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

C

B

A

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)

CONCAVE POLYGON

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 ShapeInterior 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°

5

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

You can make names using this method:

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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.

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.

exterior angle

Central angle

Center of the angle

Interior angle

Apothem

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

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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

Using the formula for the central angle of a polygon, we have

ΘC = 360˚/n = 360˚/5 = 72˚

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

8

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

Triangles can also be classified according to their angles

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.E

D

C

Base

Isosceles Triangle

At least two sides are congruent

48˚72˚

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Base

Isosceles Triangle


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Isosceles Triangle


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Isosceles Triangle


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Scalene Triangle


Scalene Triangle


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9

QUADRILATERALS

Objectives:

1. To illustrate quadrilaterals

48˚6

Right Triangle

One angle is a right angle.

leg

leg

HypotenuseThe side opposite the right angle of a right

triangle is called the hypotenuse. The two sides are called the legs.

Equiangular Triangle

All angles are equal.

The measures of each of the interior angle of an equiangular triangle are always equal to 60˚.

60˚ 60˚

60˚

10

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.

11

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.

A square also fits the definition of a rectangle (all angles are 90°), and a rhombus (all sides are equal length).

Means “right angle”

Show equal sides

http://www.mathsisfun.com/geometry/square.html

http://www.mathsisfun.com/geometry/rhombus.html

http://www.mathsisfun.com/geometry/parallel-lines.html

http://www.mathsisfun.com/rightangle.html

http://www.mathsisfun.com/geometry/rectangle.html

12

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.

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.

http://www.mathsisfun.com/geometry/trapezoid.html

http://www.mathsisfun.com/geometry/parallelogram.html

13

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

14cm

17cm7cm

Example

A triangular piece of paper measures 7cm, 14cm, and 17cm. What is the perimeter of the piece of paper?

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.

14

PERIMETER OF A RECTANGLE

Example

PERIMETER OF A SQUARE

P = 4s

Where s = length of the side of a square

Width (w)

Length (l )

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

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.

4.5m

2.5m

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?

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

15

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.

50.5 cm

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?

Width (w)

Length (l)

2 m

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 formula for the area of a rectangle.

A = l x w = 5 m x 2 m = 10 cm2

Therefore, the area of the rectangular garden is 10 m2.

16

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

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?

s

s

s

s

base

h

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 = s 2 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

17

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)

b

h

25 m

42 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

Example

h

b2

b1

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 = s 2 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.

18

COMPLETION

Name: Score:

Course and Year:

Directions: Complete the following statements and write your answers on the space

provided.

Example

19

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.

1. What is the formula to be used for finding the central angle of a convex polygon?

20

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.

1. Which of the figures is a concave polygon?

21

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?

A. 60˚ 60˚ 80˚

Figure 1 Figure 2 Figure 3 Figure 4


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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

C. 73 cm2

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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

A





inwards






have equal length.



angles


trapezoid


A





inwards






have equal length.



angles


trapezoid


A





inwards






have equal length.



angles


trapezoid


A





inwards






have equal length.



angles


trapezoid


A





inwards






have equal length.



angles


trapezoid


A





inwards






have equal length.



angles


trapezoid


A





inwards






have equal length.



angles


trapezoid


A





inwards






have equal length.



angles


trapezoid


A





inwards






have equal length.



angles


trapezoid


A





inwards






have equal length.



angles


trapezoid


A





inwards






have equal length.



angles


trapezoid


A





inwards






have equal length.



angles


trapezoid


A





inwards






have equal length.



angles


trapezoid


A





inwards






have equal length.



angles


trapezoid


A





inwards






have equal length.



angles


trapezoid


A





inwards






have equal length.



angles


trapezoid


A





inwards






have equal length.



angles


trapezoid


A





inwards






have equal length.



angles


trapezoid


A





inwards






have equal length.



angles


trapezoid


A





inwards






have equal length.



angles


trapezoid


A





inwards






have equal length.



angles


trapezoid


A





inwards






have equal length.



angles


trapezoid


A





inwards






have equal length.



angles


trapezoid


A





inwards






have equal length.



angles


trapezoid


A





inwards






have equal length.



angles


trapezoid


A





inwards






have equal length.



angles


trapezoid


A





inwards






have equal length.



angles


trapezoid


A





inwards






have equal length.



angles


trapezoid


A





inwards






have equal length.



angles


trapezoid


A





inwards






have equal length.



angles


trapezoid


A





inwards






have equal length.



angles


trapezoid


A





inwards






have equal length.



angles


trapezoid


A





inwards






have equal length.



angles


trapezoid


A





inwards






have equal length.



angles


trapezoid


A





inwards






have equal length.



angles


trapezoid


A





inwards






have equal length.



angles


trapezoid


A





inwards






have equal length.



angles


trapezoid


A





inwards






have equal length.



angles


trapezoid


A





inwards






have equal length.



angles


trapezoid


A





inwards






have equal length.



angles


trapezoid


A





inwards






have equal length.



angles


trapezoid


A





inwards






have equal length.



angles


trapezoid


A





inwards






have equal length.



angles


trapezoid


A





inwards






have equal length.



angles


trapezoid


A





inwards






have equal length.



angles


trapezoid


A





inwards






have equal length.



angles


trapezoid


A





inwards






have equal length.



angles


trapezoid


A





inwards






have equal length.



angles


trapezoid


A





inwards






have equal length.



angles


trapezoid


A





inwards






have equal length.



angles


trapezoid


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

2. Triangles 30 min. 12% 1MT

3.Quadrilaterals 40 min. 26% 2MT

4. Perimeter of Polygons 1 hr 24% 3MT

5. Area of some Plane Figures 1 hr 24% 3MT

Total 4 hrs 10 min. 100% 12MT

24

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

3. The formula to be used for finding the

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

B

2. Triangles 30 min. 12% 1MT

3.Quadrilaterals 40 min. 26% 2MT

4. Perimeter of Polygons 1 hr 24% 3MT

5. Area of some Plane Figures 1 hr 24% 3MT

Total 4 hrs 10 min. 100% 12MT

E

G

25

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?

Figure 1

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

3. The formula to be used for finding the

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

A. A = ½ h (b1 + b2)

B.Trapezium

C. Circumference

D. Square

E. Icositetragon

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?

A. Figure 2

Figure 2 Figure 4Figure 3

CB

A



http://www.mathsisfun.com/rightangle.html

http://www.mathsisfun.com/geometry/rectangle.html

27

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

20. What is the sum of the interior angles of a 35-gon?

28

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 cm 2 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 TOTAL1 2 3 4 5 6 7 8 9 10

1 1 1 1 1 1 1 1 0 1 02 1 1 1 1 1 1 1 1 1 03 1 1 1 1 1 1 1 1 0 04 0 0 1 1 1 1 1 1 1 15 1 1 1 1 1 1 1 1 1 16 1 1 1 1 1 1 1 1 1 0

32

7 1 1 1 1 1 1 1 0 0 08 0 0 1 1 1 0 1 0 0 19 1 1 1 1 1 1 1 0 1 1

10 1 1 1 1 0 1 0 1 1 111 1 1 1 0 0 1 0 1 1 012 1 1 1 1 1 1 1 1 1 013 1 1 0 1 1 1 1 1 0 114 1 1 1 1 1 1 1 1 1 115 1 1 1 1 1 1 1 1 1 116 1 1 1 1 1 0 1 0 0 117 1 1 1 0 0 0 0 1 1 118 1 1 1 0 0 0 1 0 1 019 1 1 1 1 1 1 1 1 1 120 1 1 0 0 1 0 0 1 1 021 1 1 1 1 0 0 0 1 1 122 1 1 1 1 1 1 1 1 0 023 1 1 1 1 1 1 1 1 1 124 0 1 1 1 1 0 0 0 1 125 1 1 1 1 1 1 1 1 0 126 1 1 0 0 0 1 0 0 1 127 1 1 1 1 1 1 1 1 1 128 1 0 1 1 1 1 0 1 1 129 1 1 1 1 1 1 1 1 1 130 1 1 1 1 1 0 1 1 0 1x 15 15 14 13 12 13 12 12 11 11 Ʃ x = 128x2 225 225 196 169 144 169 144 144 121 121 Ʃx2 = 1658X 12 12 13 12 12 9 10 10 11 9 Ʃ y = 110y2 144 144 169 144 144 81 100 100 121 81 Ʃy2 = 1228xy 180 180 182 156 144 117 120 120 121 99 Ʃxy = 1419

SPLIT-HALF METHOD

Where n = number of students taking the test

TABLE 1. RELIABILITY OF THE TEST (SPLIT HALF METHOD)

Reliability Index

Reliability

Correlation Coefficient

Degree of Relationship

0.00 – 0.20 .21 - .40 .41 - .60 .61 - .80

.81 – 1.00

NegligibleLow

ModerateSubstantial

High to Very High

33

x = odd/first half scores y = even/second half scores

Based on the reliability index, it shows that the test has a moderate reliability.

TABLE 2. DIFFICULTY INDEX

# of Items

Number of StudentsUPPER GROUP LOWER

GROUPp = Hc+Lc

2n

Interpretation

1 2 3 4 5 Hc 6 7 8 9 10 Lc1 1 1 1 1 1 5 1 1 0 1 0 3 0.8 E

110

(16580 – 16384)(12280 – 12100)

=r

nƩxy – ƩxƩy

[nƩx2 – (Ʃx)2][ nƩy2 – (Ʃy)2]

=r

10(1419) – (128)(110)

[10(1658) – (128)2][ 10(1228) – (110)2]

=r

nƩxy – ƩxƩy

[nƩx2 – (Ʃx)2][ nƩy2 – (Ʃy)2]

=r

110

(196)(180)

=r

110

35280

=r

110

187.8297

=r

r = 0.59

34

2 1 1 1 1 1 5 1 1 1 1 0 4 0.9 VE3 1 1 1 1 1 5 1 1 1 0 0 3 0.8 E4 0 0 1 1 1 3 1 1 1 1 1 5 0.8 E5 1 1 1 1 1 5 1 1 1 1 1 5 1 VE6 1 1 1 1 1 5 1 1 1 1 0 4 0.9 VE7 1 1 1 1 1 5 1 1 0 0 0 2 0.7 E8 0 0 1 1 1 3 0 1 0 0 1 2 0.5 MD9 1 1 1 1 1 5 1 1 0 1 1 4 0.9 VE10 1 1 1 1 0 4 1 0 1 1 1 4 0.8 E11 1 1 1 0 0 3 1 0 1 1 0 3 0.6 MD12 1 1 1 1 1 5 1 1 1 1 0 4 0.9 VE13 1 1 0 1 1 4 1 1 1 0 1 4 0.8 E14 1 1 1 1 1 5 1 1 1 1 1 5 1 VE15 1 1 1 1 1 5 1 1 1 1 1 5 1 VE16 1 1 1 1 1 5 0 1 0 0 1 2 0.7 E17 1 1 1 0 0 3 0 0 1 1 1 3 0.6 MD18 1 1 1 0 0 3 0 1 0 1 0 2 0.5 MD19 1 1 1 1 1 5 1 1 1 1 1 5 1 VE20 1 1 0 0 1 3 0 0 1 1 0 2 0.5 MD21 1 1 1 1 0 4 0 0 1 1 1 3 0.7 E22 1 1 1 1 1 5 1 1 1 0 0 3 0.8 E23 1 1 1 1 1 5 1 1 1 1 1 5 1 VE24 0 1 1 1 1 4 0 0 0 1 1 2 0.6 MD25 1 1 1 1 1 5 1 1 1 0 1 4 0.9 VE26 1 1 0 0 0 2 1 0 0 1 1 3 0.5 MD27 1 1 1 1 1 5 1 1 1 1 1 5 1 VE28 1 0 1 1 1 4 1 0 1 1 1 4 0.8 E29 1 1 1 1 1 5 1 1 1 1 1 5 1 VE30 1 1 1 1 1 5 0 1 1 0 1 3 0.8 E

P= Ʃpk

0.79 Easy

TABLE 3. DISCRIMINATION INDEX

# of Items

Number of StudentsUPPER GROUP LOWER

GROUPd = Hc−Lc

n

Interpretation

1 2 3 4 5 Hc 6 7 8 9 10 Lc

The computed value of P is 0.79. Thus, it means that the difficulty level of the overall test is easy.

Index Range Difficulty level0.00-0.20 Very Difficult0.21-0.40 Difficult0.41-0.60 Moderate Difficult0.61-0.80 Easy0.81-1.00 Very Easy

35

1 1 1 1 1 1 5 1 1 0 1 0 3 0.4 VI2 1 1 1 1 1 5 1 1 1 1 0 4 0.2 MI3 1 1 1 1 1 5 1 1 1 0 0 3 0.4 VI4 0 0 1 1 1 3 1 1 1 1 1 5 -0.4 PI5 1 1 1 1 1 5 1 1 1 1 1 5 0 PI6 1 1 1 1 1 5 1 1 1 1 0 4 0.2 MI7 1 1 1 1 1 5 1 1 0 0 0 2 0.6 VI8 0 0 1 1 1 3 0 1 0 0 1 2 0.2 MI9 1 1 1 1 1 5 1 1 0 1 1 4 0.2 MI10 1 1 1 1 0 4 1 0 1 1 1 4 0 PI11 1 1 1 0 0 3 1 0 1 1 0 3 0 PI12 1 1 1 1 1 5 1 1 1 1 0 4 0.2 MI13 1 1 0 1 1 4 1 1 1 0 1 4 0 PI14 1 1 1 1 1 5 1 1 1 1 1 5 0 PI15 1 1 1 1 1 5 1 1 1 1 1 5 0 PI16 1 1 1 1 1 5 0 1 0 0 1 2 0.6 VI17 1 1 1 0 0 3 0 0 1 1 1 3 0 PI18 1 1 1 0 0 3 0 1 0 1 0 2 0.2 MI19 1 1 1 1 1 5 1 1 1 1 1 5 0 PI20 1 1 0 0 1 3 0 0 1 1 0 2 0.2 MI21 1 1 1 1 0 4 0 0 1 1 1 3 0.2 MI22 1 1 1 1 1 5 1 1 1 0 0 3 0.4 VI23 1 1 1 1 1 5 1 1 1 1 1 5 0 PI24 0 1 1 1 1 4 0 0 0 1 1 2 0.4 VI25 1 1 1 1 1 5 1 1 1 0 1 4 0.2 MI26 1 1 0 0 0 2 1 0 0 1 1 3 -0.2 PI27 1 1 1 1 1 5 1 1 1 1 1 5 0 PI28 1 0 1 1 1 4 1 0 1 1 1 4 0 PI29 1 1 1 1 1 5 1 1 1 1 1 5 0 PI30 1 1 1 1 1 5 0 1 1 0 1 3 0.4 VI

D= Ʃdk

0.15 Poor Test

Index range Discrimination Level0.40 and above Very Good Item0.30 to 0.39 Reasonably Good0.20 to 0.29 Marginal ItemBelow 0.20 Poor ItemTABLE 4. DIFFICULTY INDEX AND DISCRIMINATION INDEX

# Of Itemsp= Hc+Lc

2n Interpretationd= Hc−Lc

n Interpretation Decision

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

1 0.8 E 0.4 VI Retain2 0.9 VE 0.2 MI Reject3 0.8 E 0.4 VI Retain4 0.8 E -0.4 PI Revise5 1 VE 0 PI Reject6 0.9 VE 0.2 MI Reject7 0.7 E 0.6 VI Retain8 0.5 MD 0.2 MI Revise9 0.9 VE 0.2 MI Reject10 0.8 E 0 PI Revise11 0.6 MD 0 PI Revise12 0.9 VE 0.2 MI Reject13 0.8 E 0 PI Revise14 1 VE 0 PI Reject15 1 VE 0 PI Reject16 0.7 E 0.6 VI Retain17 0.6 MD 0 PI Revise18 0.5 MD 0.2 MI Revise19 1 VE 0 PI Reject20 0.5 MD 0.2 MI Revise21 0.7 E 0.2 MI Revise22 0.8 E 0.4 VI Retain23 1 VE 0 PI Reject24 0.6 MD 0.4 VI Retain25 0.9 VE 0.2 MI Reject26 0.5 MD -0.2 PI Revise27 1 VE 0 PI Reject28 0.8 E 0 PI Revise29 1 VE 0 PI Reject30 0.8 E 0.4 VI Retain

P= Ʃpk

0.79 EasyRevise

D= Ʃdk

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.

TABLE 5. DISTRACTER ANALYSIS

Item 13

Item 19

37

A B* C D A* B C DHc 1 4 0 0 Hc 5 0 0 0Lc 0 4 1 0 Lc 5 0 0 0IE 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 3Lc 0 0 5 0 Lc 2 1 0 2IE 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* DHc 0 0 5 0 Hc 0 1 4 0Lc 0 0 5 0 Lc 0 1 3 1IE 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 DHc 0 5 0 0 Hc 5 0 0 0Lc 2 2 0 1 Lc 3 0 0 2IE -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 DHc 3 2 0 0 Hc 5 0 0 0Lc 3 2 0 0 Lc 5 0 0 0IE 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 DHc 0 2 0 3 Hc 1 4 0 0Lc 2 0 1 2 Lc 2 2 1 0IE -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* DHc 5 0 0 0 Hc 1 0 4 0Lc 4 1 0 0 Lc 1 0 4 0IE 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 DHc 0 1 2 2 Hc 5 0 0 0Lc 1 0 1 3 Lc 5 0 0 0IE -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 DHc 5 0 0 0 Hc 5 0 0 0Lc 5 0 0 0 Lc 3 0 1 1IE 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

39

ED = EFFECTIVE DISTRACTER

ID = INEFFECTIVE DISTRACTER

realiabilty and item analysis in assessment

Education

regular polygon

concave polygon

simple polygon

convex polygon

sided polygon

pentagon complex polygon

angle exterior angle

sides names of polygons