analysis of mathematic

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ANALYSIS OF MATHEMATICS TOPIC IN FORM 1 5

TOPIC : LINES AND ANGLES

NO FORM OBJECTIVES SKILLS NOTES

1 ONEStudents will be taught to:

1. Understand the concept of

angles

Students should be able to:

i. Recognise angles

ii. Denote and label angles

iii. Measure angles using protractors

iv. Draw angles using protractors

v. Recognise, compare and classify angles as

acute, right, obtuse and refle

vi. Draw acute, right, obtuse and refle.

vii. Draw acute, right, obtuse and refle angles

using protractors

viii. Determine angles on straight lines e!ual

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i. Determine one whole turn is $%#o

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NO FORM OBJECTIVES LEARNING OUTCOMES NOTES

2 ONE

&. Understand the concept of

parallel and perpendicular

lines


i. Determine parallel lines

ii. Determine perpendicular lines

iii. State that the angles were formed by

perpendicular lines is '#o.

3 ONE$. understand and use

properties of angles

associated with intersecting

lines to solve problems


i. (dentify intersecting lines

ii. Determine the properties of vertical,

complementary and supplementary

angles

iii. Determine the value of an angle on a

line, given the ad)acent angle

iv. Solve the problems involving angles

formed by intersecting lines


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TOPIC : PYTHAGORASTHEOREM


4 TO 1. Understand the relationship

between the sides of a right*

angled triangle

Students will be able:

i. (dentify the hypotenuse of right*

angled triangles

ii. Determine the relationship between

the lengths of sides of a right*angled

triangle

iii. +ind the length of the missing side of

a right*angled triangle using the

ythagoras-s theorem

iv. +ind the length of sides of geometric

shapes using ythagoras-s theorem

v. Solve problems using the

ythagoras- theorem


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TOPIC : GEOMETRICAL CONSTRUCTIONS


5 TOUnderstand and use the converse of

the ythagoras- theorem

Students will be able to:

i. Determine whether a triangle is a right*

angled triangle

ii. Solve problems involving the converse

ythagoras- theorem

ote that:

(f a&> b& / c&, then 0 is an

obtuse angle

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TORelate the construction to the

properties of e!uilateral triangle

5plore situation when two

different triangles can be

constructed

iv. construct:

a2 angle of %#o and 1o

b2 bisector of an angle

v. construct triangles given:

a2 one side and two angles

b2 two sides and one angle

vi. construct:

a2 parallel lines

b2 parallelogram given its sides and an angle

Students learn measuring

angle using protractors


TOPIC : LOCI IN TO DIMENSIONS

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" TOUnderstand the concept of two

dimensional loci


i. Describe and s7etch the locus of a

moving ob)ect

ii. Determine the locus of points that

are of:

a2 constant distance from a fied point

b2 e!uidistant from two fied point

c2 constant distance from a straight line

d2 e!uidistant from two intersecting lines

iii. 3onstruct the locus of a set of all

points that satisfies the condition:

a2 the point is at a constant distance from a

straight line

b2 the point is at e!uidistant from two

intersecting lines

5mphasise the accuracy

drawings

Relate to properties of

isosceles triangle


TOPIC : CIRCLES

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# TOUnderstand and use concept of arc

of a circle to solve problem


i. derive the formula of the

length of an arc

ii. find the length of arc given

the angle at the centre and

the radius

iii. find the angle at the centre

given the length of the arc

and the radius of a circle

$ TOUnderstand and use the concept of

area of sector of a circle to solve

problems

i. +ind the area of a sector given the radius

and angle at the centre

ii. +ind the angle at the centre given the radius

and area of a sector

iii. +ind the radius given the area of a sector

and the angle at the centre


TOPIC : CIRCLES II


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1% THREEUnderstand and use properties of

angles in circles


i. identify angles subtended by an arc

at the centre and at the

circumference of a circle

ii. determine that angles subtended at

the circumference by the same arc

are e!ual

iii. determine that angles subtended:

a2 at the circumference

b2 at the centre

iv. determine the relationship betweenangle at the centre and angle at the

circumference subtended by an arc

v. determine the si9e of an angle

subtended at the circumference in a

semicircle

(nclude refle angles

subtended at the centre

0ngle subtended by an arc is

the same as angle subtended

by the corresponding chord


TOPIC : LINES AND ANGLES II


i. (dentify:

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11 THREE Understand and use of

properties of angles associated

with transversal and parallel

lines

a2 transversals

b2 corresponding angles

c2 alternate angles

d2 interior angles.

ii. Determine that for parallel lines:

a2 corresponding angles are e!ual

b2 alternate angles are e!ual

c2 sum of interior angles is 1"#.

iii. +ind the values of:

a2 corresponding angles

b2 alternate angles

c2 interior angles associated with parallel lines.

iv. Determine if two given lines are parallel based on

the properties of angles associated with transversals.

v. Solve problems involving properties of angles associated

with transversals


TOPIC : POLYGONS II


12 THREE Understand and use the i. (dentify the interior angles and eterior angles of a polygon.

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7nowledge of eterior and

interior angles of polygons.

ii. +ind the si9e of an eterior angle when the interior angle

of a polygon is given and vice versa.

iii. Determine the sum of the interior angles of polygons.

iv. Determine the sum of the eterior angles of polygons

v. +ind:a2 the si9e of an interior angle of a regular polygon given

the number of sides.

b2 the si9e of an eterior angle of a regular polygon given

the number of sides.

c2 the number of sides of a regular polygon given the si9e

of the interior or eterior angle.

vi. Solve problems involving angles and sides of polygons.


TOPIC : CIRCLES II


13 THREEUnderstand and use the concepts of Students will be able to:

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cyclic !uadrilaterals

i. identify interior opposite angles of cyclic

!uadrilaterals

ii. determine the relationship between interior

opposite angles of cyclic !uadrilaterals

iii. identify eterior angles and the

corresponding interior opposite angles of

cyclic !uadrilaterals

iv. determine the relationship between eterior

angles and the corresponding interior

opposite angles of cyclic !uadrilaterals


TOPIC : TRIGONOMETRY


14 THREEUnderstand and use tangent of

an acute angle in a right*angled

triangle.

i. (dentify the:

a2 hypotenuse

b2 the opposite side and the ad)acent side with respect

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to one of the acute angles.

ii. Determine the tangent of an angle.

iii. 3alculate the tangent of an angle given the lengths of

sides of the triangle.

iv. 3alculate the lengths of sides of a triangle given the

value of tangent and the length of another side.

15 THREEUnderstand and use sine of an

acute angle in a right*angled

triangle.

i. Determine the sine of an angle.

ii. 3alculate the sine of an angle given the lengths of sides

of the triangle.

iii. 3alculate the lengths of sides of a triangle given the

value of sine and the length of another side.


TOPIC : TRIGONOMETRY


1! THREE

Understand and use cosine of

an acute angle in a right*angled

triangle.

i. Determine the cosine of an angle.

ii. 3alculate the cosine of an angle given the lengths of

sides of the triangle.

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iii. 3alculate the lengths of sides of a triangle given the

value of cosine and the length of another side.


TOPIC : THE STRAIGHT LINE


1" FOUR

Understand the concept of gradientof a straight line


i. determine the vertical and hori9ontaldistances between two given points on a

straight line

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ii. determine the ratio of vertical distance to

hori9ontal distance

1# FOUR Understand the concept of gradient

of a straight line in 3artesiancoordinates

i. derive the formula for the gradient of a

straight lineii. calculate the gradient of a straight line

passing through two points

iii. determine the relationship between the

value of the gradient and the:

a2 steepness

b2 direction of inclination, of a straight line




1$ FOUR Understand the concept of

intercept

i. determine the *intercept and y*intercept of

a straight line

ii. derive the formula for the gradient of a

straight line in terms of the *intercept and

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the y*intercept




2% FOUR

Understand and use e!uation ofa straight line

i. Draw the graph given an e!uation of the

form y ; m / cii. determine whether a given point lies on a

specific straight line

5mphasise that the graphobtained is a straight line

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iii. write the e!uation of the straight line given

the gradient and y*intercept

iv. determine the gradient and y*intercept of the

straight line which e!uation is of the form:

a2 y ; m / c

b2 a / by / c

v. find the e!uation of the straight line which:

a2 is parallel to the *ais

b2 is parallel to the y*ais

c2 passes through a given point and has a specific

gradient

d2 passes through two given points

(f a point lies on a straight line,

then the coordinates of the

point satisfy the e!uation of

the straight line




21 FOUR

Understand and use the conceptof parallel lines

i. verify that two parallel lines have the samegradient and vice versa

ii. determine from the given e!uations whether

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$%#2 to solve problems a2 the value of y*coordinate,

b2 the value of x*coordinate,

c2 the ratio of y*coordinate to x*coordinate

of several points on the circumference of the

unit

iii. Determine the values of:

a2 sine,

b2 cosine,

c2 tangent of an angle in !uadrant ( of the

unit circle.


TOPIC : TRIGONOMETRY II


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