Circles

Inflating Mattress

May 6, 2020May 6, 2020Leave a comment

Difficulty:

Rating:

GCSE Marks:
5-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?

Mattress Inflate

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

April 13, 2020April 13, 2020Leave a comment

Difficulty:

Rating:

GCSE Marks:
5-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:

chimenea

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

April 8, 2020April 8, 2020Leave a comment

Difficulty:

Rating:

GCSE Marks:
5-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

March 31, 2020March 31, 2020Leave a comment

Difficulty:

Rating:

GCSE Marks:
4-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?