Mathematics Questions (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.
On this page you will find multi-topic questions for various grades. Over time, the questions will, hopefully, cover Grades 3/4 to Grades 10/11 (and maybe beyond!)
Every three questions a Mathematics Questions – Newsletter is produced to support the use of the multi-topic questions in the classroom. Mathematics Questions – Newsletter is a feature of nilsbird training – the blog. (From Mathematics Questions – Newsletter No. 4 onwards.)
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Previous Mathematics Questions – Newsletters
Mathematics Questions – Newsletters 1 to 3 are available here. They provide support for Mathematics Questions 1 to 9 – December 2020 – February 2021
The Questions
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.
The Mathematics Questions 10 to 13 are available here in one zip file. They are supported by Mathematics Questions – Newsletter No. 4. This is part of nilsbird training – the blog, found here.
The Mathematics Questions 14 to 16 are available here in one zip file. (They are not currently supported by a newsletter.)
Wednesday 8th September 2021
Mathematics Question 17 – the skill of thinking, example 1
time (12 hour/24 hour clock, timetables), fractions – GRADES 5 through 8
This week’s question is the first in a mini series focusing on the skill of thinking. Rather than having particularly difficult mathematics, the student is presented with the need to think through a detailed situation to arrive at an answer.
Abdul lives in Gonnersburg. He travels, once a week, on the train to see his nephew, who lives in Carlson. The journey takes 57 minutes.
It takes Abdul 23 minutes to walk from his house to the train station and he always likes to arrive 10 minutes before a train is due to leave.
Train departures between Gonnersburg and Carlson are shown below:
| First train | Last train | |
| Gonnersburg to Carlson | 04:35 | 22:05 |
| Carlson to Gonnersburg | 04:55 | 22:25 |
Trains leave every 30 minutes in both directions.
On Thursday 14th August Abdul travelled to Carlson. He spent 4 hours 27 minutes with his nephew. He also spent ¾ of an hour shopping. He arrived home again at his house at 19:43.
a) What was the latest time Abdul could have left home to start his journey?
(Provide a complete, convincing argument to justify your answer.)
When Abdul was shopping, he bought a 3-DVD boxset of the documentary ‘Southern African Safari Adventures’. Each DVD contained 9 episodes. Each episode was 55 minutes long.
b) Abdul decided that he wanted to watch the complete boxset, in the evenings over several days, with his friend Mo. However, he only had time to watch the DVDs during the week, and he arrived home from work at 6:45 pm and went to sleep by 10:40 pm.
Suggest a suitable schedule that Abdul and Mo followed that allowed for breaks and time to discuss the episodes.
(Think about: what are the implications for watching a TV/DVD screen for too long? are there recommended time limits that it would be advisable to follow? how much time would a discussion take?)
Download Mathematics Question – Number 17 – without answers
Download Mathematics Question – Number 17 – with answers
Monday 20th September 2021
Mathematics Question 18 – the skill of thinking, example 2
money, percentages including percentage discount – GRADES 5 through 8
This week’s question is the second in a mini series focusing on the skill of thinking. Rather than having particularly difficult mathematics, the student is presented with the need to think through a detailed situation to arrive at an answer.
The table shows information about two books:
| Published | Retail Price | |
| Fishing For Beginners | September 2021 | $23.00 |
| 20 Songs For Every Occasion | December 2019 | $17.50 |
The two books can be purchased at Azop.com, an online store, or Reading For Pleasure, a bookstore found at Main Square, Tannersville.
Both of the stores have their own membership schemes to entice people to become regular customers.
The table shows information about the membership schemes:
| Membership Cost | Benefit | New Member Offer | |
| Azop.com | $2.50 per month | 1 point = 3.5 cents
$3.50 fixed postage charge on all purchases |
1 month free plus 5% discount off the first purchase |
| Reading For Pleasure | $4.50 per month | 1 point = 0.7% | 1 month free plus $2.00 discount off the first purchase |
Customers collect points based on the number of purchases they have made. These points can then be used to obtain discounts off future purchases.
Ashrif and Sidra are friends, who both live in Tannersville. Ashrif is a keen fisherman and Sidra loves singing. Ashrif is a member of the Reading For Pleasure scheme. He has collected 15 points. Sidra is a member of the Azop.com scheme. She has collected 150 points.
a) Decide which store is the cheapest way for Ashrif and Sidra to purchase the two books.
(Provide a complete, convincing argument to justify your answer.)
b) Find the percentage saving that Ashrif and Sidra make when they purchase their books at the cheaper store.
c) Suggest other suitable benefits that the membership schemes could provide for regular customers.
Download Mathematics Question – Number 18 – without answers
Download Mathematics Question – Number 18 – with answers
Mathematics Question 19 – the skill of thinking, example 3
money, time, percentages including percentage discount – GRADES 5 through 8
This week’s question is the third in a mini series focusing on the skill of thinking. Rather than having particularly difficult mathematics, the student is presented with the need to think through a detailed situation to arrive at an answer.
Kingswood Bowling Alley has the following opening times for ten-pin bowling:
| Mon to Fri | Sat/Sun | |
| October to March | 09:00 – 20:00 | 08:00 – 23:00 |
| April to September | 08:00 – 22:00 | 07:00 – 01:00 |
The prices for bowling are as follows:
| 12 years old and under | Over 12 years old | Special offer | |
| By the game | $7.69 | $9.49 | N/A |
| Daytime by the hour – until 17:00 | $14.89 for 2 hours | $17.79 for 2 hours | N/A |
| Late Night Pass – 22:00 until closing time | $18.69 per person |
Unlimited bowling | |
Groups of four, or more, have a 10% discount on their first game. If two, or more, games are booked, a 15% discount is provided.
Pierre, Sidra, Mo and Nat are four friends (all adults), who are planning to go bowling, together, on a regular basis; around once, or twice, a month. They are thinking about varying their playing times between the daytime and the evening.
a) Plan a suitable schedule that the four friends could follow, over a period of six months, between February and July. Think about what prices they will pay.
b) Modify your plan, planning some dates to cover occasions when:
- not all of the friends can bowl together
- the friends only have one hour to spare to go bowling
- younger family members (less than 12 years old) are also included
c) Investigate the scoring of ten-pin bowling. Plan a suitable two-game scenario, showing what scores the four friends achieved for both games.
Download Mathematics Question – Number 19 – without answers**
** there is no answer version as the answers from students will vary.
Mathematics Questions 17 to 19 are supported by Mathematics Questions – Newsletter No. 5. This is part of nilsbird training – the blog. It can be found here.
Mathematics Question 20 – the skill of thinking, example 4
time, fractions, speed/distance/time – GRADES 5 through 8
This week’s question is the fourth in a mini series focusing on the skill of thinking. Rather than having particularly difficult mathematics, the student is presented with the need to think through a detailed situation to arrive at an answer.
Amira Zulu and Verity Dwali are members of Erstwile Running Club. They are both training for the Erstwile Marathon.
As part of their preparation, Amira Zulu and Verity Dwali took part in a 20 km time trial*. This event took place around Erstwile town centre on Saturday 16th October.
* the idea of a time trial is to run as fast as you can over a fixed distance.
At the time trial, the ten runners were sent off at fixed time intervals, with 2 minutes between each runner. The ten runners’ positions were as follows:
| Position | Time sent off | Name of runner |
| 1st | 09:00 | Alison Serilaki |
| 2nd | 09:02 | Amira Zulu |
| 3rd | 09:04 | Honey Bwenza |
| 4th | 09:06 | Golden Bwenza |
| 5th | 09:08 | Verity Dwali |
| 6th | 09:10 | Tiny Serilaki |
| 7th | 09:12 | Beauty Nbola |
| 8th | 09:14 | Sarah Mweemba |
| 9th | 09:16 | Catherine Tinamba |
| 10th | 09:18 | Mary Luzamba |
Amira Zulu ran the first kilometre at an average speed of 8 km/h. She then ran the rest of the distance at an average speed 11 km/h.
Verity Dwali ran the first kilometre at an average speed of 9 km/h. She then ran the next 10 km at an average speed of 13 km/h and the rest of the race at an average speed of 10 km/h.
a) Find Amira Zulu’s and Verity Dwali’s average speed, in km/h, for the whole race.
b) Did Verity Dwali overtake Amira Zulu at any point during the race?
(Provide a complete, convincing argument to justify your answer.)
c) Who crossed the finish line first, Verity Dwali or Amira Zulu?
(Provide a complete, convincing argument to justify your answer.)
d) Write a suitable scenario that enables Beauty Nbola to overtake Honey Bwenza during the race.
Download Mathematics Question – Number 20 – without answers
Download Mathematics Question – Number 20 – 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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