis
(ii) (2, –3, –1), (–2, 4, 3)     . (2)

7. P(A) = 0.35, P(A  B) = 0.25, P(A  B) = 0.6  P(B)  P(not – B) 
. (3)

8. x2 + y2 + 8x +10y – 8 = 0     . (3)

FY-427 3 P.T.O.

Answer any six questions from 9 to 16. Each carries 4 scores. (6  4 = 24)
9. Let U = {1, 2, 3, 4, 5, 6}, A = {2, 3}, B = {3, 4, 5}

(i) Find A  B (1)

(ii) Find A' and B' (1)

(iii) Verify (A  B)' = A'  B' (2)

10. (i) Let f : R → R, g : R → R defined by f(x) = x + 1, g(x) = 2x – 3. Find (f + g) (x)
and (f⸳g) (x). (1)
(ii) The function h : R → R defined by h(x) = | x |. Draw the graph of h(x). Also write
its domain and range. (3)

11. (i) i–35 = _______. (1)
1+i
(ii) Find the multiplicative inverse and conjugate of . (3)
1–i

12. 4 cards are drawn from a pack of 52 playing cards.
(i) In how many ways it can be done ? (1)
(ii) In how many ways these 4 cards contain 2 red and 2 black ? (3)

 14
13. (i) Number of terms in the expansion of x –  (1)
 x

 14
(ii) Write the expansion of x –  (3)
 x

14. Insert 3 numbers between 1 and 256 so that the resulting sequence is a G.P. (4)

15. Find the co-ordinates of foci, vertices, eccentricity and length of latus rectum of the
x2 y2
hyperbola – = 1. (4)
9 16

FY-427 4

9  16    6  .
4  . (6  4 = 24)
9. U = {1, 2, 3, 4, 5, 6}, A = {2, 3}, B = {3, 4, 5} 
(i) A  B . (1)
(ii) A' , B'  . (1)
(iii) (A  B)' = A'  B'    . (2)

10. (i) f : R → R, g : R → R   f(x) = x + 1, g(x) = 2x – 3 
. (f + g) (x), (f⸳g) (x)  . (1)
(ii) h : R → R   h(x) = | x |   h(x)  
.  h(x)  ,   . (3)

11. (i) i–35 = _______. (1)
1+i
(ii)     . (3)
1–i

12. 52    4  .
(i)     . (1)
(ii)   4  2   2    
. (3)

 14
13. (i) x – x     . (1)
 
 14
(ii) x –    . (3)
 x

14. 1  256        G.P. . (4)

x2 y2
15. – = 1    , ,
9 16
,     . (4)

FY-427 5 P.T.O.

16. A bag contains 9 discs of which 4 are red, 3 are blue and 2 are yellow. The discs are
similar in shape and size. A disc is drawn at random from the bag. Calculate the
probability that it will be
(i) red (1)
(ii) yellow (1)
(iii) blue (1)
(iv) not blue (1)

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

17. (i) 25° = _____ radian. (1)
(ii) Find the value of sin 15°. (2)
sin 3 x  sin x
(iii) Prove that = tan 2x. (3)
cos 3 x  cos x

1
18. (i) Find the equation of a line passing through the point (–4, 3) with slope . (2)
2
(ii) Write the equation of the line passing through the points (1, –1) and (3, 5). (2)
(iii) Find the angle between the lines obtained in (i) and (ii). (2)

19. (i) Find the derivative of tan x using 1st principles. (4)
dy
(ii) If y = x . sin x, find . (2)
dx

20. Consider the following table :
Class 0-10 10-20 20-30 30-40 40-50
Frequency 5 8 15 16 6
(i) Find mean. (2)
(ii) Find variance. (3)
(iii) Find standard deviation. (1)
___________

FY-427 6

16. 9    4  , 3  , 2   .
   .   
   .   
(i)  (1)
(ii)  (1)
(iii)  (1)
(iv)  (1)
   .

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

17. (i) 25° = _____ . (1)
(ii) sin 15°   . (2)
sin 3 x  sin x
(iii) = tan 2x   . (3)
cos 3 x  cos x

1
18. (i) (– 4, 3)      
2
  . (2)
(ii) (1, –1) , (3, 5)    
 . (2)
(iii) (i)  (ii)      . (2)

19. (i) tan x –  1st   . (4)
dy
(ii) y = x . sin x  . (2)
dx

20.     :
Class 0-10 10-20 20-30 30-40 40-50
Frequency 5 8 15 16 6
(i)  . (2)
(ii)  . (3)
(iii)   . (1)
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FY-427 7 P.T.O.

FY-427 8