# AP-SSC Mathematics Model Questions Paper 1

Following are model questions for SSC Half Yearly Examinations being conducted in Andhra Pradesh. AP State Board students can use these model questions for practice and get good marks. Mathematics is considered as highly scoring and also a difficult subject. Practicing more model papers and model questions will help in understanding the subject. These questions are for the preliminary understanding of the students only. See questions here:

S.S.C. Half Yearly Examinations - Mathematics Model Paper (Paper - I )
Time: 2 1/2 Hours - (Part A and B ) - Max. Marks: 50

PART - A (Time: 2 Hours Max. Marks: 35)

SECTION - I

Note: 1) Answer any 5 questions minimum 2 from each group. 2) Each question carries 2 marks 5 x 2 = 10
Group - A (Statements - Sets, Functions, Polynomials)
1. Define conjunction. Write truth table.
2. If A B then show that A ∩ B = A
3. Define Remainder Theorem and prove it.
Group - B (Linear programming, Realnumbers, Progressions)
5. Draw the graph of 2x + 3y ≤ 6
6. The product of two numbers is 91 and their arithmetic mean is 10. Find the two numbers.

SECTION - II. Note: Answer any 4. Each question carries 1 mark.
9. Define tautology and give example.
10. Write the set-builder form of A = {-3, -2, -1, 0, 1, 2, 3}
11. Define constant function.
12. Define objective function.

SECTION - III

Note: 1) Answer any FOUR. Choose two from each group. 2) Each question carries 4 marks. 4 x 4 = 16

Group - A

16. Let f, g, h be real functions defned as follows f(x) = x + 2, g(x) = x and h(x) = x2. Find ho(gof) & (hog)of and what do you find.
17. Let ‘f’ be given by f(x) = x + 2, and f has the domain {x: 2 ≤ x ≤ 5}. find f -1 and its domain and range.

Group - B

19. A certain manufacturer has 75 Kg of cashew and 120 kg of groundnuts. These are to be mixed in 1 kg packages as follows: A low grade mixture 250 grams of cashew and 750 grams of ground nuts, where as in a high grade mixture 500
gms of cashew and 500 gms of peanuts. If the profit on the low grade mixture is Rs. 2 per package and that of high grade mixture is Rs. 3 per package. How many packages of each mixture be made for a maximum profit?
21. Find the sum of n terms of the series 0.5 + 0.55 + 0.555 + ... n terms
22. The A.M., G.M., & H.M. of two numbers are A, G, H respectively. Show that A ≥ G ≥ H

S.S.C. Half Yearly Examinations (Mathematics Paper - I)
PART - B - 15 Marks
Note: 1) Answer ALL the questions. 2) Each question carries 1/2 mark.

II. Fill in the blanks.
11. Symbol of existential quantifier ....
13. 1 + 2 + 3 + .... + n = ....
14. If f(x) = 2x + 3, g(x) = x - 1, then gof(3) = ....
15. Product of the roots of x2 - 3x + 5 = 0 is ....
16. If (x - 2) is a factor of x2 - 3x + k then k = ....
17. 161.25 = ....
18. The solution set of constraints of an LPP is a convex set called the ....
19. A line divides the plane into ..... parts
20. 'n'th term of an A.P. is ....