**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 1 ^{st} 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 310b |

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

*Find the value of b.*

*Download Mathematics Question – Number 10 – without answers
*

*Download Mathematics Question – Number 10 *–* with answers*

*Monday 8 ^{th} 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 11 – without answers
*

*Download Mathematics Question – Number 11 *–* with answers*

*Monday 15 ^{th} 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 19.00^{o} to 2 decimal places.*

*Download Mathematics Question – Number 12 – without answers
*

*Download Mathematics Question – Number 12 *–* with answers*

*Monday 22 ^{nd} 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 cm^{3} 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 13 – without answers
*

*Download Mathematics Question – Number 13 *–* with answers*

*Monday 12 ^{nd} 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 14 – without answers
*

*Download Mathematics Question – Number 14 *–* with answers*

*Monday 19 ^{th} 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 15 – without answers
*

*Download Mathematics Question – Number 15 *–* with answers*

*Monday 3 ^{rd} 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 16 – without 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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