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Scheme of work – Cambridge IGCSE® Mathematics (US) 0444
Unit 7: Co-ordinate geometry (Extended)
Recommended prior knowledge
All of Core and particularly Core 7. Only those parts of the learning objectives or notes and exemplars not included in the core units are itemised, so this document
should be read alongside the core document. As there are links to it Extended 1 should be completed too.
Context
There are five Core geometry units and this is the fourth of five Extended geometry units. Once Core 7 and the other prior experience for Core 7 and Extended 1 are
completed this unit can be slotted in at any point. It is probably best taught as a whole but used to revise some of the Core 7.
Outline
The unit extends the knowledge of Core 7 so be aware that examination questions that relate to aspects of Core 7 not listed here may have a greater degree of
challenge as they combine with other areas of mathematics. This unit covers how to find a point on a line split in a given ratio, looking at linear equations of the form
ax + by = d and the slope of a perpendicular to a line passing through a given point.
Syllabus ref
Learning objectives
Suggested teaching activities
7.2
As Core curriculum
Notes and exemplars
e.g. use co-ordinates to compute the perimeters of polygons and areas of
triangles using the distance formula.
CCSS:
G-GPE6
7.3
CCSS:
G-GPE7
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Find the point on a directed
line segment between two
given points that partitions the
segment in a given ratio
General guidance
In the core unit the skill was explored and linked to Pythagoras. It should
now be linked to work with radicals - Unit 1 Extended (1.8) when
summing the perimeter of polygons and finding areas of triangles.
General guidance
Students need to understand this in geometry before they understand
this in coordinates. i.e. if two lines in a triangle are divided in the same
ratio then the line joining the two points is parallel to the third side of the
triangle. So if a right angled triangle is formed either the ratio on the
hypotenuse of the triangle is the same as on the x or y height.
Cambridge IGCSE Mathematics (US) 0444
Learning resources
http://rpmullen.com/standards/geometry
/oncore/geounit8_3.PDF
1
Syllabus ref
Learning objectives
Suggested teaching activities
Learning resources
10
8
splitting AB in ratio 1:2 is the same as
splitting AD or BD in the ratio 1:2
6
x coordinate of p
AD is 14-2
4 = 12
1:2 = 4:8
so x coordinate is 4 more than 2 = 6
2
p
5
5
2
4
B
A
E
10
15
y coordinate of p
BD is 5- 1 = 6
1:2 = 2:4
so y coordinate of p is 2 more than
20
D
C
1 = 1
6
The only remaining idea is for students to know whether to start at A or B
when working out the split. e.g. If the line had to be split the other way it
would have been called BA and the x and y distances subtracted from
the B coordinates.
7.5
Interpret and obtain the
equation of a straight line as
ax + by = d (a, b, and d are
integers)
Notes and exemplars
e.g. obtain the equation of a straight line graph given a pair of coordinates on the line.
General guidance
Obtaining the equation of a line and plotting them when b = 0 and y is
alone on one side of the equation has been tackled in Core 7.
Past Paper 41 June 2011 Q9
(syllabus 0580)
Past Paper 23 June 2011 Q14
(syllabus 0580)
www.purplemath.com/modules/linprog4
.htm
The most common way b≠ 0 comes about when the equation is multiplied
by the denominator of a fractional gradient and terms are rearranged so
that there are no negatives. Students need some practice to see this
connection first, and obtaining lines for this form can be tackled this way.
To draw a line given in this form challenges students who want to create
a table of values for x and y and have difficulty rearranging the equation.
However, at this level they should know that only two points are needed
to draw a line, but that it is better to plot 3 so that there is a check for
errors. Therefore students also need to realise that this should be a
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Cambridge IGCSE Mathematics (US) 0444
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Syllabus ref
Learning objectives
Suggested teaching activities
Learning resources
straight line. The two obvious pairs of coordinates to plot are when x = 0
to obtain the point the line crosses the y axis, and when y = 0 to find the
point where the line crosses the x-axis. The third point is more
problematic. Using x=1 works for most cases, but when all three points
are close they need to choose a value for x of 5 or 10. This last step is
the one that requires practice so that students develop sufficient
experience to choose a realistic value.
Teaching activities
Give students three lines to draw and ask them to find the coordinates of
the intersections (tie to solving simultaneous equations Core 2 (2.6)).
7.6
CCSS:
G-GPE5
Slope of perpendicular line.
Find the equation of a line
perpendicular to a given line
that passes through a given
point
Look at problems where the solution is in the space enclosed by the
three lines by also looking at inequalities.
General guidance
This has been introduced in the Core unit and simply requires some
formalization.
http://nrich.maths.org/763
http://nrich.maths.org/7031
Teaching activities
To combine several of the parts of this unit ask students to plot a
rectangle, given one line, one vertex off the line, and the opposite vertex
on the line. They must give the equations of the other three lines. They
will have to pull together knowledge about parallel and perpendicular
lines (gradients) going through a given point, even if they manage to find
the fourth point by eye.
Similar problems with Kites and Rhombi can be produced given the
equation of the diagonal and some of the vertices.
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Cambridge IGCSE Mathematics (US) 0444
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