Assignment 6 – GeometryMathematics C10139
MATHEMATICS
FETAC Level 4(C10139)
Assignment 6 (Geometry)
INSTRUCTIONS TO THE CANDIDATES
- Enter your name below.
- Complete the questions in the space provided.
- Extra space is available at the back of this document if required.
- Use of a scientific calculator is allowed.
- Use of the formulae provided is allowed.
Name: ______
Date: ______
Construction
- Construct squares with sides of:
- 4 cm
- Construct rectangles with sides of:
- 4 cm by 3 cm
- Accurately construct the following parallelograms:
- Construct right-angled triangles with:
- Base = 5cm and height = 3½ cm
- Base = 4½ cm and height = 3 cm
- Construct isosceles triangles such that:
- Two sides are 4cm and the base is 5cm
- Base is 4½ cm and the base-angles are 45° each.
- Construct equilateral triangles with sides of:
- 3½ cm
- 4cm
- Construct circles such that:
- Radius = 3cm
- Diameter = 7cm
- Accurately construct the following composite-shapes:
- Rectangle (5cm x 2cm) and semi-circle.
- Square (3cm) and Isoceles triangle with a perpendicular height of 2cm.
- Construct cubes with sides of:
- 3 cm
- 3½ cm
- Construct cuboids with the following dimensions:
- 4 cm x 3 cm x 2 cm
- 3 ½ cm x 3 cm x 2 ½ cm
Pythagoras’ Theorem
- Find the diagonal length of a rectangular playing field of 100m x 35m.
- If a ladder is placed 2m away from a wall which is 3m in height and the ladder just reaches to the top of the wall, then how long is the ladder?
- TV screens are measured on the diagonal. What size is this screen?
- A man holds a string 2m long, level with the top of his head. The other end of the string is in the ground 120cm from his feet. How tall is the man?
- If Antrim is 120 miles due North of Dublin and Galway is 140 miles due West of Dublin, then how far is it from Antrim to Galway, as the crow flies?
3 figure bearings
Use the map to calculate the 3-figure-bearings for the following:
- Donegal Belfast______
- Gaillimh Belfast______
- Dublin Cork______
- Gaillimh Cork______
- Cork Belfast______
Perimeter and Area
Calculate the perimeter and area of each of the following shapes:
- Square of side 4cm.
Perimeter = ______Area = ______
- Rectangle of sides 4 cm x 2 cm.
Perimeter = ______Area = ______
- Parallelogram with base 10 cm and perpendicular height of 3 cm.
Perimeter = ______Area = ______
- Triangle with base 5 cm and perpendicular height of 5 cm.
Perimeter = ______Area = ______
- Circle with radius = 7cm. Take .
Perimeter = ______Area = ______
Surface Area and Capacity
A school has to replace the oil tank. One of the tanks being considered is cuboid in shape. The following details were obtained: length 2.5 metres; width (breadth) 1.5 metres and height 1.2 m.
The tank will have to be painted all over with two coats of paint before use. The paint comes in 5 litre tins and costs €17.50 per litre. Coverage in normal use: 9 m2 per litre.
In order to install the tank and have it painted the school will have to employ a person for 3 days @ €120 per day.
The tank will have to be filled with oil @ 82c per litre.
Calculate:
- The capacity of the tank.
- The cost of the tank including VAT and delivery charges.
- The cost of the paint for the tank.
- The cost of filling the tank with oil.
- The total cost to the school for buying, installing, painting and filling the tank.
- What is the tanks capacity in gallons if 1 gallon = 4.55 litres.
The second option is a cylindrical tank. It has a diameter of 1.6m and is 2m long. The oil company will install this tank for €1,200 (the cost of the oil is extra).
Calculate:
- The capacity of this tank.
- The total cost of installing and filling the tank.
Which tank would you recommend the school to buy? Outline your reasons for the recommendation.
______
Conversions
Complete the following statements.
(a).1,300 mm = ______cm= ______m
(b).1,542 m = ______km
(c).A square tile with side 200 mm covers an area of _____ mm2 or ______cm2 or ______m2.
(d).A farm covering 200,000 m2 could be measured as _____ ares or ______hectares.
(e).3,000 cm3 is ______litres.
(f).A box with a capacity of 3 m3 holds ______cm3.
(g).Someone who is 5’ 2” measures ______m.
(h).There are ______pints in 3 litres of milk.
(i).There are 103 miles or ______km from Dublin to Belfast.
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