OKAY, FIFTH CLASS, I’ve been marking your answers to the test you did yesterday – which was supposed to see how much you remember from your maths lessons last year.

How did you get on?

Scroll down to see the answers – or click here to go back and see the questions first.

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1. Make as many three-digit numbers as you can from the digits 1, 8 and 6. Give your numbers in order, beginning with the largest.
   There are a total of six numbers you can make with any three digits. The six you should have are 861, 816, 681, 618, 186 and 168.
2. Which number is nearer to 5,000: 4,328 or 5,675?
   It’s 4,328 – just about. It’s 672 away, while the other number is 675 away.
3. How many days are there in 9 full weeks?
   7 x 9 = 63.
4. Without a calculator, multiply 26 by 37.
   This is where long multiplication comes into play. We won’t try to recap that here, but the simplest way to think of it is to break the question into two parts: 20 x 37, and 6 x 37. The answer to the first one is 740, and the second one 222. Add the two together and your overall answer should be 962.
5. If 34 children each buy one packet of sweets, per day, and there are 11 sweets in every packet, how many sweets will they have bought in the month of March?
   There are 31 days in March, 34 children, and 11 sweets in each packet. 31 x 34 x 11 = 11,594.
6. How many small boxes of eggs (with 6 each) can you fill from a crate, if the crate has 350 eggs in it?
   The trick to this question is that we’re not asking you to worry about the remainder. 350 divided by 6 is 58, with a remainder of four. You can’t fill a crate of six eggs if you only have four, so ignore the four – your answer is 58.
7. What is the lowest common multiple of each of the following sets of numbers?
   a) 4 and 6 – 12
   b) 6 and 8 – 24
   c) 6 and 9 – 18
   d) 5 and 7 – 35
   e) 5, 6 and 8 – 120
8. Express 0.05 as a fraction in its simplest form.
   0.05 is another way of saying 5/100 (that is, ‘five over a hundred’) – but that’s not the simplest way of saying it. If you divide it by five on both the top and bottom, your answer is 1/20 (‘one over twenty’).
9. In the number 6.478, express the digit in italics as a fraction.
   We want you to ignore the others – it’s 0.070 you should be paying attention to. This is 7/100.
10. Write down every (whole, positive) number which could complete the following inequalities:
    a) 3 plus __ is less than 7 – 1, 2, 3
    b) 4 minus __ is greater than 3 – There aren’t any.
    c) 8 plus __ is less than 11 – 1, 2
    d) 5 times __ is less than 34 – 1, 2, 3, 4, 5, 6
    e) (4 times 4) minus __ is greater than 11 – 1, 2, 3, 4
11. Using the names of 3D shapes, how would you describe the shape of a normal box of cereal?
    If we were using 2D names we’d say it was a rectangle – but because we’re talking about 3D the answer we want is a cuboid.
12. Identify each of the following angles as being either acute, right, reflex, straight, or obtuse:
    A quick reminder: angles less than 90° are acute, exactly 90° is right, between 90° and 180° are obtuse, exactly 180° is straight, and anything higher than 180° (and less than 360°, which is the widest possible angle) is reflex. So your answers are…
    - 33° – Acute
    - 105° – Obtuse
    - 88° – Acute
    - 89° – Acute
    - 90° – Right
    - 91° – Obtuse
    - 159° – Obtuse
    - 195° – Reflex
    - 259° – Reflex
    - 359° – Reflex
13. How many:
    a) Centimetres are there in a metre? 100
    b) Square centimetres are there in a square metre? 10,000
    c) Centimetres cubed are there in a cubed metre? 1,000,000 – one million
    d) Millilitres are there in a litre? – 1,000
    e) Square millimetres in a square centimetre? 100
14. How heavy (not including the carton) is a litre of water?
    1 millilitre of water weights 1 gram (or, at least, it does at 4°C). Therefore a litre – which is 1000 millilitres – is 1,000 grams, or 1 kilogram.
15. Write each of the following times in the 12-hour clock.
    – 15:15 – 3:15pm
    - 23:19 – 11:19pm
    - 0:00 – 12:00am
    - 11:12 – 11:12am
    - 12:00 – 12:00pm
16. If there is a one-minute break between each round, and a fight consists of four rounds with two minutes each, how much time passes between the opening bell and the closing bell of a women’s boxing match?
    The four rounds in total will be eight minutes, but you only need three breaks – there’s no break after the fourth round, because the fight has finished by then. So eight minutes of boxing, and three minutes of breaks, means the whole fight is finished in 11 minutes.
17. Katie Taylor won three matches in the Olympics. Ignore the breaks between rounds. How many minutes in total did she fight for?
    You were asked how many minutes she was fighting for – that doesn’t include breaks. Three fights, with four rounds of two minutes each, means you just multiply 3 x 4 x 2. Your answer is 24 minutes.
18. Express your answer from Question 17 in seconds.
    There are 60 seconds in a minute – so 24 x 60 = 1,440 seconds.
19. If you buy groceries worth €4.39, and you give the shopkeeper a €10 note, how much should you be given in change?
    If you’re confused by the decimal point, it might be easier if you convert the two amounts into cent. €4.61 is the same as 461 cent, and €10 is the same as 1000 cent. 1000 – 439 = 561 cent, or €5.61.
20. If the shopkeeper gave you back your change from Question 19 using coins only, what is the minimum number of coins the shopkeeper could give you?
    €2 + €2 + €1 + 50c + 10c + 1c. That’s six coins. (The trick was to see whether you used three 20c coins instead of a 50c and a 10c.)

Now, the extra question for bonus marks…

Let’s pretend you’re running a boxing competition in which 15 people are taking part. Each fight will have four rounds each, where each round has three minutes. Assuming that no fights are stopped early, how many minutes of fighting will take place before a winner has been found?
(As soon as a boxer loses, they’re out of the competition. You can ignore the breaks between rounds, and should try to make sure that every entrant has to fight as many times as possible in order to win. )

This, you probably guessed, is a little bit beyond 4th Class – but it’s an interesting little mental exercise.

The trick is to remembering that each fight can only have two people, and to figuring out exactly how many fights you need to hold.

It might be easier to work backwards: you can have 2 boxers in the final, which means 4 boxers in the semi-finals (of which there are two) and 8 boxers in the quarter-finals (of which there are four). If you put another round before that, you can have a total of 16 boxers in the previous round, with 8 fights in that round.

But you’ve only got 15 boxers, not 16. If you want to give everyone as many fights as possible, the only way to run a competition with 15 people is to put one of them into the quarter-finals automatically – that is, to give them a bye.

This means you’re only going to have seven fights in the first round, which will reduce the 14 others to 7. Then your lucky fighter, who you’ve given a bye to, rejoins the competition to make 8. From here, you run your usual quarter-finals to get down to 4, who fight in the semi-finals to go down to 2, who enter the final.

So – 7 fights in the first round, 4 quarter-finals, 2 semi-finals, and 1 final. That’s a total of 7 + 4 + 2 + 1 = 14 fights.

Now, we said each fight has four rounds, with three minutes each (and that you can ignore the breaks). This means there are 4 x 3 = 12 minutes of fighting in each match.

So how many minutes of fighting will we have? 14 fights with 12 minutes each, means 14 x 12 = 168 minutes.

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You can assume that each one of the 20 questions is worth 5% (for the questions with five parts, each one is worth 1%; in question 12, each part is worth 0.5%. This means that if you answered all 20 questions right, you get the maximum of 100%.

The last question was just for fun – but if you want to include it, we can pretend this is the CAO and give you 25% extra, for a maximum of 125%.

If you want to, you can share your results in the comments below. But remember: nobody likes a show-off…

Take the test: How would you do in this 4th Class maths test?