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HALF YEARLY EXAM (2018-19)

MATHS (SET-A)

Time-3 hrs Class IX M.M.80

General Instructions

i) All questions are compulsory.

ii) Section A contains 6 questions of l mark each.

iii) Section B contains 6 question of 2 mark each.

iv) Section C contains 10 question of 3 mark each.

v) Section D contains 8 question of 4 mark each.

_____________________________________________________________________________________

Section – A

1. Simplify the expression [pic]

2. On which axes do the points (3,0) and (0,4) lie?

3. If two angles of a triangle are complementary, then what type of triangle will be formed?

Q4. Find the value of a, for which (x-3) is a factor of the polynomial x3 - 3x2 +ax – 15

Q5. Angles of a triangle are in the ratio 5: 4: 3. Find the smallest angle of the triangle.

Q6. Find the square of (8 + 5 [pic])

Section B

Q7. Express 0.4[pic] in the form [pic] where P and q are integers and q [pic] 0.

Q8. Three vertices of a rectangle are (-4,5), (-4,2) and ((3,2). Without plotting find the co-ordinates of the fourth vertex.

Q9. Find the value of x

Q10. Find the remainder, when 3x3 – 6x2 + 3x – [pic] is divided by 3x – 4.

Q11. In which quadrant do the following points lie

a) (3,2) (b) (-2,1) (c) (-1,-3) (d) (5-1,)

Q12. Factorize: [pic]

Section C

Q13. Find the value of 27x3 +8y3 if 3x +2y = 20 and xy= [pic] .

Q14. Represent [pic] cm on number line.

Q15. If x + [pic] = [pic], find the value of x3 + [pic]

Q16. If x = [pic] and y = [pic], find the value of x2 – y2.

Q17. What must be subtracted to x3 – 3x2 – 12x + 19, so that the result is exactly divisible by x2 + x – 12?

Q18. If two parallel lines are intersected by a transversal than prove that the bisectors of two interior alternate angles are parallel.

Q19. Plot the points A (-2,3), B (-2,0), C (2,0) and D (2,6) on the graph paper. Join them consecutively and find the lengths of AC and BD.

Q20. In the given figure, S is any point on the side QR of [pic] PQR. Prove that PQ +QR + RP [pic] 2PS

P

Q S R

Q21. In figure if AB = CD, then prove that AC = BD. Write the axiom related to the question.

A B C D

Q22. The perimeter of a triangular field is 240cm. If two of its sides are 78cm and 50cm. Find the area of triangle. Find the length of perpendicular on the side of length 50cm from the opposite vertex.

Section - D

Q23. The cost of a table exceeds the cost of the chair by Rs.150. write a linear equation in two variables to represent this statement. Also find three solutions for the same equation.

Q24.Prove that sum of three angles of a triangle is 180o.

Q25. The sides of a triangular park are 8m, 10m and 6m respectively. A small circular area of diameter 2m is to be left out and the remaining area is to be used for growing roses. How much area is used for roses?

A

B C

Q26. Draw a graph for the linear equation 10(x-2) –y = 5 and find the points where the line intersect x’ axis and y’ axis.

Q27. Factorize, 2x3 – 5x2 – 19x + 42.

Q28. In the given figure, bisectors of the exterior angles B and C formed by producing sides AB and AC of [pic]ABC interest each other at the point O. Prove that.

[pic] BOC = 900 – [pic] [pic]A

A

B C

O

D E

Q29.In right angled [pic]ABC right angled at C, M is the mid Point of hypotenuse AB.C is joined to M and produced to a point D. such that DM = CM. Point D is Joined to point B show that

i) [pic]AMC [pic] [pic]BMD

ii) DBC is right angle

iii) [pic]DBC [pic] [pic]ACB

iv) CM = [pic] AB

Q30. Simplify [pic]

HALF YEARLY EXAM (2018-19)

MATHS (SET-B)

Time-3 hrs Class IX M.M.80

General Instructions

vi) All questions are compulsory.

vii) Section A contains 6 questions of l mark each.

viii) Section B contains 6 question of 2 mark each.

ix) Section C contains 10 question of 3 mark each.

x) Section D contains 8 question of 4 mark each.

_____________________________________________________________________________________

Section A

1. Write [pic] in decimal form and state what kind of decimal expansion it has.

2. On which axes do the points (-7,0) and (0,7) lie?

3. If 125x = [pic]. Find the value of x.

4. Find the value of a, for which (x-2) is a factor of the polynomial a2 x3 – 4ax + 6a – 1.

5. Angles of a triangle are in the ratio 5: 4: 3 Find the largest angle of the triangle.

6. Find the square of (8-5 [pic]).

Section B

Q7. Express 0.9[pic] in the form [pic] where P and q are integers and q [pic] 0.

Q8. Three vertices of a rectangle are (-2,3), (-2,-2) and (5,-2). Without plottng these points and find the co-ordinates of the fourth vertex.

Q9. In the given figure, ABIICD find the value of x.

Q10. Find the remainder, when polynomial 2x3 – 11x2 – 4x + 5 is divided by 2x + 1.

Q11. In which quadrant do the following points lie.

a) (-3,-2) (b) (-4,5) (c) (1,3) (d) (5,-6)

Q12. Factorize: 27x3 – 8y3 – 54x2y + 36xy2

Section C

Q13. Find the value of a3 + 8b3, if a + 2b = 10 and ab = 15.

Q14. Represent [pic] cm on the number line.

Q15. If x + [pic] = 7, then find the value of x3 + [pic]

Q16. Find the values of a & b, when

[pic] = a – b [pic]

Q17. What must be subtracted from x3 – 6x2 -15x + 80 so that the result is exactly divisible by x2 + x – 12?

Q18. If two parallel lines are interested by a transversal then prove that the bisectors of corresponding angles are parallel.

Q19. Plot the points A(2,6), B(-2,3), C(-2,0) and D (2,0) on the graph paper. Join them consecutively and find the length of AC and BD.

Q20. In the given figure, S is any Point on the side OR of [pic] PQR. Prove that PQ + QR +RP [pic] 2PS.

P

Q S R

Q21. In figure if AC = BD then, Prove that AB = CD write the axiom related to the question.

A B C D

Q22. A perimeter of a triangular field is 240cm. If two of its side are 78cm and 50cm, find the area of triangle. Find the length of perpendicular on the sides of length 50cm form the opposite vertex.

Section D

Q23. Draw a graph for the linear equation 4x – 2 (y-3) = 20 and find the points where the line interested x’ axis and y’ axis.

Q24. The sides of a triangular park are 6m, 8m and 10m respectively. A small square area of side 2m is to be left out and the remaining area is to be used for growing roses.

A

B C

Q25. Prove that the angles opposite to equal sides of an isosceles triangle are equal.

Q26. The cost of a table exceeds the cost of the chair by Rs.150. write a linear equation in two variables to represent this statement. Also find three solutions for the same equation.

Q27. Factorize x3 – 10x2 – 53x – 42.

Q28. In the given figure, the bisectors of ABC and BCA, interested each other at Point O. prove that

[pic]BOC = 90o + [pic] [pic]A.

Q29. In the given figure the side QR of [pic]PQR is produced to a point S. if the bisectors of PQR and PRS meet at point T then prone that [pic]QTR = [pic] [pic]QPR.

Q30. Prove that [pic]

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