Little Steps To Be a Math Teacher :D

    

     FOR JUNIOR HIGH SCHOOL 3rd GRADE

      1.      SIMILARITY

A tree has its long shadow of 1 meter long on a plane surface.

 If the pillar with 20 meters high has shadow of 10 meters long. 

Determine the height of the tree!

Solution:

            From the problem above, we know that a tree on a plane surface has shadow 1 meter long. 

And then there is a pillar with 20 meters high has shadow of 10 meters long. 

So for determine the height of the tree, it is better for us to sketch the illustration above.

After sketch the illustration, we can determine that in this case, we use similarity concept to solve this problem, where the length shadow of the tree congruent with the length shadow of pillar. Then the height of the tree also congruent with the height of pillar. So, for determine how the height of the tree is, we can use this formula : (let the height of the tree is x)

	the height of the tree/the lenght of tree's shadow = the height of the pillar/the lenght of pillar shadow

 x/1 = 20/10

 x = 2

So from that result we can conclude that the height of the tree is 2 meters.

      2.      THREE DIMENSIONAL

A tart-cake for celebrating a birthday is in the form of cylinder with diameter is 28 cm and height is 8 cm. If it is coated with chocolate, determine the surface area of chocolate!

Solution:

            From that problem, we know that the shape of cake is cylinder with diameter is 28 cm and the height is 8cm. Then, we imagine how the cake is. As we know that the chocolate just on surface the cake. In the bottom of the cake there is no chocolate, so we must be careful to use a formula. The area that we must calculate is the area of the upper cake (circle), and the area of cover cake.  Well, to determine the surface area of chocolate, we can take this formula:

2.phi.r.t + phi.r^2 = 2.22/7.14.8+22/7.14.14 = 704+616= 1320

From that result we can take a conclusion that the surface area of chocolate is 1320 cm².

               

      3.      THREE DIMENSIONAL

Mss Tuti will make a ceremonial dish of yellow rice served in a cone shape. It has a height of 56 cm and base radius of 42 cm. Determine the volume of the dish made by Mss Tuti!

Solution:      

            From that problem we have a data that the shape of yellow rice is cone, then the height is 56 cm, and the base radius is 42 cm. We know that the volume of the cone is 1/3 from the volume of cylinder. So, if we want to looking for the volume of the cone (yellow shape) we can use the volume cylinder  formula divided into 3.

  1/3.phi.r^2.t = 1/3.22/7.42.42.56

So, we can conclude that the volume of the dish is 103488 cm².

       4.      STATISTIC

Given the data of the running speed of 9 athletes (in m/s)

	5 2 3 6 4 4 3 3 5

a.       Determine the average speed of those athletes

b.      Determine the mode of data

c.       Determine the median

Solution:

a.       If we want to find the average speed of those athletes, we have to count up all the data, then divide it by the number of data. For this case divide into 9. So, we can calculate the sum of data is 5+2+3+6+4+4+3+3+5=35.

the average speed=35/9=3.89

                    So, the average speed of athletes is 3.89 m/s

b.      To find the mode of data, the can know by checking which data that often appear. In this case, we can check first on each data:

Data	Number of Appear
2	1 time
3	3 times
4	2 times
5	2 times
6	1 time

From that table we can conclude the mode is 3 because data 3 often appear if we compare with another data.

c.        To find the median of data, we have to order data first from the smallest to greatest. Then look for the middle data. That middle data is what we called median. So, for finding the median of data above, we have to order data first.

Ordered data:

	2 3 3 3 4 4 5 5 6

 

  From that ordered data, we can see that the middle of data is on the fifth space. So median of data above is 4.

       5.      PROBABILITY

A six-sides dice was thrown 30 times. What is the expectation frequency of occurrences of the even spot side?

Solution:

            For solving the problem above, we must know that the sides of the dice consist of side 1 until side 6. There are three even numbers on the dice’s side. They are 2, 4, and 6. Then to find the expectation frequency of occurrences of the even spot side, we can use formula n(A)/n(S) then multiply with the number of throwing (let number of throwing as k). n(A) as the number of occurrences even spot side, n(S) as the number of all spot sides. Then let the expectation frequency of occurrences is P(A). Then we can calculate it:

				P(A)=n(A)/n(S).k=3/6.30
				=15

So from that result we can get the point that the expectation frequency of occurrences is 15.