Form 3 - Short Notes

Lines and Angles
1.1 Properties of angles associated with transversals and parallel lines

1. A transversal is a straight line that intersects two or more straight lines.

2. When two parallel intersects with a transversal, three types of angles are formed.

Corresponding angle

-The corresponding angles are equal.

Alternate angles

-The alternate angles are equal.

Interior angles

-The interior angles are supplementary or the sum of the interior is 180 degrees.
3. When two straight lines intersect with a transversal, then the two lines are parallel if

a)    The corresponding angles are equal

b)   The alternate angles are equal

c)    The sums of interior angles are 180 degrees.

Algebraic Expressions (III)

6.1 Expanding brackets.

1. Expansion

a)    a(p+q)= ap + aq

b)   ab(p+q-r)= abp + abq –abr

2. Expansion of two brackets

a)    (a + b) (c + d)= ac + ad + bc + bd

6.2 Factorisation

1.  Factorisation is when we write an expression as a product of two or more common factors.

2. To factorise an algebraic expression

a)    Extract the common factor

b)   Find the difference between two squares

c)    Use perfect squares

d)   Group the terms that have a common factor.

Transformation (II)

10.1 Similarity

1. Conditions for similarity

a)    All the corresponding angles are equal.

b)   All the corresponding are proportional

2. Two similar angles must satisfy condition 1(a) or (b).
3. Two other similar polygons must satisfy both conditions 1(a) and (b).
4. Vertices of similar figures must be names in corresponding order.

10.2 Enlargement

1. An enlargement is a transformation whose object and images are similar.

2. The centre of enlargement is an invariant point.

3. Under an enlargement, all the points of the object will move from the centre of enlargement to form an image according to the scale of factor.

4. Scale factor, k

            = Length of one side of image

   Length of the corresponding side of object.

Trigonometry

a) Hypotenuse is the longest side and it is opposite the right angle.

b) Opposite side is the side that lies opposite to the acute angle.

c) Adjacent side is the side that lies next to the acute angle.

tan = Opposite side   = BC

         Adjacent side      AB
sin = Opposite side  = BC

         Hypotenuse        AC
cos = Adjacent side   = AB

           Hypotenuse         AC

Entry contributed by: Farah Sofea