Download Pre-Learning - Mathematics Mastery

Pre-Learning
Assessment
Year 8 Module 3: Geometry
Name: ………………………………………………………………….
Class: ……………………………………………………………………
Teacher: ……………………………………………………………….
You need:
 A Pen
 A Pencil
 A Ruler
 A Protractor
 A Compass
You DO NOT need:
 A Calculator
What are we learning this half term?
Unit 5: Constructing Triangles and Quadrilaterals

In this Unit you will practise measuring, identifying, naming and drawing angles. You will learn to define a variety of
triangles and quadrilaterals, and to construct them from a given set of properties.
Unit 6: Length and Area – Parallelograms and Trapezia

In this Unit you will learn to convert between common units for area, and develop your understanding of area and
perimeter by investigating parallelograms and trapezia. You will extend this further through worded problems and
composite shapes.
Pre-Learning Assessment Mark:
50
Teacher Comment:
1) Write the mathematical name below each of these quadrilaterals.
(4)
2)
a) Tina measures the angles in a triangle. The sketch shows her results.
Not drawn accurately
How can you tell that Tina has made a mistake?
………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………
(1)
b) Using a ruler and protractor draw a triangle with one angle of 35° and one angle of
45°. Use the line below as one side of the triangle.
_____________________________
(2)
3)
The grids below are made up of squares.
a) On this grid, draw a triangle
with no right angles.
(1)
b) On this grid, draw a quadrilateral
with no right angles.
(1)
4)
Construct a triangle with lengths 7cm, 5cm and 8cm. Do not rub out your construction
lines.
(3)
5)
a) Construct a triangle with a base of 5 cm and two angles of 60°
b) What type of triangle have you drawn?
………………………………………… (3)
6)
The diagram shows a sketch of a rhombus, side length 8 cm.
Not drawn accurately
A
The size of angle A is 100o.
Use a ruler and protractor to make an accurate drawing of the rhombus.
(3)
7) An isosceles triangle has one angle equal to 80°.
(a) Write one set of possible sizes of the angles in this triangle
.................°,
..................°,
..................° (1)
(b) Write another set of possible sizes of the angles in this triangle
..................°,
..................°,
..................° (1)
8)
Look at the right-angled triangle below.
Not drawn accurately
The shaded square fits exactly inside the triangle.
Work out the sizes of angles x, y and z
x = ............................°
y = ............................°
z = ............................°
(3)
9)
This diagram shows a line intersecting two parallel lines. Find the size of the missing
angles x and y.
Not drawn accurately
x = ............................°
y = ............................°
(2)
10) In this diagram the two parallel lines are marked with arrows. Work out the value of y
Not drawn accurately
y = ……..…….. (2)
11) The diagram shows a rectangle that just touches an equilateral triangle.
Not drawn accurately
a) Find the size of the angle marked x
Show your working
....................° (3)
b) Now the rectangle just touches the equilateral triangle so that ABC is a straight line.
Not drawn accurately
Show that triangle BDE is isosceles
(2)
12) All of the squares in these grids are 1cm by 1cm
(a) By doing calculations, show that the rectangle and the triangle have the same area.
(2)
(b)
What is the area of this shaded trapezium?
.................. cm2 (1)
13) What is the area of this parallelogram? Give your answer in cm2.
5m
6m
Not drawn accurately
8m
............................... cm2 (3)
14) The diagram shows four identical white rectangles around a shaded square.
Not drawn accurately
What is the area of the shaded square?
............................... (3)
15) What is the area of this shape?
Show your working.
Not drawn accurately
............................ cm2 (4)
16) Cyril wants to do some work in his garden. He has a rectangular patio. He decides to tile
it using 50cm by 50cm tiles.
Not drawn accurately
a) How many tiles does he need so that there are no gaps?
............................. (3)
b) The following formula is used to calculate the cost of paving.
Cost (in £) = number of tiles x 4 + 25
Can Cyril pave his patio for less than £250?
........................... (2)
Finishing Task
You will need colouring pencils for this.
In 1852 a mathematician called William Guthrie investigated how many colours he would need to
colour in a map so that no countries of the same colour would share a border.
This is good; the two
yellow countries
don’t touch
This is good; it’s ok if
they just share a
corner
This fails; the two
lilac countries share
a border
This works, but could
it use fewer colours?
On the space below make up your own bigger map, give it at least 20 countries (or shapes). Try to
colour it in using the least number of colours possible. Can you work out the minimum number of
colours required for ANY map? (If not don’t worry – it took Mathematicians 124 years and a
computer to prove how many colours are needed!)