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MATHS PROJECT

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TRANSFORMATION
GEOMETRY
TRANSLATION
- a horizontal or vertical ‘slide’ from one position to another
- the object DOES NOT change its shape or size
EXAMPLE:
Left & Right  x co-ordinate
Up & Down  y co-ordinate
 Point A has been translated to Point A’. It moved 2 units right and 1 unit up.
The rule for this translation is (x + 2, y + 1).
 Point B has been translated to Point B’. It moved 4 units left and 3 units down.
The rule for this translation is (x – 4, y – 3).
 Point C has been translated to Point C’. It moved 3 units left and 2 units up.
The rule for this translation is (x - 3, y + 2).
Left & Down  minus
Up & Right  plus
 ∆DEF has been translated to ∆D’E’F’.
It moved 5 units right and 3 units down.
The rule for this translation is (x + 5, y - 3).
REFLECTION
- a mirror image of a shape about a line of reflection
- the object DOES NOT change its shape or size
reflection about the
y-axis
y: stays the same
x: changes sign
reflection about the
x-axis
x: stays the same
y: changes sign
reflection about the
y=x line
the co-ordinates swop
around (x; y)  (y; x)
EXAMPLE:
 Point A has been reflected to Point A’ about the y-axis.
 Point B has been reflected to Point B’ about the x-axis
 Point C has been reflected to Point C’ about the y=x line.
 ∆DEF has been reflected to ∆D’E’F’ about the y-axis.
 ∆GHI has been reflected to ∆G’H’I’ about the x-axis.
 ∆JKL has been reflected to ∆J’K’L’ about the y=x line.
ENLARGEMENT AND REDUCTION
- making a shape bigger or smaller
EXAMPLE:
 ∆ABC has been enlarged to ∆A’B’C’ by a factor of 3.
 ∆DEF has been reduced to ∆D’E’F’ by a factor of ½.
*make sure that ALL the co-ordinates were multiplied/divided
TRANSFORMATION GEOMETRY
NAME:____________________
Answer the questions on this page.
GRADE:___________________
____________
1.
Translate point A 6 units left and 2 units up.
(2)
2.
Translate point B 2 units right and 4 units down.
(2)
3.
Write the rule of the translation of point C.
(2)
4.
Determine the translations:
4.1
D(4, -7)  D'(2,-4)
(2)
4.2
E(0,4)  E'(-4,2)
(2)
5.
Write down the co-ordinate if G is reflected about the x-axis.
(2)
6.
Write down the co-ordinate if H is reflected about the y-axis.
(2)
7.
Write down the co-ordinate if I is reflected about the y=x line.
(2)
8.
Reflect ∆JKL about the x-axis. Draw the reflected triangle.
(3)
9.
∆MNO is enlarged by a factor of 3. Draw the enlarged triangle.
(3)
10.
∆PQR is reduced by a factor of ½. Draw the reduced triangle.
(3)
TOTAL TRANSFORMATIONS: [25]
GEOMETRY
OF 3D
SHAPES
VERTEX - corner of the polyhedron
EDGE - side of a polygonal face
FACE - sides of the polyhedron
POLYHEDRON
VERTICES
EDGES
FACES
6
9
5
8
12
6
10
15
7
EULER'S LAW: V - E + F = 2
* if the solid's vertices, edges and faces are put in the formula
and the answer equals 2, then it is a polyhedron
GEOMETRY OF 3D SHAPES
NAME:____________________
Answer the questions on this page.
GRADE:___________________
____________
1.
Study the polyhedrons below and complete the table.
Polyhedron
Vertices
Edges
Faces
(9)
2.
3.
If a solid has 12 vertices, 14 edges and 4 faces, is it a polyhedron?
Make use Euler's law.
(3)
If a solid has 18 vertices, 17 edges and 3 faces, is it a polyhedron?
Make use Euler's law.
(3)
TOTAL 3D SHAPES : [15]
DATA HANDLING
MEASURE
DEFINITION
HOW TO CALCULATE
EXAMPLE
2, 2, 3, 5, 5, 7, 8
MEAN
average
1. add all the values
2. divide by the number of values
ODD number of values:
1. Arrange the values in order
2. Find the middle number
MEDIAN
MODE
RANGE
middle value
EVEN number of values:
1. Arrange the values in order
2. Find the two middle numbers
3. Add them together and divide
the answer by 2.
Find the value that appears the
the value that appears the most most. It is possible to have more
than one mode.
difference between the biggest
and the smallest number
Subtract the lowest number from
the highest number
1. 2+2+3+5+5+7+8=32
2. Mean = 32 ÷ 7 = 4.57
5,7,1,3,9
1. Arrange: 1, 3, 5, 7, 9
2. Median = 5
2,6,11,7,1,9
1. Arrange: 1,2,6,7,9,11
2. Median = (6 + 7)
2
= 6.5
2, 2, 3, 5, 5, 7, 8
Mode = 2 and 5
2,6,11,7,1,9,7
Mode = 7
2,6,11,7,1,9,7
Range = 11 - 1 = 10
DATA HANDLING PART 1
NAME:____________________
Answer the questions on this page.
GRADE:___________________
____________
1.
Peter rolled a dice ten times. He wrote down the numbers that the dice
landed on.
Here are the numbers:
2.
3 2 4 6 3 3 4 2 5 4
a) Calculate the mean.
(2)
b) Calculate the median.
(2)
c) Calculate the range.
(2)
d) What is the mode?
(2)
A rugby team played 7 games. Here is the number of points they scored
in each game.
3 5 8 9 12 12 16
Calculate the median.
(2)
The team played another game. They scored 11 points. Calculate the
median number of points scored in these 8 games.
(2)
3.
The following test marks were recorded from 6 girls and 4 boys.
Girls
Boys
5
2
3
5
10
9
2
3
7
3
a) Write down the mode of the 10 marks.
(2)
b) Calculate the median mark of the boys.
(2)
c) Work out the range of the girls' marks.
(2)
d) Calculate the mean of all 10 students.
(2)
TOTAL DATA HANDLING PART 1: [20]
REPRESENTING
DATA
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