ACHIEVEMENT EXAMINATION OF THE FIRST SEMESTER ACADEMIC YEAR 2010 / 2011

1.     The diagram shows a scale drawing of the plan of department store with a scale  1 : 400. The shape of each store is a rectangle. The area, in m², of the shoe store is….

A.      24                                                   

B.        48   

C.       72                                       

D.      96

2.             In the diagram, PQR and TUV are similar triangles. The length, in cm, of TU is ….

A.         2                                                

B.           6                           

C.          6                        

D.         7





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Table of Specification of Final Semester Test Items

1.      Given some figures, students determine which two figures are similar.

2.      Given that trapezoid ABFE and EFCD are similar, students determine the length of EF.

3.      Given the sides of a triangle, students choose another triangle that is similar.

4.      Students determine that two triangles are congruent.

5.      Given the lengths of two congruent triangles, students determine   the measures of the corresponding angles.

6.      Given a diagram, students determine the length of a ladder

7.      Given a diagram consisting of a combination of two right triangles, students determine the height of the top

8.      Given a diagram, students determine the height of a man using the concept of similarity.

9.      Students calculate the height of a tree using the concept of similarity.

10.  Given some regular polygons, students determine the regular polygons that can form a regular tessellation

11.  Given some figures of a tessellation, students determine the figure   tessellation with three shapes

12.  Given the shapes of solids with curved surfaces, students determine their elements.

13.  Given the radius and the lateral surface area of a cone, students calculate its height.

14.  Given the radius and the height of a cylinder, students calculate its surface area.

15.  Given the volume of a sphere, students calculate its radius.

16.  Given the surface area of a cylinder, and the ratio of the radius to the height, students calculate the height.

17.  Given the diameter, and the slant height of a cone, students calculate its surface area.

18.  Given the radius of a sphere, students calculate its surface area.

19.  Given the ratio of the radii of two spheres, students determine the ratio of their areas.

20.  Given the radius and the height of a conical hat, students calculate the area of the material for making 10 hats.

21.  Given the object constructed of a hemisphere and a cone, students calculate its volume.

22.  Given the volume and the height of a conical object, students determine its radius.

23.  Given two wheels with different radii and heights, students calculate the difference of the surface areas.

24.  Given math scores from 10 to 15, students determine the mean of the data.

25.  Given some data, students determine the value of the data, if the mean is known.

26.  Given the mean score of several students, some other students joining them and the new mean score, students determine the mean score of the newly joining students.

27.  Given random data, students determine the median of the data.

28.  Given random data, students determine the mode of the data

29.  Given a frequency distribution table and the mean, students determine the value of the data.

30.  Given a bar diagram, students determine the mean of the data.

31.  Given a line diagram, students are able to interpret the data.

32.  Given a pie diagram, students determine the value of the data.

33.  Given a bar diagram, students estimate the median.

34.  Given 1 dice and 1 coin, students determine the sample space.

35.  Given an event of rolling a coin and two dice, students determine the total of sample points.

36.  Given an event of rolling two dice, students determine the probability of getting the dice.

37.  Given an event of tossing three coins, students determine the probability of the appearance of the head and the tail

38.  Given a word randomly, students determine the probability of a letter to appear.

39.  Given the probability of an event, students determine the complementary probability of an event.

Remidial Test

Do the following problem in detail

1.  A cylindrical candle has a diameter of 3 cm and a height of 20 cm.  The candle is burned and it melts 2 cm3 every minute.  How long does it take for the candle to melt completely!

2.  A cylinder has a radius of 10 cm and a height of 60 cm. The cylinder is filled with water. The height of the water in the cylinder is 40 cm.  An iron ball with a radius of 5 cm is put into the cylinder.   Taking phi = 3,14, find the height of the water now!

3.  Look at the figure.The radius of the cylinder's base is 5 cm and the height of the cylinder is 30 cm. 

Find the ratio of the volume of the cylinder to the volume of the cone.

4.  Three spheres have radii of 2 cm, 3 cm, 4 cm.  Denote the surface areas of the three spheres by L1, L2, and L3 and their volumes by V1, V2, and V3. Find:

a.  L1 : L2 : L3

b.  V1 : V2 : V3

5.  A solid is made of a cylinder and cone as shown in the figure.  The diameter of the cylinder's base is 14 cm and the cylinder's height is 20 cm.  The height of the cone is 12 cm.  Find the total surface area of the solid!

 

SUMMARY

1.  Two figures are called congruent if all the pairs of corresponding sides and angles are equal in measure. In the other words, two figures are congruent if their shapes, sizes, and measurements are identical.

2.  Two figures are similar if all the corresponding angles are equal in measure and all the corresponding sides are porpotional.

3.  Condition for congruent of two triangles.
a.  The  three sides of one triangles are equal in length to the corresponding three sides of the other triangle (SSS property)
b.  Two sides and the included angle of one triangle are equal to two sides and the included angle of the other triangle (SAS property)
c.  Two angles and a side of one triangle are equal to two angles and the corresponding side of the other triangle (ASA property)

Chapter 1 SIMILARITY

Two figures which are the same in shape but different in size are said to be similar figures. 

Two figures are similar if  

1.the corresponding angles have the same measure and;

2.the ratio of the lengths of corresponding sides is equal.

Two similar figures

1.   Equilateral Triangles 

2.  Squares

3.  Regular  Pentagons

4.  Regular Polygons

5.  Circles

6.  Cubes 

7.  Spheres