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Imagine a mirror with its edge placed along the dotted line, shiny side to the right. If you were to look in it, what shape would you see?

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If you think of the calculation as 95 - 67 = 28, you could turn that into an addition by rearranging it as 95 = 28 + 67. This is what you get by adding 67 (the subtracted part) to both sides.

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Your answer must be in centimetres. The smallest divisions on the ruler are millimetres. Do not try to measure the distance by putting a ruler up against the computer screen, it won't be accurate.

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You don't really need the box diagrams to solve this, but if you are stuck, notice how the number of shaded areas relates to the numerators.

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Even though Paris was colder than Rome, the temperature difference is a positive number.

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For each city, you could start with the midnight temperature and add 6, to see if that then matches the midday temperature of the same city - if so then you've got the answer.

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Before you start to do some difficult subtractions, look hard at the numbers — can you spot a simple pattern?

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Make sure you tick two answers. Clue: One is a decimal fraction, and one isn't.

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The large box is twice the size of the small box. So you might find it quicker to think of the 3 large boxes as 6 small boxes. Then it's the same as (6+2) small boxes.

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Just use the facts given in the question to find an answer. Don't jump to any conclusions.

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You don't have to do all the multiplications and divisions if you are good at making estimates and spotting simplifications. For the first statement, you can make an estimate. 11 x 12 is close to 10 x 12. (The difference is only 12). 15 x 10 is clearly much bigger, because 15 is quite a lot more than 12.  In the second statement, you can simplify things if you spot that 90 ÷ 30 is the same as 9 ÷ 3, and 60 ÷ 20 is the same as 6 ÷ 2.  In the fourth statement, all of the numbers of the right-hand multiplication are bigger than those on the left-hand side, so the right-hand side must be a bigger number.

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Quick revision of some terms: Faces means sides. Think of a dice. It has six sides = that's six faces. Vertices really just means corners. An edge is where two faces meet. If you were to draw a cube you'd probably just draw the edges. The edges meet at corners (vertices).

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Some things to remember: The order of a coordinate pair is (X, Y), not (Y, X). Translation does not cause rotation, reflection or scaling.

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All the answers are in eighths. So start by converting the 6 into eighths. (It helps if you can remember your 6 times table, because you'll need to know 6 X 8). Then you can add on the seven eighths to get the total number of eighths.

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There are several ways to tackle this. For example you could find a common denominator, and convert them so they all have the same denominators, then compare numerators. The bigger numerator would indicate the bigger number. That's quite a slow method. Or you could convert them so they all have the same numerators, then compare denominators. The one with the smaller denominator would be the bigger number. That's also quite a slow method. Or you could spot that one of the numbers is bigger than the number one, and the others are smaller than one, so you know which is the biggest of the three. Then you've made a start and it's easier to compare the remaining two. Maybe you can even imagine what fractions look like. Would you rather have three-fifths of your favourite pie or three quarters of it? What would six-fifths of a pie look like?

Hint

First of all, how many melons are there in one box? On a piece of paper, write down your method. There is less chance of a mistake when you write things down. And in the real test your method can gain you a mark, even if you get the final answer wrong.

Hint

Mental methods are usually based on doing the maths in simple stages. In the suggested methods, which stages would make any sense?

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Start by working out how much orange juice the 28 children drink. Multiply the amount each child is given by 28. Is there any left? Always make notes on paper to show your method because even if you make a mistake you might pick up a mark or two for method, in the real test.

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To calculate the mean, you need to work out the total cost and divide by the number of tickets.

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It's easy enough to round each part to the nearest whole number, and that's generally a good way to make estimates because it's quick and the errors tend to balance out. But when you only have a very few numbers to deal with, keep an eye on the errors introduced by rounding. If the errors are all in the same direction, it might change the overall result. (If you really don't like working in mixed fractions, you might find it easier to convert the three numbers to decimals.)

Hint

You could work out the estimated lengths of each alligator and then subtract the smaller length from the larger. That's three calculations. Or you could save yourself some effort and simply work out the difference between the two eye-nose distances, and multiply this difference by 12. That's only two calculations, and the numbers are smaller too, and so easier to handle. Here's why this works: (A x 12) - (B x 12) = (A-B) x 12

Hint

You'll need to use algebraic equations to solve this. An example of an algebraic equation is 2A + B = 10. A and B are the names of numbers we don't know. In this case, we want to know the numbers Amina has chosen for her shapes. Instead of simply asking her, which would be sensible, we can work them out if we have enough information. And we do. THE SLOW WAY: To work out the values of two such unknown numbers, we need at least two equations. On a piece of paper, see if you can write down two algebraic equations, one for each of the designs. To start off, give each shape a name, such as A and B. Amina has at least told us the total value for each design; you'll need these in your equations. Once you have your equations, rearrange one of them so you have an equation of the form A = {something here with B in it}.  Now you 'know' what A is, in terms of B. So you can use this in the other equation, giving you an equation that's only got B's in it plus some numbers.  By rearranging it, you can solve it for B. Once you have the value of B, you can put this value into the first equation and solve it for A. THE FAST WAY: Spot the difference between the components of the two designs. One design has an extra hexagon. The total values differ; the difference must therefore be the value of one hexagon.

Hint

You'll need to use algebraic equations to solve this. An example of an algebraic equation is 2A + B = 10. A and B are the names of numbers we don't know. In this case, we want to know the numbers Amina has chosen for her shapes. Instead of simply asking her, which would be sensible, we can work them out if we have enough information. And we do. THE SLOW WAY: To work out the values of two such unknown numbers, we need at least two equations. On a piece of paper, see if you can write down two algebraic equations, one for each of the designs. To start off, give each shape a name, such as A and B. Amina has at least told us the total value for each design; you'll need these in your equations. Once you have your equations, rearrange one of them so you have an equation of the form A = {something here with B in it}. Now you 'know' what A is, in terms of B. So you can use this in the other equation, giving you an equation that's only got B's in it plus some numbers. By rearranging it, you can solve it for B. Once you have the value of B, you can put this value into the first equation and solve it for A. THE FAST WAY: Spot the difference between the components of the two designs. One design has an extra hexagon. The total values differ; the difference must therefore be the value of one hexagon. The question tells you that the right-hand design has a value of 111; given this information you should be able to figure out a value for one of the smaller grey shapes.

Hint

The volume of a cube is equal to the length of one side, cubed. i.e. multiplied by itself, twice. You're only given one dimension here, and it isn't the length of a side. What is it the length of?

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Break the problem down into small parts that you can solve separately. 5823 has two parts: 58 and 23