This document provides a summary of topics covered in the 1st trimester of Grade 11 Mathematics, including: 1) Classifying polygons using properties like side lengths, slopes, and angles 2) Distinguishing between functions and relations based on their domains and ranges 3) Writing equations to represent loci like lines, circles, and parabolas 4) Calculating directed distance to determine if a point lies on, above, or below a line 5) Finding the intersection of lines algebraically or by checking if a point satisfies both line equations 6) Recognizing circle equations in standard and general form and writing circle equations from graphs 7) Describing parabolas as loci of points equid

1. GRADE 11 MATHEMATICS
1ST TRIMESTER COVERAGE
REVIEWER (sort of)
…as compiled from the works of 11A, 11C, and 11D…

2. I. VERIFYING/CLASSIFYING POLYGONS
The diagram below serves as a guide in classifying polygons as prepared by 11A and 11C.

3. We can also refer to this explanation prepared by 11D.
Side Note:
To Ms.Tan’s group, please use black ink next time.

4. 2
12
2
12 yyxxd
12
12
xx
yy
m
21
211
1
tan
mm
mm
By distance, we mean distance between two points given by
This computes for the lengths of the sides of
the polygon for comparison.
We also have slope which is given by
If the slopes of the sides of the polygon are
equal, then the sides are parallel.
If the slopes of the sides of the polygon are
negative reciprocals of each other, then the
sides are perpendicular.
To confirm angles formed by the sides, we use their slopes
to measure the angle between them.
Do note that this formula only returns
measures of acute angles.
This also cannot use slope of a vertical line, or
slopes that are negative reciprocals.

5. 121121 , yyryxxrx
2
,
2
2121 yyxx
Let’s not forget division of a line segment.
This gives the coordinate of a point that divides a segment with
endpoints (x1
, y1
) and (x2
, y2
) in a specific ratio r.
Its most common form is the midpoint formula given by
This tells the coordinate that divides a
segment into two equal parts.
This also helps in confirming if segments bisect each
other, especially in the case of diagonals of parallelograms.

6. II. RELATIONS AND FUNCTIONS
A relation is a correspondence between the x values and the y values.
A function is a relation that maps each x value to a unique y value.
A relation can be represented as a set of points, an equation, or a graph.
The following examples discuss how to differentiate functions from non-functions.
It should be clear that a function should
have a unique y mapped to at least one x.

7. A relation has its domain and range. The domain is the set of all x values in the
relation, while the range is the set of all the y values of the relation.
Here are some examples of relations which are not functions with their domain and range.
4,0:
5.1,5.1:
R
D
4,0:
2,2:
R
D
2,3.2:
5.2,:
R
D

8. While these are some examples of functions with their domain and range.
,:
,:
R
D
5.2,3.1:
,:
R
D
1,0,1,2|:
,11,00,11,:
yyR
D

9. III. EQUATION OF A LOCUS
Generally, a locus is a set of points that follow a certain rule.
A line is an example of a locus, a parabola is also a locus, and as well a circle.
We all know that a line is determined by two distinct points.
As 11D said here
A line is a locus of points that have a constant slope.
but considering other properties of a line, its main characteristic is that any pair
of points taken from the line have the same slope.

10. A locus is represented by an equation.
Here are examples of writing an equation for a locus. In this
case, the locus results to a line.
We can also describe a line
differently based on these
examples.
A line is also a locus where
each point is equidistant to
a pair of points not on the
line.

11. Here are examples of writing an equation for a locus courtesy of 11C and 11A.

12. IV. DIRECTED DISTANCE
The concept of directed distance allows us to identify the location of a point in
relation to a line.
In this case, we just use a formula without having to sketch the point and the line.
As you can see in this work of 11C, the directed distance is used when…
Don’t forget to make sure that
the equation of the line is in
the form Ax + By + C = 0.

13. According to 11A and 11D, this is how we interpret the value obtained
after using the formula.

14. Here are examples of using the formula.
This means (2,3) is above
x + 3y + 6 = 0.
This means (5,3)
is below
5x – 10y + 6 = 0.
0
43
0
2
3
423
043;
2
3
,2
22
d
yx
This means is on the line
3x – 4y = 0.
2
3
,2

15. V. INTERSECTION OF LINES
In the Cartesian plane, lines could be parallel to each other, perpendicular and form
a right angle, or they could just intersect.
We have learned various ways in determining the intersection of lines. We can do it
algebraically, by graphing, or through Cramer’s rule.
Regardless of the method the intersection of lines was determined, we should
know what being an intersection means.
According to 11D…
Correction! Lines intersect especially if
their slopes are negative reciprocals!

16. If you are asked if a point is an intersection of a group of lines, you don’t have to
solve for the point.
All we need to do is check if the point satisfies both equations. If it does, the point
is contained in both lines and is their intersection.
We can see in this work that the two equations of the lines both
use the coordinate of the point in their intersection.

17. Be very careful! A
mistake in the
coordinates used will
determine a different
linear equation from the
intended equation.
This group intended to
use (-4, 4) but used (4, 4)
instead.
I think.

18. VI. CIRCLES
Another example of a locus is the circle.
It is a locus that consist of points that are equidistant to a fixed point
referred to as the center.
A circle can be recognized as an equation since it follows a specific form.
It can follow any of these two forms according to 11C.

19. Each form can be converted into the other. A group from 11A and 11D
shows how and discusses certain cases if the equation is a circle or not.

20. Since we know how the equation of a circle looks like, we can write the
equation of a circle given its graph.
This is demonstrated by the folowing examples.

22. VII. PARABOLAS
Lastly, also another example of a locus, the parabola.
A parabola is a locus whose points are equidistant to a fixed point and a line.
The fixed point is the called the focus, the line is the directrix, and the point
located in the middle of the focus and the directrix is the vertex of the
parabola.
Since it is a locus, it takes up the form of equation below.

23. Basically, if you see an
equation of the second
degree, the highest degree
should belong to the either
x or y, but never both.

24. Writing equations of a parabola given its properties is illustrated by the
following.

26. That covers the review…
Not all topics are discussed
thoroughly though…
I leave that to you.
GOOD LUCK GRADE 11!!