SCERT Kerala Mathematics Sample Question Paper 2016

Organisation : State Council of Educational Research & Training
Exam : SSLC Examination
Subject : Mathematics
Document Type : Sample Question Paper
Year : 2016-17
Class : X STD
Website : http://scert.kerala.gov.in/
Download Sample Question Paper : https://www.pdfquestion.in/uploads/22223-Mathematics.pdf

Mathematics Question Paper :

Instructions :
1. Read and understand each question carefully and then only write the answers.
2. Give explanations wherever necessary

Related : SCERT Kerala Class X Social Science Sample Question Paper 2016 : www.pdfquestion.in/22214.html

3. If there is an ‘OR’ between any two questions, you may answer only one among them
4. The first 15 minutes is given as “Cool-off Time.”You may read and understand the questions during that time.

5. Simiplification using irrational like π, 2 3 etc with their approximate values is not required if not specified in the questions.

1. The scores of some students in an examination are given below 34, 44, 32, 41, 38, 46, 45 (2) Find the mean and median of the scores

2. The difference of two terms of an arithemetic sequence whose common difference is a natural number is 105. Can 9 be its common difference? Why? (2)
3. Is it possible to draw a rectangle with perimeter 48cm and area 150 sq.cm? Why? (3)

4. Two sides of a parallelogram are 12cm and 8cm. Their included angle is 63o. (3)
a) Find the distance between the bigger sides
b) Find the area of the parallelogram. [ sin 630 = 0.9, cos 630 = 0.45, tan 630 = 1.96 ]

5. From the following questions, only one is to be attended. (3) The sequence obtained by multiplying the consecutive terms of a arithmetic sequence 1,4,7,10….. is 4,28……….

a) Is the new sequence an arithmetic sequence?
b) Write down the algebraic form of this sequence

6. The sum of first two terms of the arithmetic sequence 8,15,22…….. is 23, which is not a term of this sequence (4)
a) What is its algebraic form? [(6n + 2 ; 7n + 1; 8n – 1; 8n)].
b) Can the sum of any two consecutive terms of this sequence be a term of this sequence? Why?

c) Can the sum of any two terms of this sequence be a term of this sequence? Why?
8. Draw a square of side 6cm and construct a rectangle of same area and with oneside 7cm. (4)

9. In 10A class, there are 20 boys and 20 girls and in 10B class , 15 boys and 25 girls. For participating in a quiz competition, if one student from each class is selected, what is the probability of (4)
a) Selecting both students boys
b) Selecting only one girl
c) Selecting at least one girl

10. A sector of central angle 216o is cut out from a circular sheet of 20 cm . It is rolled up to form a conical vessel of largest size. (4)
a) Find the radius of the vessel
b) Find the height of the vessel
c) Is this vessel sufficient for filling 2½ litres? Why?

11. From the following questions, only one is to be attened (4) When the sun is at an elevation of 55o, the shadow of a tree is 8 metres. What would be the length of the shadow, when the sun is at an elevation of 35o [ sin 550 = 0.82, cos 550 = 0.57, tan 550 = 1.43, sin 350 = .57, cos 350 = 0.82 tan 350 = 0.7]
OR

Can we cut out a triangle of sides 8 centimetre and its opposite angle 37o from a circular sheet of diameter 12 centimetre? [ sin 370 = 0.6; cos 370 = 0.8, tan 370 = 0.75 ]

12. Draw a circle of radius 3.5 centimetres. Construct a triangle having two angles 50o and 70o whose sides touch the drawn circle. (4)

13. A circle drawn with centre A(15, 5) cuts the x axis at B(3,0) (4)
a) Find the radius of the circle.
b) If C is the point of intersection of the circle with x axis, find the coordinates of C.
c) Find the perimeter of trinangle ABC

14. P is a point 5 centimetre distant from the centre O of a circle. The chord AB drawn through P has length 25 cm. If PA = 9 cm, (4)
a) What is PB?
b) If the radius of the circle is taken as r, find the shortest distance from P to the circle? Find the maximum distance also?

14. The product of the terms at the same position of two arithmetic sequences 5, 7, 9, . . . and 3, 6, 9, . . is 357. (4)
a) Write down the algebraic form of the sequences
b) By taking term position as n, frame a second degree equation
c) Find the terms to get a product 357.

15. From the following questions, only one is to be attended. In the figure, the incircle of triangle ABC touches the sides of the triangle at L, M and N. QR, ST and UP are other three tangents

(a) Prove that AL is half the perimeter of ΔAPU
(b) The perimeters of ΔAPU, ΔBQR and ΔCST are 16 cm, 12 cm and 14 cm respectively. Find the lengths of the sides of ΔABC
(c) Find the area of the ΔABC
OR

The incircle of ΔABC, touches its 3 sides at P, Q and R as shown AP = 7 cm. BQ = 6 cm. CR = 8 cm.
(a) Finds the sides of the ΔABC
(b) Find the area of the triangle
(c) Calculate its inradius

16. A solid sphere is cut into two hemispheres, from one a largest cone and from the other a largest square pyramid is cutout. Find the ratio of the volumes of the cone and the square pyramid

First Terminal Evaluation – 2016 :
Mathematics :
Standard : X
Time : 2½ hours
Score : 80
Instructions :
1. The first 15 minutes is given as ‘cool off time’. You may read and understand the questions during this time.
2. Answer all the questions.

3. If there is an OR between any two questions, you may answer one among them.
4. Simplification using irrationals like p, 2 , 3 etc., with their approximate values is not required if not specified in the question.

1. Algebraic form of an arithmetic sequence is 7n + 3. What is its common difference? What is its 16th term? (2)
2. ABCD is a rectangle. If a circle is drawn with AB as diameter, will it pass through C? Justify your answer. (2)

3. Paper slips with numbers 1 to 50 are kept in a box. If a slip is taken without looking into it,
i) What is the probability of getting an even number?
ii) What is the probability of getting a multiple of 3 or 7?
iii) What is the probability of getting a prime number?

4. The product of two alternate odd numbers is 621. What are the numbers? (3)
5. The common difference of an arithmetic sequence is 8 and its 7th term is 45. Find the 12th term and the position of 285 in the sequence.