# Blog

## Aircraft Registrations

 Difficulty: Rating: GCSE Marks:

GCSE Text:
All aircraft in the UK have a unique registration code painted on the side. The code has 5 letters of the alphabet, each A-Z. For the UK, the first letter must be a ‘G’ followed by a dash and then four more A-Z letters that can repeat.

example: A helicopter has the registration of G – HPDG

a) How many unique codes exist for UK aircraft?

For ‘lighter than air’ aircraft (hot air balloons and airships), there are extra rules. In addition to starting with a ‘G’ and dash, the second letter must be an ‘F’ and this time the letters must not repeat.

example: A hot air balloon has the registration of G – FBES

b) How many unique codes exist for ‘lighter than air’ aircraft in the UK?

Suggestions:
This is a good consolidation question for students who have learned listing strategies and probability outcomes and they will need to consider the repeating or non-repeating nature of the codes. Some students like to sketch a probability tree diagram whilst other just remember the rule of multiplication. students as the method is not specified in the question. Students need to select the appropriate trigonometric approach to take as well as consider different units. The extension task works well for higher paper GCSE students too.

Teachers could extend the learning by considering:

• Because aircraft codes are never reused, even for retired or scrapped aircraft, available UK codes are running out as new aircraft are being made. A suggestion is to add an extra letter on the end in future. How many more codes would a 6 letter pattern create compared to the existing 5 letter pattern?

## Patio Tile Cuts

 Difficulty: Rating: GCSE Marks:

GCSE Text:
As part of a patio laying project, a square tile needs to be cut according to the design shown in this diagram.

An angle grinder is used to cut the tile, and the cut speed is 1mm per second. How long will it take to make the cut on this tile? Give your answer in minutes and seconds.

Suggestions:
This is a good starter question for GCSE students as the method is not specified in the question. Students need to select the appropriate trigonometric approach to take as well as consider different units. The extension task works well for higher paper GCSE students too.

Teachers could extend the learning by considering:

• It is the triangle that is needed as part of the patio, the trapezium will be discarded. What percentage of the full time will be discarded? Give your answer rounded to 1 d.p.

## Porcelain Primer

 Difficulty: Rating: GCSE Marks:

GCSE Text:
A patio consists of 92 porcelain tiles, each one measuring 600mm x 600mm. Each tile needs to have a primer painted to the underside before getting placed onto the cement bed.

The primer is supplied in tubs, each tub containing 2 packets of dry power and each packet covering 8m² when mixed with water.

How many tubs of primer are needed to complete the patio?

Suggestions:
This is a good question to test students’ understanding of area, particularly with mixed units. Students normally take 3-4 minutes to answer. The extension task works well for higher paper GCSE students too.

Teachers could extend the learning by considering:

• The tiles are 18mm thick and are supplied in packs of 2. Each pack weighs 25kg. What is the density of the porcelain? Give your answer in g/cm³.

## Time Lapse Videos

 Difficulty: Rating: GCSE Marks:

GCSE Text:
Charlie’s video camera normally records smooth video at a rate of 25 frames per second.

Today though, Charlie is using it in time lapse mode, where one frame is captured every 15 seconds instead. He records in time lapse mode for 2 hours continually.

a) When the time lapse recording is played back at 25 frames per second, how long will the clip last (in seconds)?

b) The camera has the option to play back at a faster 30 frames per second rate. How much shorter will the clip last if it is played back at this faster rate?

Suggestions:
This is a good question to test students’ understanding of worded questions. Normally words like ‘per’ need to be highlighted, and this is easily a non-calculator arithmetic question. Students take 1-2 minutes to answer this question in full.

Teachers could extend the learning by considering:

• The normal frame resolution is 1280 x 720 pixels, but has a full HD option of 1920 x 1080.   How many more pixels are there in a full HD frame than the normal frame?

## Expanding Sponge

 Difficulty: Rating: GCSE Marks:

GCSE Text:
A sponge is supplied in a vacuum sealed pack. The thickness of the sponge will expand when it is released from the packet. The sponge thickness currently measures 12mm and on the label it says that the packed thickness is one fifth of the final sponge thickness.

a) What will be the final thickness of the sponge when it is released from the packet?

b) The label also says that the product weight has been reduced by 40% by supplying the product vacuum sealed. If it weighs 24g whilst sealed, how many grams of plastic packaging have been saved per sponge by provided it vacuum sealed?

Suggestions:
Whilst the first question is accessible to all, many students struggle with the numbers on the second question. Discussions normally flow surrounding the percentage that we have or have lost, and of course the sponge is a constant so it’s only the plastic weight that is being affected by the reduced size.

This works well as a consolidation for reverse percentage learning, and students take 3-4 minutes to answer this question in full.

Teachers could extend the learning by considering:

• Before vacuum packing was introduced, a trade box could hold only 30 sponges. How many can it hold now that it contains vacuum packed sponges instead?
• What other benefits are associated with vacuum packing the sponges?

## Inflating Mattress

 Difficulty: Rating: GCSE Marks:

GCSE Text:
A new mattress arrives as a rolled up vacuum sealed cyclinder. The mattress is laid out flat as shown below, but air needs to be allowed into the packaging so it inflates to its final cuboid shape. As the mattress expands, the width and length won’t change, but the depth will increase significantly. The current depth is just 15% of the final depth of the mattress.

What is the difference in the finished volume of the mattress, and the volume of the cyclinder that was delivered?

Suggestions:
This question stretches the most able GCSE students. For those that don’t know where to start, it is always useful to remind them that marks are awarded for part of the final answer even if not completed. As no formulae are given for a question like this, the question works well to consolidate volume learning.  Students take 3-4 minutes to answer this question in full.

Teachers could extend the learning by considering:

• Express the inflated volume as a percentage of the packed volume

## Chimenea Surface Area

 Difficulty: Rating: GCSE Marks:

GCSE Text:
A garden chimenea is made from a frustum with a circular base and a cylindrical chimney on the top. The legs are made from metal cut from the opening in the front. Here is the design for the chimenea body:

Calculate the area of metal used to construct the chimenea, giving your answer in cm² and rounded to the nearest whole number.

Suggestions:
This question stretches the most able GCSE students. Many students assume that some measurements are missing (they’re not), and often benefit from drawing the frustum as two separate cones.  Students can be confident of being given the formula for the curved surface area of a cone in a GCSE exam. This question is a good consolidator once students have learned cones, cylinders and similar shapes. Students take 5-6 minutes to answer this question in full.

Teachers could extend the learning by considering:

• A smaller chimenea is on offer where all measurements in the diagram are 10% less. By what percentage will the area of metal be reduced?

## Cog Ratios

 Difficulty: Rating: GCSE Marks:

GCSE Text:
A handle is attached to cog A that has 8 teeth. This small cog meshes with a medium size cog B that has 16 teeth, and this medium size cog meshes with a large cog C that has 20 teeth.

a)  Express the number of teeth on cog A to cog B to cog C as a ratio in its simplest form.

The handle is turned once per second.

b)  How many times will cog C rotate per hour?

c)  If an Engineer needs to replace cog C with a different cog that will turn 600  times per hour, how many teeth will the replacement cog need to have?

Suggestions:
This question overlaps nicely with Physics learning and encourages students to employ higher order thinking to apply learning on ratio and circle circumference.  Often much discussion occurs regarding the need for calculators or for diameters, but this could easily appear on a non-calc Higher GCSE paper. Students take 4-5 minutes to answer this question in full.

Teachers could extend the learning by considering:

• If the handle on cog A was turned anticlockwise, which direction does cog C turn? What link is there between the number ‘n’ of the cog in the sequence, and the direction in which it turns?

## Waffle Sharing

 Difficulty: Rating: GCSE Marks:

GCSE Text:
A family of 2 adults and 3 children need to share 3 waffles between them.

a)  What fraction of a waffle will each person receive if the waffles are shared equally between 5?

b)  The three children insist that their portion is provided in a single piece of waffle (no cuts). What will be the size of the reflex angle at the centre of each waffle for them to receive the correct amount in a single piece?

c)  The waffles each measure 9cm in diameter. What area of waffle does each person receive? Give your answer rounded to 1 d.p.

Suggestions:
This question works well as a consolidate to work on sectors of circles. Often the second question confuses students, so getting them to sketch a waffle generally helps to visualise what is being asked and clarifies the presence of a reflex and obtuse angle when cutting.  Students take 3-4 minutes to answer this question in full.

Teachers could extend the learning by considering:

• The thickness of each waffle is 3mm, and 20% of each waffle is made from caramel filling. What volume of caramel will each person receive in their share?

## Rollercoaster Distance & Speed

 Difficulty: Rating: GCSE Marks: