Realiabilty and item analysis in assessment

1
POLYGONS
Objectives:
1. To identify polygons and their classifications
2. To name a polygon
3. To solve the area, sum of the interior angles, and the measure of the central angle of a
polygon.
A closed plane figure formed by connecting three or more segments at their
endpoints is called polygons. A Polygon comes from Greek. Poly- means "many" and -
gon means "angle". They are made of straight lines, and the shape is "closed" (all the
lines connect up). The segments are the sides of the polygon while the endpoints of these
polygons are the vertices of the polygon. Two sides of a polygon are adjacent (or
consecutive) if they have a common endpoint. Two angles of a polygon are adjacent (or
consecutive) if they are the endpoints of a side.
In the figure above, the endpoints A, B, and C are vertices of the polygon and the
segments AB, BC, and CD are the sides of the polygon. The angles of the polygon are
CAB, ABC, and BCA.
Types of Polygons
Regular or Irregular
If all angles are equal and all sides are equal, then it is regular, otherwise it is
irregular
Regular Irregular
A
B
C

2
Concave or Convex
A convex polygon has no angles pointing inwards. More precisely, no internal
angle can be more than 180°.
If any internal angle is greater than 180° then the polygon is concave. (Think:
concave has a "cave" in it)
Simple or Complex
A simple polygon has only one boundary, and it doesn't cross over itself. A
complex polygon intersects itself! Many rules about polygons don't work when it is
complex.
Simple Polygon
(this one's a Pentagon)
Complex Polygon
(also a Pentagon)
CONCAVEPOLYGON
The figure at the left side is an
example of a CONCAVE
POLYGON because it has an
internal angle whose measure is
greater than 180˚ degrees.

3
DIFFERENT NAMES OF POLYGONS ACCORDING TO THE NUMBER OF THEIR
SIDES
Names of Polygons
If it is a Regular Polygon...
Name Sides Shape
Interior
Angle
Triangle (or Trigon) 3 60°
Quadrilateral
(or Tetragon)
4 90°
Pentagon 5 108°
Hexagon 6 120°

4
Heptagon
(or Septagon)
7 128.571°
Octagon 8 135°
Nonagon
(or Enneagon)
9 140°
Decagon 10 144°
Hendecagon (or
Undecagon)
11 147.273°

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Dodecagon 12 150°
Triskaidecagon 13 152.308°
Tetrakaidecagon 14 154.286°
Pentadecagon 15 156°
Hexakaidecagon 16 157.5°
Heptadecagon 17 158.824°
Octakaidecagon 18 160°
Enneadecagon 19 161.053°
Icosagon 20 162°
Triacontagon 30 168°
Tetracontagon 40 171°
Pentacontagon 50 172.8°
Hexacontagon 60 174°
Heptacontagon 70 174.857°
Octacontagon 80 175.5°
Enneacontagon 90 176°
Hectagon 100 176.4°
Chiliagon 1,000 179.64°
Myriagon 10,000 179.964°
Megagon 1,000,000 ~180°
Googolgon 10100 ~180°
n-gon N
(n-2) × 180°
/ n

6
You can make names using this method:
Sides Start with...
20 Icosi...
30 Triaconta...
40 Tetraconta...
50 Pentaconta...
60 Hexaconta...
70 Heptaconta...
80 Octaconta...
90 Enneaconta...
100 Hecta...
etc..
Sides ...end with
+1 ...henagon
+2 ...digon
+3 ...trigon
+4 ...tetragon
+5 ...pentagon
+6 ...hexagon
+7 ...heptagon
+8 ...octagon
+9 ...enneagon
Example: a 62-sided polygon is a Hexacontadigon
BUT, for polygons with 13 or more sides, it is OK (and easier) to write "13-gon", "14-
gon" ... "100-gon", etc.
Interior
angle
Center
of the
angle
Centra
l angle
exterior
angle
The total space inside of any polygon
which is enclosed by the line segments is called
the area of a polygon. An interior angle of a
polygon is an angle on the inside of a polygon
formed by each pair of adjacent sides. A
central angle is an angle formed by the
segments joining consecutive vertices to the
center of a regular n-gon. The center of a circle
in which a regular polygon is inscribed is
called the center of the polygon. An exterior
angle is an angle formed by a side of the
regular n-gon.
A diagonal of a polygon is a segment joining
two consecutive vertices of a convex polygon.
Apothem

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Example
Find the area, sum of the interior angles, and the measure of the central angle of a
convex pentagon which has a side of 3 cm long and an apothem of 2.5 cm.
Solution:
To solve the area of a pentagon, we need to find first its perimeter and the length of its
apothem.
Given: s = 5cm, apothem = 2.5 cm, and a pentagon has 5 sides
Perimeter (P) = the sum of the lengths of the sides of a polygon
Or since the lengths of the sides of a polygon are all equal, so we can also use this
formula for the perimeter of any polygon P = ns, where n is the number of sides and s is
the length of a side.
P = 5 cm + 5 cm + 5 cm + 5 cm + 5 cm
P = 5(5 cm)
P = 25 cm
Solve for the area
A = ½ Pa = ½ (25 cm) (2.5 cm) = ½ 62.5 cm2 = 31.25 cm2
Solve for the sum of the interior angles
Using the formula for the sum of interior angles of a polygon, we have
ΘI = (n – 2) 180˚ = (5 – 2) 180˚ = (3) 180˚ = 540˚
Solve for the measure of the central angle of a polygon
The formula to be used for finding the area of any convex polygon is given
by A = ½ Pa, where P is the perimeter and a is the apothem.
The formula used for finding the sum of the interior angles of any convex
polygon is given by S = (n – 2) 180˚.
The formula to be used for finding the measure of the central angle of any
convex polygon is given by θ = 360˚/n, where n is the number of sides of any
polygon.

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Using the formula for the central angle of a polygon, we have
ΘC = 360˚/n = 360˚/5 = 72˚
Therefore, the area of the polygon is 32.25 cm2, the sum of its interior angles is 540˚, and
the measure of its central angle is 72˚.
Triangles
Objectives:
1. To identify triangles according to the number of congruent sides and
according to their angles.
Classification of Triangles
Triangles can be classified according to the number of congruent sides
Scalene Triangle
No two sides are
congruent
Equilateral Triangle
Three sides are congruent.
Triangle is a polygon with three sides. If a
triangle has vertices C, D, and E. we name the triangle
as triangle CDE, or in symbols, ∆CDE. In the figure at
the right, the line segments CD, DE, and CE are the
sides of the triangle while the ∠CDE or ∠D, ∠DCE or
∠C and ∠DEC or ∠E are the angles of the triangle.
C
D
E
Base
Isosceles Triangle
At least two sides are congruent

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Triangles can also be classified according to their angles
QUADRILATERALS
Objectives:
60˚
72˚
48˚
Acute Triangle
All the angles are
acute.
125˚
Obtuse Triangle
One angle is obtuse.
Hypotenuse
leg
leg
Right Triangle
One angle is a right angle.
The side opposite the right angle of a right
triangle is called the hypotenuse. The two sides are
called the legs.
60˚
60˚60˚
Equiangular Triangle
All angles are equal.
The measures of each of the
interior angle of an equiangular
triangle are always equal to 60˚.

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1. To illustrate quadrilaterals
2. To define and illustrate the types of quadrilaterals
3. To differentiate the types of quadrilaterals
Quadrilateral just means "four sides"
(quad means four, lateral means side).
Any four-sided shape is a Quadrilateral.
But the sides have to be straight, and it has to be 2-dimensional.
Properties
 Four sides (edges)
 Four vertices (corners)
 The interior angles add up to 360 degrees:
Try drawing a quadrilateral, and measure the angles. They should add to 360°
Types of Quadrilaterals
There are special types of quadrilateral:
Some types are also included in the definition of other types! For example a
square, rhombus and rectangle are also parallelograms.

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The Rectangle
means "right angle"
and show equal sides
A rectangle is a four-sided shape where every angle is a right angle (90°).
Also opposite sides are parallel and of equal length.
The Rhombus
A rhombus is a four-sided shape where all sides have equal length.
Also opposite sides are parallel and opposite angles are equal.
Another interesting thing is that the diagonals (dashed lines in second figure) meet
in the middle at a right angle. In other words they "bisect" (cut in half) each other at right
angles.
A rhombus is sometimes called a rhomb or a diamond.
The Square
A square has equal sides and every angle is a
right angle (90°)
Also opposite sides are parallel.
Means “right angle”
Show equal sides

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A square also fits the definition of a rectangle (all angles are 90°), and a rhombus
(all sides are equal length).
The Parallelogram
A parallelogram has opposite sides parallel and equal in length. Also opposite
angles are equal (angles "a" are the same, and angles "b" are the same).
NOTE: Squares, Rectangles and Rhombuses are all Parallelograms!
Example:
A parallelogram with:
 all sides equal and
 angles "a" and "b" as right angles
is a square!
The Trapezoid (UK: Trapezium)
A trapezoid has a pair of opposite sides parallel. It is a quadrilateral with exactly
one pair of opposite sides.

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It is called an isosceles trapezoid if the sides that aren't parallel are equal in length
and both angles coming from a parallel side are equal, as shown.
And a trapezium is a quadrilateral with NO parallel sides:
The Kite
A kite has two pairs of sides. Each pair is made up of adjacent sides that are equal
in length. The angles are equal where the pairs meet. Diagonals (dashed lines) meet at a
right angle, and one of the diagonal bisects (cuts equally in half) the other.
PERIMETER OF POLYGONS (TRIANGLE, RECTANGLE, SQUARE, and
PARALLELOGRAM)
Objectives:
1. To determine the perimeter of a polygon
2. To solve problems involving perimeter
The perimeter is the distance around a polygon.
PERIMETER OF A TRIANGLE
The perimeter of a triangle is the sum of the lengths of its three sides.
The perimeter of a triangle with sides a, b, and c is given by
P = a + b + c
Example
A triangular piece of paper measures
7cm, 14cm, and 17cm. What is the perimeter of
the piece of paper?
7c
m
17cm
14cm

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PERIMETER OF A RECTANGLE
Example
PERIMETER OF A SQUARE
The perimeter of a rectangle is the sum of twice its
length and twice its width
The perimeter of a rectangle with length l and width w is
given by
P = 2l + 2w
Length(l )
Width(w)
A rectangular tablecloth has a width
of 2.5m and a length of 4.5m. How meters of
lace trimmings should be bought to make its
border?
2.5
m
4.5m
Solution:
The problem asks for the perimeter of the tablecloth.
Using the formula for the perimeter of a rectangle, we have
P = 2l + 2w = 2(4.5m) + 2(2.5m) = 14m
Therefore, 9m of the lace trimmings should be bought.
Solution:
Using the formula for the perimeter of a triangle, we have
P = a + b + c = 7cm + 14cm + 17cm = 38cm
Therefore, the perimeter of the paper is 38cm.
Since the sides of a square are of equal
lengths, its perimeter is four times the length of a
side.
The perimeter of a square with side s is given by

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P = 4s
Where s = lengthof the side of a square
AREA OF SOME PLANE FIGURES (TRIANGLE, RECTANGLE, SQUARE,
PARALLELOGRAM, TRAPEZIOD)
Objectives:
1. To derive and find the area of a rectangle, square, triangle, parallelogram, and a
trapezoid.
2. To use square units when finding area.
Area of a closed plane figure is the measure of the region (surface) enclosed by
its boundary or the line segments.
Area of a Rectangle
The area of a rectangle is the product of its length and width.
The area of a rectangle with length l and width w is given by
A = l x w
Solution
The problem asks for the perimeter of the mat. Using the formula for
the perimeter of a square, we have
P = 4s = 4(50.5 cm) = 202 cm
Therefore, 202 cm long of lace material is needed to borders the mat.
Example
One side of a square mat is of length 50.5 cm. How long
of a lace material is needed to put borders on it?
50.5 cm
Length (l)
Width (w)
Example
A rectangular garden has a length of 5 m and a width
of 2 m. What is its area?
Solution:
Since the garden is in rectangular formed, use the
2 m

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Area of a Square
Area of a Triangle
The area of a triangle is one half of the product of its base and height.
The area of a triangle with base b and height h is given by
s
s
s
s
h
base
5 m
Since the lengths of the sides of a square are all
equal, so its area must be the product of its two sides or the
square of a side.
The area of a square with side s is given by
A = s2 where s is the length of the side
of a square
Example
What is the floor area of a square room which
measures 6.5 m on each of its sides?
Solution:
Using the formula for the area of a square, we have
A = s2 = (6.5 m)2 = 42.25 m2
Therefore, the floor area of the room is 42.25 m2.
6.5 m

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A = ½ bh
Example
The base of a triangular flaglet is 10 cm long. If the height of the flaglet is 4.2 cm,
what is its area?
Solution:
Using the formula for the area of a triangle, we have
A = ½ bh = ½ (10 cm x 4.2 cm) = ½ 42 cm2 = 21 cm2
Therefore, the area of the flaglet is 21 cm2.
Area of a Parallelogram
The area of a parallelogram is the product of its base and height.
The area of a parallelogram with base b and height h is given by
A = bh
Area of a Trapezoid
The area A of a trapezoid of height h and bases b1 and b2 is given by
A = ½ h(b1 + b2)
h
b
25 m
Example
A rice field is in the shape of a parallelogram. If its base is 42 m and
its height is 25 m, what is its area?
Solution:
Using the formula for the area of a parallelogram, we have
A = bh = (42 m) (25 m) = 1050 m2
Therefore, the area of the rice field is 1050 m2
42 m
b1

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COMPLETION
Name: Score:
Course and Year:

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Directions: Complete the following statements and write your answers on the space
provided.
1. A closed plane figure formed by connecting three or more segments at their endpoints
is called _____________.
2. A polygon that consists of eight sides is called _____________.
3. A polygon with all angles are equal and all sides are equal is called _____________.
4. The formula to be used in finding the sum of the interior angles of any convex polygon
is _____________.
5. A polygon with fifteen sides is called _____________.
6. A triangle with no equal sides is called _____________.
7. A triangle with an obtuse angle is called _____________.
8. An angle formed by the segments joining consecutive vertices to the center of a regular
n-gon is called _____________.
9. A segment joining two nonconsecutive vertices of a convex polygon is called
_____________.
10. A quadrilateral with exactly one pair of parallel sides is called _____________.
SHORT ANSWER
Directions: Supply what is asked in each statement. Write your answer on the blank
provided before each number.

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1. What is the formula to be used for finding the central angle of a convex
polygon?
2. What is the name of the polygon with twenty sides?
3. What kind of triangle with two equal sides?
4. What is an angle formed by the segments joining consecutive vertices to
the center of a regular n-gon?
5. What type of quadrilateral with two pairs of parallel sides?
6. What kind of rectangle with four equal sides?
7. What is the formula to be used for getting the perimeter of a rectangle?
8. What kind of triangle with three equal sides?
9. What is the formula to be used for finding the area of a triangle?
10. What is the formula to be used for getting the area of a trapezoid?
ESSAY
Directions: Answer the following statements/questions.
1. In three to four sentences, explain why is it that every square is a rectangle?
2. In four to five sentences, write an essay comparing perimeter and area of a polygon?
3. Write an essay discussing the classification of triangles according to its sides?
MULTIPLE CHOICE
DIRECTIONS: Choose the right answer and write the letter of your choice on the space
provided.

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1. Which of the figures is a concave polygon?
A. Figure 3
B. Figure 2
C. Figure 1
D. Figure 4
2. Which of the figures is a hexagon?
A. Figure 2
B. Figure 3
C. Figure 4
D. Figure 1
3. How many sides does a dodecagon have?
A. 12
B. 11
C. 18
D. 19
4. What is the sum of the interior angles of a decagon?
A. 1240 ˚
B. 1460˚
C. 1440˚
D. 1570˚
5. Which of these could be the measures of the angles of an equilateral triangle?
Figure 1 Figure 2 Figure 3 Figure 4

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A. 60˚ 60˚ 80˚
B. 45˚ 60˚ 45˚
C. 60˚ 60˚ 60˚
D. 30˚ 90˚ 60˚
6. What type of parallelogram with four congruent angles?
A. rhombus
B. square
C. rectangle
D. trapezoid
7. The length of one side of a square is 4.5 m long. What is its area in cm?
A. 1800 cm
B. 2025 cm
C. 17500 cm
D. 18 cm
8. The width and the perimeter of a rectangle are 8cm and 54 cm, respectively.
What is its length?
A. 6.75 cm
B. 29 cm
C. 46 cm
D. 19 cm
9. A rectangular photo album is 30 cm long and 27 cm wide. What is the area of
the photo album?
A. 810 cm2
B. 630 cm2
C. 114 cm2
D. 405 cm2
10. The base and the height of a triangle are 14 cm and 22.5 cm, respectively. What
is its area?
A. 702.25 cm2
B. 315 cm2

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C. 73 cm2
D. 157.5 cm2
MATCHING TYPE
Directions: Match the items in column A with the items in column B. Write the letters of
your choice on the space provided.
A
1. A polygon with eleven sides
2. A polygon with sixty sides
3. A polygon with one thousand sides
4. A polygon with no angles pointing
inwards
5. A polygon with only one boundary and
it doesn’t cross over itself
6. The measure of the interior angle of an
equilateral triangle
7. A four-sided shape where all sides
have equal length.
8. A parallelogram with all sides are
equal and all interior angles are right
angles
9. The formula for finding the area of a
trapezoid
10. The total space inside of any polygon
B
A. A = ½ bh
B. 60˚
C. Area of the polygon
D. Square
E. Rectangle
F. A = ½ h(b1 + b2)
G. Hendecagon
H. Rhombus
I. Dodecagon
J. 45˚
K. Hexacontagon
L. Convex
M. Chiliagon
N. Regular
O. Concave
P. Hexacontadigon
Q. Simple
R. Megagon

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MATCHING TYPE AND MULTIPLE CHOICE
Name: Score:
I. Directions: Match the items in column A with the items in column B. Write the letters
of your choice on the space provided.
A
1. The name of the polygon with a 24 sides
2. An angle formed by a side and an
extension of adjacent side of the regular n-
gon
A. A = ½ h (b1 + b2)
B.Trapezium
C. Circumference
B
TableofSpecification
TopicsTimeAllotmentPercentage
Allocation
Remembering
40%
Understanding
20%
Analyzing
40%
1.Polygons1hr24%3MT2MC2MC
2.Triangles30min.12%1MT1MC2MC
3.Quadrilaterals40min.26%2MT1MC2MC
4.PerimeterofPolygons1hr24%3MT1MC3MC
5.AreaofsomePlaneFigures1hr24%3MT1MC3MC
Total4hrs10min.100%12MT6MC12MC
E

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II. Directions: Choose the right answer and write the letter of your choice on the space
provided.
13. Parallel lines are lines that going to the same direction without intersecting
each other. Base on this definition, which of the figures has two of its sides parallel to
each other?
G
D
B
I
N
H
A
P
O
M
K

26
A. Figure 4
B. Figure 1
C. Figure 3
D. Figure 2
14. A convex polygon has no angles pointing inwards and no internal angle can
be more than 180°. Base on this description, which of the figures does not belong to the
group?
A. Figure 1
B. Figure 2
C. Figure 3
D. Figure 4
15. The side opposite to the right angle of a right triangle is called the hypotenuse.
In the figure below, what is its hypotenuse?
A. AB
B. BC
C. AC
D. CB
16. A rectangle is a four-sided shape where every angle is a right angle (90°).
Which of the figure is a rectangle?
Figure 1 Figure 2 Figure 4Figure 3
A
B C

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A. Figure 2
B. Figure 4
C. Figure 1
D. Figure 3
17. The perimeter of a rectangle is the sum of twice its length and twice its
width. Which of the formulas is the formula for the perimeter of a rectangle?
A. P = B1 + B2 + H1 + H2
B. P = ½ (2l + 2w)
C. P = bh
D. P = l + w
18. Area of a closed plane figure is the measure of the region (surface) enclosed
by its boundary or the line segments. Which of formulas does not belong to the group?
A. A = bh
B. A = ½ h(b1 + b1)
C. A = 1/2bh
D. A = 4s2
19. What is the area of an octagon with a side of 5 cm long and with an apothem
of 3.5 cm long?
A. 70 cm2
B. 80 cm2
C. 50 cm2
D. 55 cm2

28
20. What is the sum of the interior angles of a 35-gon?
A. 1225°
B. 360°
C. 170°
D. 5940°
21. If the lengths of the sides of an equilateral triangle are all equal, then what
would be the measures of its interior angles?
A. 70° 70° 70°
B. 45° 45° 45°
C. 60° 60° 60°
D. 65° 65° 65°
22. Which of these could be the measures of the angles of an acute triangle?
A. 45° 55° 80°
B. 36° 72° 82°
C. 65° 45° 35°
D. 25° 85° 45°
23. If the measure of one side of a square is 5 cm, then what is the measure of
each remaining side of the square?
A. 5 cm
B. 4 cm
C. 6 cm
D. 8 cm

29
24. What kind of angle that can be formed through the intersection of the
diagonals of a rhombus?
A. acute angle
B. right angle
C. obtuse angle
D. reflex angle
25. If the length and the width of the floor of a classroom are 8 m and 4 m,
respectively. What is the perimeter of that classroom?
A. 24 m
B. 32 m
C. 80 m
D. 12 m
26. Find the distance around a triangle in meters whose sides are 14 ½ cm, 16
cm, and 9 cm?
A. 3.95 m
B. 0.0395 m
C. 39.5 m
D. 0.395 m
27. A square garden is to be fenced. One side is 8 ¾ m. How long is the fence
needed to surround it on all side?
A. 35 m
B. 45 m

30
C. 76.5 m
D. 56.5 m
28. A triangle has an area of 45 cm2 and a base of 5 cm. What height corresponds
to this base?
A. 28 cm
B. 20 cm
C. 18 cm
D. 15 cm
29. The area of a rectangular swimming pool is 375 square meters. If the length is
25 m, what is its width?
A. 15 m
B. 25 m
C. 10 m
D. 17 m
30. A man is buying a lot for 5,000 pesos per square meter. If the lot is 35 meters
long and 27 meters wide, how much will be pay for it?
A. Php 4 725 000
B. Php 2 362 500
C. Php 1 295 000
D. Php 4 885 000

31
# of
Items
Number of Students TOTAL

32
1 2 3 4 5 6 7 8 9 10
1 1 1 1 1 1 1 1 0 1 0
2 1 1 1 1 1 1 1 1 1 0
3 1 1 1 1 1 1 1 1 0 0
4 0 0 1 1 1 1 1 1 1 1
5 1 1 1 1 1 1 1 1 1 1
6 1 1 1 1 1 1 1 1 1 0
7 1 1 1 1 1 1 1 0 0 0
8 0 0 1 1 1 0 1 0 0 1
9 1 1 1 1 1 1 1 0 1 1
10 1 1 1 1 0 1 0 1 1 1
11 1 1 1 0 0 1 0 1 1 0
12 1 1 1 1 1 1 1 1 1 0
13 1 1 0 1 1 1 1 1 0 1
14 1 1 1 1 1 1 1 1 1 1
15 1 1 1 1 1 1 1 1 1 1
16 1 1 1 1 1 0 1 0 0 1
17 1 1 1 0 0 0 0 1 1 1
18 1 1 1 0 0 0 1 0 1 0
19 1 1 1 1 1 1 1 1 1 1
20 1 1 0 0 1 0 0 1 1 0
21 1 1 1 1 0 0 0 1 1 1
22 1 1 1 1 1 1 1 1 0 0
23 1 1 1 1 1 1 1 1 1 1
24 0 1 1 1 1 0 0 0 1 1
25 1 1 1 1 1 1 1 1 0 1
26 1 1 0 0 0 1 0 0 1 1
27 1 1 1 1 1 1 1 1 1 1
28 1 0 1 1 1 1 0 1 1 1
29 1 1 1 1 1 1 1 1 1 1
30 1 1 1 1 1 0 1 1 0 1
x 15 15 14 13 12 13 12 12 11 11 Ʃ x = 128
x2
225 225 196 169 144 169 144 144 121 121 Ʃx2
= 1658
X 12 12 13 12 12 9 10 10 11 9 Ʃ y = 110
y2
144 144 169 144 144 81 100 100 121 81 Ʃy2
= 1228
xy 180 180 182 156 144 117 120 120 121 99 Ʃxy = 1419
TABLE 1. RELIABILITY OF THE TEST (SPLIT HALF METHOD)

33
SPLIT-HALF METHOD
Where n = numberof studentstakingthe test
x = odd/firsthalf scores
y = even/secondhalf scores
Based on the reliability index, it shows that the test has a moderate
reliability.
Reliability
Index
Reliability
Correlation
Coefficient
Degree of
Relationship
0.00 – 0.20
.21 - .40
.41 - .60
.61 - .80
.81 – 1.00
Negligible
Low
Moderate
Substantial
High to Very
High
r =
(16580 – 16384)(12280 – 12100)
110
r =
[nƩx2 – (Ʃx)2][ nƩy2 – (Ʃy)2]
nƩxy – ƩxƩy
r =
[10(1658) – (128)2][ 10(1228) – (110)2]
10(1419) – (128)(110)
r =
[nƩx2 – (Ʃx)2][ nƩy2 – (Ʃy)2]
nƩxy – ƩxƩy
r =
(196)(180)
110
r =
35280
110
r =
187.8297
110
r = 0.59

34
TABLE 2. DIFFICULTY INDEX
# of
Items
Number of Students
UPPER GROUP LOWER
GROUP
p =
𝐻𝑐+𝐿𝑐
2𝑛
Interpretation
1 2 3 4 5 Hc 6 7 8 9 10 Lc
1 1 1 1 1 1 5 1 1 0 1 0 3 0.8 E
2 1 1 1 1 1 5 1 1 1 1 0 4 0.9 VE
3 1 1 1 1 1 5 1 1 1 0 0 3 0.8 E
4 0 0 1 1 1 3 1 1 1 1 1 5 0.8 E
5 1 1 1 1 1 5 1 1 1 1 1 5 1 VE
6 1 1 1 1 1 5 1 1 1 1 0 4 0.9 VE
7 1 1 1 1 1 5 1 1 0 0 0 2 0.7 E
8 0 0 1 1 1 3 0 1 0 0 1 2 0.5 MD
9 1 1 1 1 1 5 1 1 0 1 1 4 0.9 VE
10 1 1 1 1 0 4 1 0 1 1 1 4 0.8 E
11 1 1 1 0 0 3 1 0 1 1 0 3 0.6 MD
12 1 1 1 1 1 5 1 1 1 1 0 4 0.9 VE
13 1 1 0 1 1 4 1 1 1 0 1 4 0.8 E
14 1 1 1 1 1 5 1 1 1 1 1 5 1 VE
15 1 1 1 1 1 5 1 1 1 1 1 5 1 VE
16 1 1 1 1 1 5 0 1 0 0 1 2 0.7 E
17 1 1 1 0 0 3 0 0 1 1 1 3 0.6 MD
18 1 1 1 0 0 3 0 1 0 1 0 2 0.5 MD
19 1 1 1 1 1 5 1 1 1 1 1 5 1 VE
20 1 1 0 0 1 3 0 0 1 1 0 2 0.5 MD
21 1 1 1 1 0 4 0 0 1 1 1 3 0.7 E
22 1 1 1 1 1 5 1 1 1 0 0 3 0.8 E
23 1 1 1 1 1 5 1 1 1 1 1 5 1 VE
24 0 1 1 1 1 4 0 0 0 1 1 2 0.6 MD
25 1 1 1 1 1 5 1 1 1 0 1 4 0.9 VE
26 1 1 0 0 0 2 1 0 0 1 1 3 0.5 MD
27 1 1 1 1 1 5 1 1 1 1 1 5 1 VE
28 1 0 1 1 1 4 1 0 1 1 1 4 0.8 E
29 1 1 1 1 1 5 1 1 1 1 1 5 1 VE
30 1 1 1 1 1 5 0 1 1 0 1 3 0.8 E
𝑃̅ =
Ʃ𝑝
𝑘
0.79 Easy
Index Range Difficulty level
0.00-0.20 Very Difficult
0.21-0.40 Difficult
0.41-0.60 Moderate Difficult
0.61-0.80 Easy
0.81-1.00 Very Easy
The computed value of P is 0.79.
Thus, it means that the difficulty level
of the overall test is easy.

35
TABLE 3. DISCRIMINATION INDEX
# of
Items
Number of Students
UPPER GROUP LOWER
GROUP
d =
𝐻𝑐 − 𝐿𝑐
𝑛
Interpretation
1 2 3 4 5 Hc 6 7 8 9 10 Lc
1 1 1 1 1 1 5 1 1 0 1 0 3 0.4 VI
2 1 1 1 1 1 5 1 1 1 1 0 4 0.2 MI
3 1 1 1 1 1 5 1 1 1 0 0 3 0.4 VI
4 0 0 1 1 1 3 1 1 1 1 1 5 -0.4 PI
5 1 1 1 1 1 5 1 1 1 1 1 5 0 PI
6 1 1 1 1 1 5 1 1 1 1 0 4 0.2 MI
7 1 1 1 1 1 5 1 1 0 0 0 2 0.6 VI
8 0 0 1 1 1 3 0 1 0 0 1 2 0.2 MI
9 1 1 1 1 1 5 1 1 0 1 1 4 0.2 MI
10 1 1 1 1 0 4 1 0 1 1 1 4 0 PI
11 1 1 1 0 0 3 1 0 1 1 0 3 0 PI
12 1 1 1 1 1 5 1 1 1 1 0 4 0.2 MI
13 1 1 0 1 1 4 1 1 1 0 1 4 0 PI
14 1 1 1 1 1 5 1 1 1 1 1 5 0 PI
15 1 1 1 1 1 5 1 1 1 1 1 5 0 PI
16 1 1 1 1 1 5 0 1 0 0 1 2 0.6 VI
17 1 1 1 0 0 3 0 0 1 1 1 3 0 PI
18 1 1 1 0 0 3 0 1 0 1 0 2 0.2 MI
19 1 1 1 1 1 5 1 1 1 1 1 5 0 PI
20 1 1 0 0 1 3 0 0 1 1 0 2 0.2 MI
21 1 1 1 1 0 4 0 0 1 1 1 3 0.2 MI
22 1 1 1 1 1 5 1 1 1 0 0 3 0.4 VI
23 1 1 1 1 1 5 1 1 1 1 1 5 0 PI
24 0 1 1 1 1 4 0 0 0 1 1 2 0.4 VI
25 1 1 1 1 1 5 1 1 1 0 1 4 0.2 MI
26 1 1 0 0 0 2 1 0 0 1 1 3 -0.2 PI
27 1 1 1 1 1 5 1 1 1 1 1 5 0 PI
28 1 0 1 1 1 4 1 0 1 1 1 4 0 PI
29 1 1 1 1 1 5 1 1 1 1 1 5 0 PI
30 1 1 1 1 1 5 0 1 1 0 1 3 0.4 VI
𝐷̅ =
Ʃ𝑑
𝑘
0.15 Poor Test
Index range Discrimination Level
0.40 and above Very Good Item
0.30 to 0.39 Reasonably Good
0.20 to 0.29 Marginal Item
Below 0.20 Poor Item
The computed value of D is
0.16 which is below 0.20. Thus, it
means that the Discrimination level
of the overall test is poor.

36
TABLE 4. DIFFICULTY INDEX AND DISCRIMINATION INDEX
# Of Items
𝑝 =
𝐻𝑐 + 𝐿𝑐
2𝑛 Interpretation
𝑑 =
𝐻𝑐 − 𝐿𝑐
𝑛 Interpretation Decision
1 0.8 E 0.4 VI Retain
2 0.9 VE 0.2 MI Reject
4 0.8 E -0.4 PI Revise
5 1 VE 0 PI Reject
8 0.5 MD 0.2 MI Revise
10 0.8 E 0 PI Revise
11 0.6 MD 0 PI Revise
14 1 VE 0 PI Reject
15 1 VE 0 PI Reject
17 0.6 MD 0 PI Revise
19 1 VE 0 PI Reject
21 0.7 E 0.2 MI Revise
23 1 VE 0 PI Reject
24 0.6 MD 0.4 VI Retain
26 0.5 MD -0.2 PI Revise
27 1 VE 0 PI Reject
29 1 VE 0 PI Reject
𝑃̅ =
Ʃ𝑝
𝑘
0.79 Easy
Revise
𝐷̅ =
Ʃ𝑑
𝑘
0.15 Poor Test
Since the difficulty level and discrimination level of the overall test are 0.79(easy)
and 0.15(poor test), respectively. Therefore, the decision for the overall test is to revise.

37
TABLE 5. DISTRACTER ANALYSIS
Item
13
Item
19
A B* C D A* B C D
Hc 1 4 0 0 Hc 5 0 0 0
Lc 0 4 1 0 Lc 5 0 0 0
IE 0.2 0 -0.2 0 IE 0 0 0 0
Interp. ID P MEd ID Interp. P ID ID ID
Item
14
Item
20
A B C* D A B C D*
Hc 0 0 5 0 Hc 2 0 0 3
Lc 0 0 5 0 Lc 2 1 0 2
IE 0 0 0 0 IE 0 -.02 0 0.2
Interp. ID ID P ID Interp. ID MEd ID P
Item
15
Item
21
A B C* D A B C* D
Hc 0 0 5 0 Hc 0 1 4 0
Lc 0 0 5 0 Lc 0 1 3 1
IE 0 0 0 0 IE 0 0 0.2 -0.2
Interp. ID ID P ID Interp. ID ID P Med
Item
16
Item
22
A B* C D A* B C D
Hc 0 5 0 0 Hc 5 0 0 0
Lc 2 2 0 1 Lc 3 0 0 2
IE -O.4 0.6 0 -0.2 IE 0.4 0 0 -0.4
Interp. MEd VG ID ED Interp. VG ID ID Med
Item
17
Item
23
A* B C D A* B C D
Hc 3 2 0 0 Hc 5 0 0 0
Lc 3 2 0 0 Lc 5 0 0 0
IE 0 0 0 0 IE 0 0 0 0
Interp. P ID ID ID Interp. P ID ID ID

38
Item
18
Item
24
A B C D* A B* C D
Hc 0 2 0 3 Hc 1 4 0 0
Lc 2 0 1 2 Lc 2 2 1 0
IE -0.4 0.4 -0.2 0.2 IE -0.2 0.4 -0.2 0
Interp. MEd ID ED P Interp. ED VG ED ID
Item
25
Item
28
A* B C D A B C* D
Hc 5 0 0 0 Hc 1 0 4 0
Lc 4 1 0 0 Lc 1 0 4 0
IE 0.2 -0.2 0 0 IE 0 0 0 0
Interp. P MEd ID ID Interp. ID ID P ID
Item
26
Item
29
A B C D* A* B C D
Hc 0 1 2 2 Hc 5 0 0 0
Lc 1 0 1 3 Lc 5 0 0 0
IE -0.2 0.2 0.2 -0.2 IE 0 0 0 0
Interp. MED ID ID P Interp. P ID ID ID
Item
27
Item
30
A* B C D A* B C D
Hc 5 0 0 0 Hc 5 0 0 0
Lc 5 0 0 0 Lc 3 0 1 1
IE 0 0 0 0 IE 0.4 0 -0.2 -0.2
Interp. P ID ID ID Interp. VG ID ED ED
LEGEND:
VG = VERY GOOD
P = POOR
MEd = MOST EFFECTIVE DISTRACTER
ED = EFFECTIVE DISTRACTER
ID = INEFFECTIVE DISTRACTER

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