KELSO HIGH SCHOOL MATHEMATICS DEPARTMENT

GENERAL BLOCK 5
REASONING & ENQUIRY HOMEWORK
[1] / A parallelogram is made by
tiling eight congruent triangles.
Four are shaded.
aCalculate the area of the tiling
bWhat area is shaded? / [4]
[2] / A football stall is set up at a fair.
A board with five holes is fixed to goalposts.
The front of the board is to be painted.
The board is 73 metres by 24 metres.
The holes are 45 cm in diameter.
Calculate the area to be painted.
(Be careful with units!) / [6]
[3] / A fish tank is shown in the diagram.
The water in the tank is 20 cm deep.
What volume of water could be added to
the tank before it overflows? / [6]
[4] / This vase is cylindrical.
Its base has a radius of 6 cm.
The height of the vase is 22 cm.
It contains 2036 litres of water.
What is the depth of the water in the vase? / [6]
[5] / Write down a formula for calculating the perimeter, P cm, of these shapes.
All lengths are in centimetres.
[6]
[6] /
aComplete the table:
No. of trapezia (n) / 1 / 2 / 3 / 4
No. of matches (M)
bWrite down the formula for calculating M when you know n.
cUse the formula to find how many matches are needed for 33 trapezia.
[5]
[7] / The diagram below shows the fan belt from a machine.
The fan belt passes around 2 wheels whose centres are 30 centimetres apart.
Each wheel is 8 centimetres in diameter.
Calculate the total length of the fan belt. / [5]
[8] / (a)The edge of a stock cube measures 1.5 centimetres.
Calculate the volume of the stock cube.
(b)A number of the above stick cubes are packed into a cuboid box.
The box is 6 centimetres long, 3 centimetres broad and 9 centimetres high.

How many stock cubes are needed to fill the box ? / [6]
[9] / Amy needs to replace fencing in her garden.
She has taken the measurements shown above, but has forgotten to measure the part of the fence marked x metres.
The garden centre has only 28 metres of fencing in stock.
Is this enough to completely replace the existing fencing ? / [4]

TOTAL = 48 MARKS