This video is quite long so you might want to watch it in two sittings, but it does explain clearly what higher GCSE students need to know about transformation of graphs. Thank you Ukmathsteacher!
Maths is fun has a good explanation of this with some nice interactive activities and questions. Bitesize activities are here.
Thanks to Ron Barrow for this helpful example of how to use probability tree diagrams. 158,411 views is impressive! You need to know this if you are taking the GCSE Higher paper.
This video by Luke Redding is also very clear and takes the topic a bit further because it includes experiments where the item is not replaced.
Maths is fun also explains this well and includes some interactive questions. GCSE Bitesize is another good site to test yourself on this.
Some students find it incredibly difficult to visualise nets being folded up into 3 dimensional shapes. The best way to gain confidence with this is having fun making lots of different shapes and I have already blogged about an excellent site for this where you can print off all sorts of nets and make some amazing shapes. With exams rapidly approaching you may not have time for that so here is a page from Nrich where you can watch 24 different nets being folded up to make 3d shapes. Before you press play each time try to work out what the shape will look like when it is folded, then see if you were right.
If you are studying GCSE you need to be able to draw and recognise graphs of simple functions, both straight lines and curves. If you are at college your computer might have software on it such as Omnigraph. If you are at home you can download free open source software that does the same job, called “Graph”. You can read more about Graph and download it here. When you have downloaded it experiment with different functions and see what happens to the graph. To enter x² you have to use x^2.
Here are some ideas of functions to try.
y=x, y=2x, y=3x, y=4x etc
y=x+1, y=x+2, y=x+3 etc
y=-x, y=-2x, y=-3x etc
y=x-1, y=x-2, y=x-3 etc
y=x^2, y=x^2+1, y=x^2+2 etc
y=x^2+x, y=x^2 +2x, y=x^2 +3x etc
y=x^3, y=x^3 +1, y=x^3 +2 etc
Here is a crossword to help you with some of the important vocabulary you need for statistics at GCSE level. You can do the interactive version or print off a paper copy and check you answers later on the interactive version. There are a few non-mathematical clues!
Do you understand the difference between a formula, expression, identity and equation?
A formula is a rule written using symbols that describe a relationship between different quantities. Typical maths formulae include
A = πr² (area of a circle)
C=πd (circumference of a circle)
An expression is a group of mathematical symbols representing a number or quantity. Expressions never have equality or inequality signs like =, >, <, ≠ ,≥ ,≤. Some examples
3a
3xy + 4x
t² + t³
An identity is an equation that is always true, no matter what values are chosen.
Examples
3a + 2a = 5a
x²+x² = 2x²
5 x 10 = 10 x 5
An equation is a mathematical statement that shows that two expressions are equal. It always includes an equals sign.
Examples
x² =100
3x(x+5)= 42
(x+3)(x-2)=0
Use this exercise to make sure you understand the difference.
I am becoming increasingly concerned by students who seem to have developed a complete addiction to their mobile phone! Many struggle to concentrate for a minute without having to check their device. So, mobile phone addicts, here is my solution to get you engaged in maths again! Download these great apps, and prepare for your GCSE. They both have limited free versions so you can try them out, but the price for the full version is very reasonable and much less than a revision book.
https://play.google.com/store/apps/details?id=com.webrich.gcsemathslite
GCSE students need to be able to work out the equation of a graph from what it looks like.
If it’s a straight line graph you just need to look for two things.
1. The Intercept. This is where the line crosses the y axis.
2. The gradient. This is the steepness of the line. If the line goes up from left to right it will be positive. If the line goes down from left to right it will be negative. The larger the number the steeper the line.
This example shows the line y=2x-4. The line goes up two units for each unit it goes across. The gradient is 2÷1=2. It crosses the y axis at -4, so the intercept is -4.
Mathematicians use y=mx+c as the general formula for any straight line. The gradient is m and the intercept is c.
Try this exercise to see if you can match the graphs with their equations.
Try this exercise to see if you can match the equations with the correct gradient and intercept.
Great video from Numberphile that explains the controversy!
In the last exercise you learnt how to factorise quadratic expressions. We will now use this in order to solve simple quadratic equations.
Suppose x²+9x +20 = 0
If we factorise we get (x+4) (x+5) = 0
In other words, two numbers multiply together to make 0. This means one of those numbers must be 0!
So we know EITHER x+4 = 0 OR x+5 = 0
If x +4 = 0 x = -4
If x+5 =0 then x=-5
So the solution is x = -4 or -5
Remember quadratic equations will nearly always have 2 solutions.
Try this- you will probably need pencil and paper to factorise the equations first.
To solve simple quadratic equations you need to be able to factorise quadratic expressions, like x²+9x +20
To do this look for a pair of numbers that add up to 9 and muliply together to make 20.
If you can’t find the right pair, write down all the pairs of factors of 20.
1 x 20
2 x 10
4 x 5
Now we can see the correct pair is 4 and 5.
So x²+9x +20=(x+4)(x+5)
Check this by multiplying out the brackets.
Lets try one involving negative numbers.
x² -x -12
The pairs of factors of -12 are
-12 x 1
-6 x 2
-4 x 3
-3 x 4
-2 x 6
-1 x 12
The pair that add up to -1 (because there is -x in the expression) are -4 and 3
So x² -x -12=(x-4)(x+3)
If you are studying GCSE you need to learn the names of all the parts of a circle. This should help!
Circle Vocabulary
My Higher GCSE students really enjoyed using this tool to discover Circle Theorems this week. Highly recommended!
