When you are asked to do a currency conversion, you will usually be given an exchange rate first, as in this question:

“George changes some pounds into Euros. The exchange rate is £1=€1.18. If he changes £350 into Euros, how many Euros will he receive?”

Draw a simple Ratio Grid and give headings of £ and €. Put the numbers 1 and 1.18 in the correct columns. Then, the final number from the question, £350, goes in the £ column under the 1. Putting the numbers into their correct places is easy if you have headings! Put a ring around the empty space – that is where your answer will go.

In this grid, the 2 multiplying numbers are the “1.18” and the “350”, and you will divide by 1. So the sum will be 1.18×350÷1.

The answer is 413, and it is clearly in the Euros column, so give your answer as €413.

It’s easy if you get the headings right!

If you want lots of practice, Mr Corbett has a great set of currency conversion questions.

** Some of these questions are really challening – they may require 2 ratio grids, so think carefully! If an exchange rate changes, you will need a new grid for the new rate.

Ratio Grids can be used whenever you have a problem that starts with 3 numbers, and you have to times and divide. They are a clear way of laying out your working, and knowing which order to do the calculation.

You will need a calculator to do the practice questions, but first, here are 2 videos. The first shows you how to solve a small ratio grid, the second deals with the larger ones:

This post is practicing simple equations. In 3 days there will be another one to change the subject of more simple equations. If you write your answers in the box at the bottom I will check them and reply to you. I won’t publish them on the page though!

“I am forty-one years older than you” is my point of view. In algebra language I would write R=C+41

What’s your point of view?

C=R-41

Looking at some of the people in my family then,

R=D+26 (I am 26 years older than D, my oldest daughter)

What’s her point of view?

D=R-26

Now let’s look at another relationship in my family,

R=G+28

Who is older? R or G?

R is older than G, by 28 years.

so how would G see it?

G=R-28

Now here’s something you can work out, given I am 54 at the moment,

How old is C?

How old is D?

How old is G?

One more person in my family is T. R=T (that’s my point of view) How old is T?

What is T’s point of view, in other words write T=…

We have just spent 2 lessons on Trigonometry and here is the writeup as promised. You were getting everything right but these notes are in case you forget a small step and need to revise.

Sorry you couldn’t remember SOH CAH TOA, but it’s really quite complicated, what with labelling the triangle, writing out SOH CAH TOA, remembering which way round they go, what they mean and how to use them…

So anyway we were just using the SINE RULE and CROSS SUMS to find the missing side or the missing angle.

Before you start, make sure you have revised

Cross Sums

Pythagoras’ Theorem

Finding an unknown side, given a right angled triangle, with one known side and one known angle.

Work out the value of the missing angle and write it into the correct corner. (For example, the 3rd angle in a 90/42/? triangle would be found by doing 180-90-42=)

Draw a cross sum. In the top line, write the KNOWN SIDE and an x (or ?, or whatever the exam is calling the side you are looking for. In the images below we labelled it “?”)

Underneath the KNOWN SIDE write down the sin of its opposite angle

Underneath the “?” side, write the sine of its angle. That’s sin(?)

Write down the sum you plan to type into your calculator

And do it!

Write the answer back on the diagram and check it looks sensible

Finding an unknown angle given a right angled triangle, with two known sides.

If the Hypotenuse is unknown you will have to use PYTHAGORAS’ Theorem to find it, first.

Draw a cross sum. In the top line, write the KNOWN SIDES and an x (or ?, or whatever the exam is calling the side you are looking for. In the images below we labelled it “?”)

underneath the known sides, write sin(of their opposite angle), one should be sin(90), the other will be sin(?)

Write down the sum you plan to type into your calculator

This time the cross sum’s answer will be weird (0.67834 in the example below) and you need to write sin(?)= 0.67834 or whatever.

You found the sine of the angle – to find the angle itself, press Shift, Sin, ANS, =

Write the answer onto the diagram and check it looks reasonable.

If the hypotenuse and one other side is given, then you wont need Pythagoras. So its easier.

I am grateful to Mr. Holding who teaches locally for this link. So simple! Lots of GCSE questions presented one at a time. A couple of examples are reproduced below.

From the dice, construct 2 or perhaps 3 numbers. For example, if you throw a two and a three, you can make 5, 23 and 32 (3+2=5, two followed by three is 23 and three followed by two is 32)

Score one point for each prime number you have made (so this example scores one for the 5 and one for the 23, scoring two points in total).

For a collection of questions that encourages students to *think* about mean and median rather than just crunch numbers, there’s no resource to beat this one that is available free to download from the TES site. (You will need to create a TES login account – that’s free too).