CBSE based Class IXth Maths Sample Paper From Chapter 12 – Heron’s Formula

M.M: 49 marks                                                   Date: 21/08/2011

Time: 1 hour 30 minutes

Q 1: Fill in the blanks (1 mark each question x 12 = 12 marks)

1. Area of a triangle (normal formula) = __________________________.
2. The formula given by Heron about the area of a triangle is also known as _____________ formula.
3. Heron’s formula for finding area of a triangle is = ______________________________ (more than one character will come).
4. Heron’s formula to find the area of a triangle should be used when it is not possible to find ____________ of the triangle.
5. Area of a quadrilateral whose sides and one diagonal are given can be calculated by dividing the quadrilateral into ______  ______________ and using ___________ formula.
6. Area of a parallelogram = _________________ (more than one word will come).
7. Area of a trapezium = __________________________ (more than one word will come).
8. The base and hypotenuse of a right triangle are respectively 5 cm and 13 cm long. Its area is ___________.
9. In Heron’s formula to calculate area of a triangle, semi perimeter, ____ = _________________.
10. Area of a square with side “a” = ______.
11. Perimeter of an equilateral triangle with each side “x” cm is _____ ____.
12. With reference to Heron’s formula for finding area of a triangle, 2s = ___________________(more than one letter or word will come).

Q 2: An isosceles triangle has perimeter 40 cm and each of the equal sides is 15 cm. Find the area of the triangle.                          (3 marks)

Q 3: The perimeter of a triangular field is 675 m and its sides are in the ratio of 7:8:10. Find the area of the triangle.                   (3 marks)

Figure 1

Q 4: The triangular side walls of a flyover, shown in figure 1 have been used for advertisements. The sides of the walls are 82 m, 18 m and 80 m. The advertisements yield an earning of Rs. 4000/m2 per year. A company hired both walls for 4 months. How much rent did it pay?                                                                                                (5 marks)

Q 5: A field is in the shape of a trapezium whose parallel sides are 10 m and 25 m. The non parallel sides are 14 m and 13 m. Find the area of the field.                                                                          (4 marks)

Q 6: Students of a school staged a rally for a cleanliness campaign. They walked through the lanes in two groups. One group walked through the lanes AB, BC and CA while other through AC, CD and DA (check figure 2). Then they cleaned the area enclosed within their lanes. If AB = 9 m, BC = 40 m, CD = 15 m, DA = 28 m and angle B = 900, which group cleaned more area and by how much? Find the total area cleaned by the students.                     (5 marks)

 

Q 7: Vimla has a triangular field with sides 240 m, 200 here shem, 360 m w grew wheat. In other triangular field with sides 240 m, 320 m, 400 m adjacent to the previous field, she wanted to grow potatoes and onions as shown in figure 3. She divided the field into two parts by joining the mid-point of the longest side to the opposite vertex and grew potatoes in one part and onions in the other part. How much area (in hectares) has been used for wheat, potatoes and onions? (1 hectare = 10,000 m2).                                       (6 marks)

 

Q 8: A kite in the shape of a square with a diagonal 32 cm and an isosceles triangle of base 10 cm and sides 8 cm each is to be made of three different shades as shown in figure 4. How much paper of each shade had been used in it?    (5 marks)

Q 9: Kiran made a picture of an aeroplane with coloured paper as shown in figure 5. Find the total area of the paper used.  (6 marks)

CBSE NCERT Class IXth Maths Test From Coordinate Geometry -1

M.M: 33 marks                                                   Dated: 03/07/2011

Time: 1 hour 15 marks

Note: If you don’t have graph paper, then make the axes with scale preferably on a plane paper and plot the points.

Q 1: Fill in the blanks.                       (1 mark each x 13 = 13 marks)

1. If ________, then (x,y) is not equal to (y,x).
2. The coordinates of origin are _________.
3. To locate the position of an object or a point in a plane, we need ___________   _____________ lines.
4. On a graph paper, the plane is called _________________ or ________________ plane.
5. The two lines, XOX’ and YOY’ are called _____________ and ____________.
6. The coordinate axes divide a plane into _________ parts called ______________.
7. The distance of a point from the _____________ is called its y coordinate or _____________.
8. The coordinates of a point on y axis are _____________.
9. The distance of a point from the _____ axis is called its x coordinate or __________.
10. Each point in a plane is represented by an ordered pair of real numbers called the _________________ of that point.
11. ___________________    ________________ is the branch of mathematics in which geometric problems are solved through algebra by using the coordinate system.
12. The distances measured along OX and OY on graph are taken as _____________.
13. The distances measured along OX’ and OY’ on graph are taken as _____________.

Q 2: Plot the following points on a graph paper:                 (3 marks)

1. (1, 5)
2. (-5,1)
3. (0, -7)
4. (6, 0)
5. (-2, -7)
6. (0, 0)

Q 3: Write down the coordinates of the following points A, B, C, D marked on the graph paper given below.                             (2 marks)

 

Q 4: In which quadrants/axis do the following given points lie?                  (3 marks)

1. (-2, -6)
2. (0, 5)
3. (6, -7)
4. (-7, 0)
5. (-3, 5)
6. (5, 5)

Q 5:  Plot the points (-1, 0), (1, 0), (1, 1), (0, 2), (-1, 1) and join them in order. What figure do you get?                              (3 marks)

Q 6: Plot the following pairs of numbers as points in the Cartesian plane. Use the scale 1 cm = ½ unit on the axes.                 (3 marks)

x	-3	0	-1	3	2	-2
y	4	-3.5	-2.5	3	-4	-4

Q 7: How will you locate the position of a cylindrical glass on a rectangular table? Explain in brief.                                     (2 marks)

Q 8: Who invented the idea of placing two perpendicular lines to each other on a plane and locating points on the plane by referring them to these lines?                                                               (1 mark)

Q 9: If the ordinate of a point is 5 and its abscissa is 6, then what are the coordinates of the point?                                          (1 mark)

Q 10: Draw XOX’ and YOY’ intersecting each other at origin. Show the signs of the coordinates in the quadrants formed.

(2 marks)

Euclid Geometry Model Paper Of CBSE NCERT Class IXth

M.M: 38 marks                                                                         Dated: 01/07/2011

Time: 1 hour

Q 1: Fill in the blanks (1 mark per question x 15 = 15 marks)

1. Two distinct ______________ lines cannot be parallel to the same line.
2. According to Euclid’s fourth postulate, all _____________ angles are equal to one another.
3. A terminated _____________ can be produced indefinitely.
4. According to Euclid’s seventh axiom, things which are ____________ of the same things are equal to one another.
5. According to Euclid’s fourth axiom, things which ______________ with one another are ___________ to one another.
6. According to Euclid’s third axiom, if equals are ______________ from equals, the _______________ are equal.
7. ______________ are statements which are proved using definitions, axioms, previously proved statements and deductive reasoning.
8. ______________ or ____________ are the assumptions which are obvious universal truths and hence are not proved.
9. The terms which are taken as undefined by mathematicians are __________, __________ and ____________.
10. Two distinct points in a plane determine a ______________ line.
11. Two distinct ______________ in a plane cannot have more than one point in common.
12. In _____________ geometry, lines are not straight.
13. Euclidean Geometry fails on the _____________ surfaces.
14. Euclid used the term _____________ for the assumptions that were specific to geometry.
15. _______________ means measuring Earth.

Q 2:  Write True or False for the following statements. Also write the correct statements for the false statements.                                                    (1 mark per question x 6 = 6 marks)

1. Two distinct points always determine a line –
2. Every ray has a finite length –
3. A segment has one end-point only –
4. The ray BC is same as ray CB –
5. Only a single line can pass through a given point –
6. Two lines are coincident if they have only one point in common –

Q 3: What is Playfair’s axiom? How can it be stated in other form? Make a diagram to explain it.                                                                                                         (2 marks)

Q 4: If A, B and C are three points on a line and B lies in between A and C, then prove that AB + BC = AC.                                                                                                (2 marks)

Q 5: Give a definition for each of the following terms.               (1 mark each x 6 = 6 marks)

1. Parallel lines
2. Line segment
3. Radius
4. Straight line
5. Plane surface
6. Square

Q 6: In the following figure, if PR= QS, then prove that PQ = RS.                       (2 marks)

Q 7: Write Euclid fifth postulate and explain it with the help of a diagram.             (3 marks)

Q 8: What is Euclid’s fifth axiom? Explain it.                                                       (2 marks)