Mathematics Sample Question for Grade- IX

                                                      Mathematics Sample Question for Grade- IX

Subject: Mathematics

Total Time: 2 Hours                                                                                                   Total Marks: 60

Structured Questions:

(N.B.: Answer any six (06) questions by taking at least two questions from group - A and at least one question from group - B and group - C):

Group - A

1. a. Determine the set: {xN: 6 < x < 7}.

b. A and B are the sets of factors of 315 and 525 respectively. Determine AB.

c. If U = {1, 2, 3, 4, 5, 6}, A = {1, 3, 5}, B = {2, 4, 6}, C = {2, 3, 4, 5}; verify the following statements:         (i) (AB)^c = A^cB^c         (ii) (BC)^c = B^cC^c

2. a. If A = {a, b, c} and B = {p, q}, find AB and BA.

b. If A = {a, b}, B = {2, 3} and C = {3, 4}; find A(BC) and A(BC). 

c. If A = {x: xN and x² – 5x + 6 = 0} and B = {x: xN and x² – x – 6 = 0}; find AB and BA.

3. a. Using number line, determine the distance between – 3 and 4.

b. Solve: | x – 5| > 4.

c. Find the approximate values of √2 and √3 up to 4 decimal places using calculator and find two rational and irrational numbers between them.

4. If x += 2; what is the value of        a. x – ?                     b. x⁴ +?                   c. ?

Group - B

5. Read the following statement attentively and answer the questions given below:

"ABC is a triangle and D is the mid–point of BC. Join (A, D).''

a. According to the given data draw a geometric figure and give a brief description.

b. Prove that, AB + AC > 2AD.

c. If ABC is an isosceles triangle, AB = AC = 5 cm, BC = 6 cm and AD is the perpendicular bisector of BC; verify the above proposition.

6. Read the following statement attentively and answer the questions given below:

"ABC is an isosceles triangle whose vertex is A. The side BA is produced up to D such that, BA = AD. (C, D) are joined''.

a. According to the given data draw a geometric figure and give a brief description.

b. Prove that, BCD = 90^o.

c. If AB = 5 cm and BC = 6 cm; find the length of CD.

7. Read the following statement attentively and answer the questions given below:

''ABCD is a rhombus and AC and BD are two diagonals of it intersect at O''

a. Define rhombus and according to the given data draw a geometric figure and give a brief description.

b. Prove that OA = OC and OB = OD.

c. Prove that ÐAOB = ÐAOD = ÐBOC = ÐCOD = 90^o.

Group - C

8. (a) If in the adjacent right triangle ∆POM, ÐPOM = θ and ÐPMO = 90^o; find the complementary relationships of sinθ, cosθ and tanθ.

(b)Show that: (i)        (ii)

(c)Prove That: .

9. If A = 30^o, show that (a) sin2A =  (b) tan2A =       (c) cos2A = .