Kerala SSLC 2022 Question Paper Maths

(Pages:8) S 1731

SI. No.

SSLC EXAMINATION, MARCH 2022
MATHEMATICS
(English)
Time: 2h Hours Total Score : 80

General Instructions to Candidates:
There is a 'Cool-off time' of 15 minutes in addition to the writing time. Use this time to get

familiar with questions and to plan your answers.
Questions with different scores are given as distinct parts.
Read the instructions carefully before answering the questions.
Keep in mind, the score and time while answering the questions.
The maximum score for questions from 1 to 35 will be 80.
No need to simplify irrationals like 2 . 3 , T etc., using approximations unless you are

asked to do so.

PART-I

Questions from 1 to 10 carries 1 score each.
4x1-4
(A) Answer
any 4 questions from1 to 6.
1. What is the common difference of the Arithmetic sequence 3, 7, 11, .

D 1

C
110

In the figure 2C=110. Find the measure of ZA.

3. A box contains 7 white balls and 3 black balls. Ifa ball is taken from it, what is the
probability of it being black ?

Find the distance between the points (0, 0) and (4, 0). 1
.

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5. the circle of radius 12 centimetres, a sector of central angle 0° is cut out and 1
From
made into a cone. What is the base radius of this cone ?

. If (x-1) is a factor of the 1
polynomial p(x), write p(1).
8) Answer all questions from 7 to 10. Choose the correct answer from the4x1=4
brackets.

7. What is the value of tanx if x =30° ? 1

8. f the perimeter of a triangle is 24 centimetres and its inradius is 2 centimetres, 1
find its area in square centimetres.

(12; 20; 24; 26)

9. The lateral faces of a square pyramid are equilateral triangles. If the length of 1
one base edge is 20 centimetres, what will be the measure of its slant height in
centimetres?

20 20

20

(10; 10/2; 10/3; 20)

10. The equation of a line is 2x +y=5 if the x co-ordinate of a point on this line is 1
2, what is the y co-ordinate of this point ?
(0; 1; -1;2)

PART III
Questions from 11 to 18 carries 2 scores each.
(A) Answer any three questions from 11 to 15. 3x2=6

11. 5,8, 11, ... is an arithmetic sequence.
a) What is 20th term?
(b) What is the algebraic expression for this sequence?

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12. A triangle is drawn by joining the mid-point of one side of a parallelpgram and
the endpoints of the opposite side. The triangle is shaded as shown in the figure.

a) What is the area of the triangle, if the area of the parallelogram is 50 square 1
centimetres

(b) Find the probability of a dot put without looking, to be within the triangle. 1

13.
6

60
A ladder leans against a wall. The ladder makes an angle 60° with the floor,
Length of the ladder is 6 metres.

(a) What is the height of the top of the ladder from the ground?

(b) How far is the foot of the ladder from the wall?

14. Write the second degree polynomial x- +x as the product of two first degree
polynomials.

15. The weight of 7 pupils in a class are given (in kilograms). Find the median weight. 2

35, 43, 38, 45, 32, 44, 42

(B) Answer any 2 questions from 16 to 18. 2x2-4

16. The algebraic expression for the sum of n terms of an arithmetic sequence is n-+n.

(a) Find the first term of this arithmetic sequence.

(b) Find the sum of first 10 terms of this arithmetic sequence.

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2

In the figure PA=4 centimetres, AB=5 centimetres and PC is a tangent to the
circle. Find the length of PC.

18. Find the coordinates of the point which divides the line joining the points
(1,2) and (7, 5) in the ratio 2:1.

PART-III

Questions from 19 to 25 carries 4 scores each.

(A) Answer any three questions from 19 to 23. 3x4-12

19. Draw a triangle of circumradius 3 centimetres and two of its angles 50° and 60.

20.

A strip of width 4 centimetres is attached to one side of a square to form a rectangle
The area of the new rectangle is 77 square centimetres.

(a) If w e take the width of the new rectangle as x, what will be its length ?
(b) Find the measure of the side of the square by constructing an equation.

21. Draw a circle of radius 2.5 centimetres and mark a point ó centimetres away from
the centre of the circle. Draw tangents to the circle from this point.

22. Find the surface area of a cone having base radius 9 centimetres and height
12 centinmetres.

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23. D4,6)

A(2,2) B(8,4)

The coordinates of three vertices of a
parallelogram are given.
(a) Find the coordinates of the vertex C.

6) Find the coordinates of the midpoint of the diagonal
AC

(B) Answer any one of the questions 24, 25. 1x4=4

24. A box contains four slips numbered 1, 2,3, 4 and another box contains five slips
numbered 5, 6, 7, 8, 9. If one slip is taken from each box.

(a) How many number pairs are possible ? 1

b) What is the probability of both being odd ?

(c) What is the probability of getting the sunm of the numbers 10? 2

25
n

20

Two sides of a parallelogram are 20 centimetres and 10 centimetres. If the angle
between them is 40P,

(a) What is the height of the parallelogram ? 2

(b) Find the area of the parallelogram.

(sin 40 0.64; cos 40=0.77; tan 40=0,84)

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PART IVN
Questions from 26 to 32 carries 6 scores each.
(A) Answer any three questions from 26 to 29. 3x6 18

26. (a) 2

S P2B

D

Inthe tigure AB is the diameter of the circle. Line CD is perpendicular to
AB. AP=8 centimetres and PB =2 centimetres. Find the length of PC.
(6) Draw a rectangle of sides 5 centimetres and 3 centimetres. Draw a square of 4
the same area.

60 20 45c

In the figure AC is the diameter of the circle. Given that AC=20 centimetres,
BAC=60° and ZACD=45°.
(a) What is the measure of LADC ?

(b) Find the perimeter of the quadrilateral ABCD. 5

28.
C(7,5)

A (2,1)
The rectangle has sides parallel to the axes. The co-ordinates ot one pair ot opposite

vertices are (2, 1) and (7,5).
(a) Find the co-ordinates of the other two opposite vertices.
(b) Find the length and breadth of the rectangle.

(c) Find the length of the diagonal AC.

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29. The radius of a solid metal sphere is 6
centimetres.
(a) Find the volume of the sphere. 3

(6) This sphere is melted and recast into a solid cone of radius 6 centimetres. 3
Find the height of the cone.

(5) Answer any two questions from 30 to 32. 2x6-12
30. The product of a number and 5 more than that number gives 104.

(a) If we take the first number as 'r', what will be the second number ?
(b) Forma second degree equation using the given details. 2
(c) Find the number.

31. Consider the second degree polynomial p() =**-3x+5.
(a) Find pl).
Write one first degree factor of the polynomial
(b) p(t)-P(1)
()Write p()- p(1) as the product of two first degree factors and find the
solutions ot the equation p{x)- p(1) =0.

32 The table below shows the households of an area sorted according to consumption
of electricity.

Consumption Number of
(in units) households
100-120
120-140
140-160

160-180 10

180-200 6
200-220
220-240

(a) lt the households are arranged according to the consumption of electricity, 1
the consumption of which house is taken as median ?
(b) What is the consumption of 20th household according to our assumption ? 2

()What is the median consumption? 3

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PART-V

Questions from 33 to 35 carries 8 scores each.
2x8 16
(A) Answer any two questions from 33 to 35.
33. 6, 10, 14, ..is an arithmetic sequence.
(a) Find the sum of the first 15 terms of this arithmetic sequence
What is the difference between the first term and the 16 term?
(b)
2
(c) Find the ditference between the sum of first 15 terms and sum of the next
15 terms.

34. (a 2

o)110

The two tangents AC and BC of the circle with centre O meets at C.
What is the measure of ZOAC? If ZAOB=110 find the measure of ZACB.
(b) Draw a circle of radius 2.5 centimetres. Draw a triangle with angles 50", 60°,
70° and all its sides are tangents to this circle.

35. (a) Draw the coordinate axes and mark the points (2, 1) and (4, 3). 3
(b) Find the slope of the line joining these points 2

(C) The centre of a circle is (3, 2) and the coordinates of one end of its diameter 3
is (1, 2). Find the coordinates ot the other end of the diameter.

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