Kerala SSLC Pre Model Question Paper 2023 Maths

MALAPPURAM 108 A

SSLC PRE MODEL EVALUATION JANUARY 2023
MATHEMATICS
Time : 1½ Hrs ( English Medium ) Score : 40

Answer any 3 questions from 1 to 4 . Each question carries 2 scores . (3 × 2 = 6)

1. In the figure O is the centre of the circle . ∠AOB = 1000 .

(a) What is the measure of ∠ACB ?

(b) What is the measure of ∠ADB ?

2. Consider he arithmetic sequence 2 , 4 , 6 , . . .

(a) What is its 10th term ?

(b) Write the algebraic form of the sequence .

3. When each side of a square was increased by 5 centimetres , the area became 121 square -

centimetres .

(a) By taking the length of a side of the original square as x centimetres , write a second

degree equation using the above detail .

(b) What was the length of a side of the original square ?

4. Each letter of the word “ RAMANUJAN “ is written on paper slips and put in a box . A slip is

to be drawn from it .

(a) What is the probability of getting the letter A ?

(b) What is the probability of not getting the letter A ?

Answer any 4 questions from 5 to 10 . Each question carries 3 scores . ( 4 × 3 = 12)

5. Draw a triangle of circumradius 3 centimetres and two of the angles ‍ 500 and 700 .

6. 1 is added to the product of two consecutive even numbers gives 289 .

(a) By taking the smaller number as x centimetres , write a second degree equation using

the above detail .

(b) Find the numbers .

7. In the figure ‍AB is the diameter of the semicircle and P is a point

on it .The perpendicular drawn through P meets the semicircle

at C . AB = 10 centimetres , PA = 8 centimetres .

(a) What is the length of PB ?

(b) Compute the length of PC .

8. The sum of the first 5 terms of an arithmetic sequence is 35 and the sum of the first 9 terms

is 99 .

(a) What are the 3rd and the 5th terms of the sequence ?

(b) What is the common difference of the sequence ?

9. In the figure a square is touching the sides of a square . A dot is put in the

figure without looking .

(a) If the length of the square is taken as 2 x centimetres , what is the

diameter of the circle ?

(b) What is the probability that the dot being inside the circle ?

(c) What is the probability that the dot being outside the circle ?

10. The sum of the 5th and the 6th terms of an arithmetic sequence is 24 .

(a) What is the sum of the first and the 10th terms of the sequence ?

(b) If the 4th term of the sequence is 9 , what is its 7th term ?

Answer any 3 questions from 11 to 16 . Each question carries 4 scores. ( 3 × 4 = 12)

11. Draw a rectangle of length 5 centimetres and breadth 4 centimetres . Draw a square of the

same area .

12. Compute the following sums .

(a) 1 + 2 + 3 + . . . + 20

(b) 3 + 6 + 9 + . . . + 60

(c) 4 + 7 + 10 + . . . + 61

(d) 8 + 15 + 22 + . . . + 141

13. In class 10 A , there are 30 boys and 20 girls . In 10 B , there are 25 boys and 20 girls .

One student is to be selected from each class .

(a) What is the number of the possible pairs ?

(b) What is the probability of both being boys ?

(c) What is the probability of one boy and one girl ?

(d) What is the probability of at least one boy ?

14. The sum of the first n terms of an arithmetic sequence is n2 + 4 n .

(a) What is its first term ?

(b) What is the sum of the first two terms ?

(c) What is its common difference ?

(d) Write the algebraic form of the sequence .

15. In the figure , ∠ ADB= 400 , ∠ ACD = 300 , ∠ CBD = 500

Find the measures of the following angles .

(a) ∠ ACB

(b) ∠ ABD

(c) ∠ BAC

(d) Central angle of the arc BCD .

16. (a) What number is to be added to x2 + 6 x to get a perfect square ?

(b) If x 2 + 6 x = 315 , find the natural number represented by x .

Answer any 2 questions from 17 to 21 . Each question carries 5 scores . ( 5 × 2 = 10)

17. Draw a rectangle of length 6 centimetres and breadth 3 centimetres .

Draw another rectangle of the same area with a side 7 centimetres .

18. Look at the number pattern given below .
1

2 3

4 5 6

7 8 9 10
.........................................
.......................................................
(a) Write down the next two more lines of this pattern ?

(b) What is the last number in the 9th line ?

(c) What is the first number in the 10th line ?

(d) What is the middle number in the 11th line ?

19. In the figure , two chords AB and CD of the circle are

extended to meet at P .

(a) If ∠ A = 800 , what is the measure of ∠ BDC ?

(b) Check whether the angles of the triangles APC and BPD

are the same or not .

(c) Prove that PA × PB = PC × PD .

20. The longer side of rectangle is 7 centimetres more than its shorter side and its area is

144 square centimetres .

(a) By taking the length of the shorter side as x centimetres , write a second degree

equation using the above details .

(b) Compute the length and the breadth of the rectangle .

21. The measures of the angles of a quadrilateral are in arithmetic sequence . The smallest angle is
300 .
(a) What is the sum of the angles of a quadrilateral ?
(b) What is the sum of the largest and the smallest angles of this quadrilateral ?
(c) What is the common difference of the sequence .
(d) Find the measures of the remaining angles of the quadrilateral .