10th Class Mathematics – Page 5

Following are model questions for AP Board SSC Half Yearly Public Examinations. These questions are for practice only. This may not resemble the structure of original questions paper.

S.S.C. Half Yearly Examinations
Mathematics Paper – II (Model Questions)

1. Find the equation of the line passing through (4, -3) and is perpendicular to the line 2x – 5y + 4 = 0
2. In what ratio does P(4, 6) divide the join of A (-2, 3) and B(6, 7).
3. The mean of 10 observations is 16.3. By an error, one observation is registered as 32 instead of 23. Find the correct mean.
4. Draw the structure of a computer.
5. Define Thales theorem.
6. Find the Y-intercept of a line 2x – 3y = 12.
7. Define Algorithm.
8. If AM = x, Median = y, then find the mode.
9. State and prove Pythagorean theorem.
10. Find the equation of the line that cuts off intercepts a & b on the X and Y-axes such that a + b = 3, ab = 2.
11. Find the equation of the line which passes through the point (1, -6) and whose product of the intercepts on the coordinate axes is one.
12. Solve the following simultaneous equations using matrix inversion method. 3x + 8y = 7, 6x – y = 31
13. A flagstaff stands on the top of a building. At a distance of 40 mts away from the foot of the building, the angle of elevation of the top of the flagstaff is 60° and the angle of elevation of the top of the building is 30°. Find the height of the flagstaff.

14. If two circles touch internally, then the number of their common tangents is ( )
A) 2 B) 1 C) 4 D) none.
15. Equation passing through the points (4, -7), (1, -5) is ( )
A) 2x – 3y + 13 = 0 B) 3x – 2y + 13 = 0 C) 2x + 3y – 13 = 0 D) 2x + 3y + 13 = 0
16. Which of the following pair is perpendicular ( )
A) y = 3x, x = 3y B) y = 3x, x = -3y C) y = 4, y = 6 D) none
17. Average of a – 2d, a – d, a + d, a + 2d is ( )
A) a B) d C) 3d D) 4a
18. The following generation used Transistors in computers ( )
A) First B) Second C) Third D) Fourth

18. Angles in the same segment of a circle are —-
19. Two circles are of radii 3 cm & 1 cm. The distance between their centres is 5 cm. The length of their transverse common tangent is ——
20. The line 3x + 4y = 0 cuts the Y-axis at —–
21. If P(6, -1), Q(1, 3), R(x, 8). If PQ = QR then x = —
22. If average of 10 observations is 7, average of 15 observations is 12, then the average of total observations is —–
23. All parts of a computer are controlled by —–

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 ….

10th Class Mathematics Paper 2 Model Questions

AP-SSC Mathematics Model Questions Paper 1