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Mathematics Resources

Multi-topic questions

Students find questions more challenging when different topics are combined within a question and the setting of the question is slightly unfamiliar. The level of the questions available will, over time, cover Grades 3/4 to Grades 10/11 (and hopefully beyond!)

Sign up here to receive the Mathematics Questions – Newsletter. Once you sign up to the newsletter, you will receive it periodically for those mathematics questions where I can provide extra help, ideas and other support for their use in the classroom. Plus, over time, the newsletter will include feedback from teachers who have used the questions in the classroom.

The Mathematics Questions – Newsletter is now a feature of nilsbird training – the blog. Find the blog here. From Mathematics Question 17, the questions will also become a feature of the blog.

The Questions

Mathematics Questions 1 to 9 – December  2020 – February 2021

The Mathematics Questions 1 to 3 are available here in one zip file.

The Mathematics Questions 4-6 are available here in one zip file.

The Mathematics Questions 7-9 are available here in one zip file.

To receive Mathematics Questions 1 to 13, plus the supporting newsletters, sign up here for the Mathematics Questions – Newsletter.

Monday 1st March 2021

Mathematics Question 10 ratio, mean, simple algebra

This week’s question is for lower grades. Looking at handling data for the first time.

Here are two sets of data – S and T.

S T
    210   150   114   90  260  410  473  310  b

mean of set S : mean of set T = 3 : 7

Find the value of b.

Download Mathematics Question – Number 10without answers

Download Mathematics Question – Number 10 with answers

Monday 8th March 2021

Mathematics Question 11 co-ordinates, properties of quadrilaterals, critical thinking

This week’s question is another for lower grades. Looking at co-ordinates for the first time.

A quadrilateral ABCD is drawn on a co-ordinate grid.

A has the co-ordinates (3, 2). B has co-ordinates (6, 1).

a) If ABCD is a parallelogram, find possible co-ordinates for C and D.

 C is plotted at (7, 4).

b) Explain why ABCD cannot be a rhombus or a parallelogram.

Which quadrilaterals could it be?

Download Mathematics Question – Number 11without answers

Download Mathematics Question – Number 11 with answers

Monday 15th March 2021

Mathematics Question 12 3D trigonometry, bounds

This week’s question ventures into the territory of 3D trigonometry and bounds.

The diagram shows a cuboid – not to scale.

All measurements are to the nearest 0.5 m.

a) Find the upper and lower bound of length CE.

b) Show that the lower bound of angle CEG is 19.00o to 2 decimal places.

Download Mathematics Question – Number 12without answers

Download Mathematics Question – Number 12 with answers

Monday 22nd March 2021

Mathematics Question 13 – surface area and volume of prisms, ratio, pythagoras theorem

This week’s question focuses on finding the surface area of a triangular prism, via volume, ratio and pythagoras theorem.

A triangular prism has a volume of 800 cm3 with length 32 cm and AB = BC.

The ratio of the length of the triangular prism to its width, AC, is 4:1.

Find the surface area of the triangular prism.

Download Mathematics Question – Number 13without answers

Download Mathematics Question – Number 13 with answers

Monday 12nd April 2021

Mathematics Question 14 – conversion of units, scale factor (linear, area and volume)

This week’s question focuses on scale factor, with the added spice of conversion of units.

The pictures show trains.

In the left-hand picture there is an orange TGV Sud-Est and blue/white Shinkansen.

In the right-hand picture there is a Steam Loco.

Use a scale of 3.5 mm:304.8 mm in all question parts.

a) The TGV Sud-Est was in service in France for around 20 years. It was around 200 m long.

Find the length of its equivalent model in centimetres, to three significant figures.

b) A traveller on the Shinkansen is limited to two pieces of luggage.

The total of the length, width and height of a piece of luggage must be no more than 250 cm.

Suggest suitable dimensions for a model of a piece of luggage.

c) A Steam Loco has a boiler capacity of 15 000 litres.

Find the boiler capacity of the model of the Steam Loco in centimetre cubes, to three significant figures.

Download Mathematics Question – Number 14without answers

Download Mathematics Question – Number 14 with answers

Monday 19th April 2021

Mathematics Question 15 – geometric sequences, ratio, surds

This week’s question is the first to cover geometric sequences and surds, with the addition of one of my favourite inclusions – ratio.

a) A, B and C are three consecutive terms in a geometric sequence.

A:B:C is 1: 16: 256.

Suggest suitable values for A, B and C.

b) P, Q and R are three non-consecutive terms, within the first six terms of a geometric sequence.

P:Q:R is 1:9:81.

Suggest suitable values for the first six terms of the geometric sequence.

c) A geometric sequence is given as:

V, 1, (√5 + 2), Y, Z

Find the values of V, Y and Z.

Download Mathematics Question – Number 15without answers

Download Mathematics Question – Number 15 with answers

Monday 3rd May 2021

Mathematics Question 16 – area of shape, addition/subtraction of decimals/fractions, ratio

This week’s question is another offering for younger students. The first question to show calculations as the dimensions of shapes.

The diagram shows a rectangle and a triangle. (Not to scale.)

a) Without using a calculator, find the ratio of the area of the rectangle to the area of the triangle.

b) Using a calculator, or otherwise, write the answer to part a) in its simplest form.

Download Mathematics Question – Number 16without answers

Download Mathematics Question – Number 16 with answers

Sharing your students feedback

To share students’ solutions to any question, and any feedback they give you about working with the questions, email nilsbird training. They can then be shared in the Mathematics Questions – Newsletter and on this page.

To share your experiences of using any question with students, email nilsbird training. They can then be shared on this page.

Books for sale

Two ex-author copies available of Cambridge IGCSE® Additional Maths Teacher’s Guide, supporting IGCSE® and O Level Additional Mathematics syllabuses (0606/4037), examination from 2020.
£70 each plus postage.

Please email nilsbird training for further information.

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