triangle and its popperties

The triangle and its Properties

1.      The angles of triangles are in the ratio 1:2:3. Determine the corresponding angles.

2.      Which of the following triplets can be angles of a triangle?

i.                    76^o, 64 ^o, 40 ^o                                  ii.           56 ^o, 62 ^o, 62 ^o

3.      Two angles of triangle are of measures 60^o and 75 ^o. find the measure of the third angle.

4.      One of the acute angles of a right angled triangle is 42 ^o. find the other acute angle.

5.      Two acute angles of a right angled triangle are equal. Find the two angles.

6.      In the given five sided closed figure, find ∠EAB+ ∠ABC+ ∠BCD+ ∠CDE+ ∠DEA

7.      The angles of a triangle are in the ratio 5:4:3. Find the measure of each angle.

8.      One side of a triangle is produced and the exterior angle so formed is 120^o. if the interior opposite angles are in the ratio 2:3, find the measure of each angle of the triangle.

9.      If the sides of a triangle are produced in order, prove that the sum of the exterior angles so formed is 360^o.

10.  In the figure given below find the value of x and y

11.  In △PRQ side QR is extended to S. if ∠PRS=150 ^o and RP=RQ, find the three angles of △PRQ

12.  AM is a median of a △ABC. Prove that AB+BC+CA>2AM

13.  Find the length of the diagonal of a rectangle having sides 16cm and 12cm.

14.  ABC is a triangle, right angled at C. If AB=25cm and AC=7cm, find BC

15.  A 10m long ladder reached a window 8m high from the ground on placing it against a wall at a distance x. find the distance x?

16.  Identify the Pythagorean triplets from the following:

i.                    3,7,9                   ii.           7,24,25                             iii.          4,5,7

         

VII perimeter and area

Perimeter and Area

1.            A marble tile measures 20cm by 15cm. how many tiles will be required to cover a

            wall of size 5m by 3m?

                      2..   One side of a square field is 92m. find the cost of raising a lawn on the field at the rate of                    $1.5 per sq.m

       3.       The area of 4 walls of a hall is 266sq.m. The length and breadth of the hall are 12m and 7m                 respectively. Find the height of the wall.

          4.       A sheet of paper measures 50cm by 30cm. A strip 6cm wide is cut from all around. Find the              area of the remaining sheet and also the area of the strip cut out.

      5.       A room 12.5m long and 10.5m wide is surrounded by a verandah 2m wide all round it. Find              the area occupied by verandah.

    6.       A rectangular lawn measuring 50m by 36m is surrounded externally by a path which is 2m                  wide. Find the area of the path. Also, find the cost of leveling the path at $3.25 per m².

      7.       Find the area of parallelogram with base 9.5cm and height 5.6cm

   8.       If the side of a rhombus is 8.5m and its altitude is 5m, find its area.

        9.       The area of rhombus is 63sq.m. If its perimeter is 28m, find its altitude.

    10.   A field in the form of a parallelogram has a base 32m and altitude 1.75m. Find the cost of                   watering the field at $8 per sq.m

    11.   Find the area of triangle whose base is 15cm and altitude is 12.6cm

  12.   The area of triangle is 126sq.cm and its base is 18cm. Find its altitude

13.   Find the area of the following triangles

14.   A race track in the form of a ring whose inner circumference is 264m and the outer circumference is 308m. Find the width of the track

15.   The circumference of a circle is 62.8m. Find the radius of the circle.

16.   The circumference of a circle is 616m, find its radius and area

17.   Area of a circle is 2826sq.cm, find its radius

18.   Area of a circle is 75.46sq.m. Find its diameter.

19.   Find the cost of polishing the top of a circular table of diameter 4.2m, if the rate of polishing is $12 per sq.m.

20.   From a circular card sheet of radius 28cm, two circle of radii 7cm and a rectangle of length 3 cm and breadth 2 cm are removed. Find the area of remaining sheet.

21.   Find the perimeter of the adjoining figure which is semi-circle including its diameter.

                                                                                                                                              

                                                                                                                                              

VI j algebra

                                                            ALGEBRA

           1.       Write the following using numbers, literals and signs of basic operations:

i.                     One-third of x is taken away from one-fifth of y.

ii.                   The product of x and 4 is subtracted from the sum of y and 7.

iii.                 My age is x years. My father’s age is 3 years less than four times my age. What is my father’s age?

iv.                 The product of 11 and x is 5 less than y.

v.                   One-fourth of x is multiplied by twice the sum of y and z

             2.       Riya has drawn a Rangoli. She has 13 dots in a row. How many dots will her Rangoli have                  for P rows?

            3.       Lalita spends $x per week and saves $y daily. What is her income of two weeks?

           4.       Write the numerical coefficient of each term of the following algebraic expressions:

i.                     6x⁴ + 5x³ – 2x + 7                           ii.           4a³ – 5b³ + 2c³ – 6abc

            5.       Write down the terms of following algebraic expressions:

i.                     ax² – bx – c                                     ii.           p²q – pq + 9

             6.       Write down the coefficient of x:

i.                     6x³-5x²+8x                                       ii.           -3xy+4x²+6

            7.       Identify the like terms in the following.

i.                     X²y,xy²,y²x,xy                                  ii.           x²,y²,-3x²,y³,4x

            8.       Write down the coefficient of a in the following algebraic expressions:

i.                     3a² – 4a                             ii.           2a +                iii.          4a³ + a

            9.       Write each of the following statements as an equation:

i.                     A number exceeds seven by three

ii.                   A number is divided by three. The quotient is added to four and the result is six.

iii.                 Thirty less than twelve times a number gives eighteen.

            10.   Write the statement for each of the equations given below:

i.                     2x – 6 = 8                          ii.           4x = x + 9

            11.   Verify by substitution that

i.                     The root of 4x – 1 = 11 is 3

ii.                   The root of 3x – 6 = x + 2 is 4

iii.                 The root of 5x – 11 = x + 9 is 5

            12.   Solve the following equations by trial and error method:

i.                     9 + x = 14            ii.            = 2                   iii.          5x – 6 = x + 6             

iv.                 3x + 6 = 9 +2x                   v.           2x + 7 = 3x

VI J integers

INTEGERS

          1.       In each of the following pairs, which number is to the right of the order on the number line?

i.                     5,9                       ii.           -4,-6                    iii.          0,-3                     iv.          -7,7

          2.       Write the following integers in ascending order:

i.                     7,12,-14,-12,0,3,-1          ii.           -15,17,-235,-325,104      iii.              -27,19,0,-11,-33,-2

          3.       Write the absolute value of each of the following

i.                     -19                       ii. 23                    iii. 0                     iv. -211               v. 1021                vi. -53

         4.       Evaluate the following:

i.                     |-13| + |-5|       ii.           |-7| - |3|            iii.          |-11| - |-14|              iv.          |10| - |9|

          5.       Write the additive inverse of the following:

i.                     -13                       ii.           -2012   

         6.       Add the integers in each of the following:

i.                     124,-8                 ii.           51,-63                 iii.          -6290,-2110

         7.        Find the predecessor of each of the following:

i.                     0                           ii.           -121                     iii.          -1

         8.       Simplify:

i.                     23 + (-17) + (-11) + 16                   ii.           (-230) + 109 + (-10) + 210 + -(2)

          9.        Find an integer a such that:

i.                     -5 + a = 0            ii.           a + (-15) = 0

         10.   A car travelled 90km to the north and then 52km to the south. How far from the initial position             was the car finally?

         11.   Evaluate the following

i.                     -576 – (-425)                    ii.           380 – (-120) – (-65)       

         12.   Subtract the number which is successor of -27 from the number which is predecessor of -39.

        13.   What must be added to:

i.                     -72 to get 45                     ii.           -37 to get -19

        14.   Find an integer a such that

i.                     a + 9 = 0                            ii.           3 + a = 0

        15.    From the sum of -5376 and 3744, subtract the sum of-2150 and 1125.

         16.   The sum of two integers is -23. If one of the integers is 145, find the other.

         17.   The sum of two integers is 79. If one of the integers is -43 find the other.