Download Fetac Mathematics Level 4 Code 4N1987 Geometry Name : Date:

Fetac Mathematics Level 4 Code 4N1987 Geometry
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Fetac Mathematics Level 4 Code 4N1987
Geometry Brief
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Fetac Mathematics Level 4 Code 4N1987 Geometry
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2 GEOMETRY
Description of contents.
2.1 Describe simple geometric shapes associated with the home
and workplace
2.2 Recognize folding symmetry and rotational symmetry in common
shapes
2.3 Plot graphs of ordered pairs in the coordinate plane showing the
relationship between two variables, using real life situations and
the correct terminology
2.4 Use formulae for calculations in the coordinate plane correctly,
including distance between two points, mid-point of a line
segment, slope of a line, parallel lines, perpendicular lines,
equation of a line, equation of a circle with centre (0,0) and
radius r, and tangent to a circle
2.5 Construct, using drawing instruments, a variety of angles and
simple geometric shapes to given criteria to include naming of
angle types and sides associated with the shapes and angles
2.6 Solve practical problems by using the correct formula(e) to
calculate the area and perimeter of a square, rectangle, triangle,
and circle, giving the answer in the correct form and using the
correct terminology
2.7 Solve practical problems by using the correct formula(e), to
calculate the volume/capacity and surface area of a cube,
cuboid, cylinder, cone, and sphere, giving the answer in the
correct form and using the correct terminology
2.8 Apply standard axioms and theorems of geometry, including
Pythagoras Theorem, to solve real life or simulated problems
involving straight lines, parallel lines, angles, and triangles.
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Fetac Mathematics Level 4 Code 4N1987 Geometry
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2.1 Describe simple geometric shapes associated with the home
and workplace
2.1.1 Discussion questions: Why are manhole covers mostly circular?
Why are most window panes rectangular?
2.1.2 We use the language of geometry to describe the shape of objects. Name some household or
workplace object whose shape could be described by each of the following terms
Square
Circular
Rectangular
Triangular
Cube shaped
Cone shaped
Cylindrical
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Fetac Mathematics Level 4 Code 4N1987 Geometry
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2.2 Recognize folding symmetry and rotational symmetry in common
Shapes
On the following shapes, mark the axis of folding symmetry and the axis of rotational symmetry.
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Fetac Mathematics Level 4 Code 4N1987 Geometry
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2.3 Plot graphs of ordered pairs in the coordinate plane showing the
relationship between two variables, using real life situations and
the correct terminology
In this section we wish to graph some real life data. The graph should have a caption, and both axes
should be labeled appropriately. A brief description of how the data was collected should be
included.
Three possible data collection exercises are given below, other data collection exercises may be used
if your tutor agrees.
Suggestion 1 Gather data on the drop in temperature a a container of hot water cools. Suggested
apparatus a cup of boiling or close to boiling water, a thermometer, and some method for keeping
track of time.
Sugestion 2 Measure the loss in weight of a candle or set of candles as they burn. Suggested
apparatus: four night lights, and a digital weighting scales. The weight loss should be recorded over
a period of half an hour or so
Suggestion 3 Light levels are measured moving away from a light source, and both the light level
and the distance are recorded and ploted.
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Fetac Mathematics Level 4 Code 4N1987 Geometry
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2.4 Use formulae for calculations in the coordinate plane correctly,
including distance between two points, mid-point of a line
segment, slope of a line, parallel lines, perpendicular lines,
equation of a line, equation of a circle with centre (0,0) and
radius r, and tangent to a circle
For the following pair of points (1,2), (6,12) do the following
1)
2)
3)
4)
Calculate the distance between them
Find the mid point of the line Joining them
Calculate the slope of a line joining these two points
Find the equation of a line parallel to the line segment joining these two points, but passing
though the point (4,1)
5) Find the equation of a line passing through the mid point of the line segment found in 2) but
perpendicular to the line joining the two points.
6) Find the equation of a circle with center (0,0) which passes through the mid point found in 2)
7) Find the equation of a line tangent to the circle at the point found in 2)
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Fetac Mathematics Level 4 Code 4N1987 Geometry
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2.5 Construct, using drawing instruments, a variety of angles and
simple geometric shapes to given criteria to include naming of
angle types and sides associated with the shapes and angles.
1)
2)
3)
4)
5)
Draw a square with 4cm long sides
Draw a triangle with sides which have the following lengths, 4.5 cm, 6 cm, and 7.5 cm.
Draw a right angled triangle which has a height of 6cm and a hypotenuse which is 9 cm long.
Draw a triangle which contains an obtuse angle, and label all the angles appropriately
Choose one of the acute angles in the triangle drawn in 3) above and label it with the symbol
Θ, Then label the sides of the triangle appropriately.
6) Draw a circle with a 4.5 cm radius.
7) Draw a rectangle of length 10cm. and width 6 cm.
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Fetac Mathematics Level 4 Code 4N1987 Geometry
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2.6 Solve practical problems by using the correct formula(e) to
calculate the area and perimeter of a square, rectangle, triangle,
and circle, giving the answer in the correct form and using the
correct terminology.
Calculate the area of all shapes drawn in section 2.6 above and mark them on the drawing indicating
the units, and the equation used.
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Fetac Mathematics Level 4 Code 4N1987 Geometry
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2.7 Solve practical problems by using the correct formula(e), to
calculate the volume/capacity and surface area of a cube,
cuboid, cylinder, cone, and sphere, giving the answer in the
correct form and using the correct terminology.
This material is assessed by examination, however we will walk through this section in class as part
of your mathematical education in this course.
For this section we are going to pretend you are setting up a dairy company called the “Cubical
Cow”™.
1) Find the size and surface area of a 1 and a 2 liter cubical milk carton.
2) Design two shipping boxes for the milk cartons. The first should contain 12 1 liter cartons,
the second should contain 12 2 liter cartons. These boxes should be cuboid in shape.
Calculate the volume and surface area of both boxes.
3) Your customers complain that the 2 liter cubical milk carton is awkward and difficult to pour.
You decide to redesign it, and choose a cylindrical shape.
4) If the height of the cylinder is to be 20 cm, find the other dimensions and the surface area of
the new cylindrical carton.
5) You decide to sell cream in cone shaped cartons. A friend has told you that a cone with a
radius of 6cm and a height of 10cms would be large enough for 330ml of cream, with a little
space at the top. Calculate the volume and surface area of the proposed conical cream
carton, and see if your friend is right.
6) Apart from the cartons and boxes, you need a holding tank for bulk milk and bulk cream.
Choose appropriate volumes for these. These tanks will be chilled, and will be spherical, so
as to minimize the surface area. Calculate their dimensions and surface areas.
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Fetac Mathematics Level 4 Code 4N1987 Geometry
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2.8 Apply standard axioms and theorems of geometry, including
Pythagoras Theorem, to solve real life or simulated problems
involving straight lines, parallel lines, angles, and triangles.
The cluster document suggests the following in addition to Pythagoras’s theorem as mentioned
above.
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
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Ruler axiom
Protractor axiom
Axiom of parallels
Vertically opposite angles
Alternate & corresponding angles
Angles in a triangle add to 180°
In a parallelogram opposite sides are equal and opposite angles are
equal
Axiom 1. (Ruler Axiom: Line Measure)
The points on any straight line can be numbered so that number differences measure distances.
Axiom 2. (Protractor Axiom: Angle Measure)
All half-lines having the same endpoint can be numbered so that number differences measure
angles.
Axiom 3 Axiom of parallels
If a straight line crossing two straight lines makes the interior angles on the same side less
than two right angles, the two straight lines, if extended indefinitely, meet on that side on
which are the angles less than the two right angles.
Vertical angles are a pair of non-adjacent angles formed by the intersection of two straight lines.
When two lines intersect, four angles are formed. Each opposite pair are called vertical angles and
are always congruent. The red angles ∠JQM and ∠LQK are equal, as are the blue angles ∠JQL and
∠MQK. Vertical angles are also called opposite angles
Alternate and corresponding angles refer to the angles made when a line crosses two parallel lines.
Angles in a triangle add up to 180 degrees. These are the interior angles of a triangle.
Parallelogram In a parallelogram opposite sides are equal and opposite angles are equal
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Fetac Mathematics Level 4 Code 4N1987 Geometry
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 Ruler axiom
Your ruler has snapped in half, and you only have the end marked from 10cm to 25cm.
Describe how you might use this to measure the length of a pencil.
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Fetac Mathematics Level 4 Code 4N1987 Geometry
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 Protractor axiom
The same dog, that ate your ruler, also ate your protractor. Describe how you might measure an
angle, using only the part of the protractor marked from 60 degrees to 150 degrees.
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Fetac Mathematics Level 4 Code 4N1987 Geometry
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Axiom of parallels
I claim that the following pair of lines are parallel.
Draw another straight line crossing these and indicate which of the resulting angles you might
measure to either prove or disprove this claim
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Fetac Mathematics Level 4 Code 4N1987 Geometry
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 Vertically opposite angles
In the following diagram mark both pairs of vertical angles.
Test the assertion that vertically opposite angles are equal by measure the example above.
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Fetac Mathematics Level 4 Code 4N1987 Geometry
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Alternate & corresponding angles
On the following diagram mark alternate and corresponding angles.
State which of these angles, have the same angle measure.
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Fetac Mathematics Level 4 Code 4N1987 Geometry
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
Angles in a triangle add to 180°

Identify the unmarked angle in the following triangle, using the fact
that angles in a triangle add to 180°
30 degrees
90
degrees
Measure two of the angles in the following triangle and calculate the size of the third angle.
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Fetac Mathematics Level 4 Code 4N1987 Geometry
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In a parallelogram opposite sides are equal and opposite angles are
equal
Use this fact to fill in the blanks on the following shape.
5cm
long
30
degrees
3cm
150
degrees
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