How to get an A grade in GCSE maths
A or A* GCSE maths
Getting an A or A* in GCSE maths requires learning some very simple arithmetical rules. Many A and A* questions are based on knowing how to manipulate such things as equivalent fractions. B Grade questions are often based on no more than manipulating 3x2=6. So you get 3 = 6/2 or 2 = 6/3. The rule being any multiplying number jumping over an equal sign becomes a divider. A grade questions often conform to 2/3 = 4/6 and here you need to realise that so long as you know 3 out of 4 numbers , you can always find the missing number. The rule is to cross multiply the 2 numbers and use the other one as a divider. So if 2 was the missing number you would calculate (3x4) /6 = 2. Or if 6 was the missing number (3x4)/2 = 6. Another useful thing to realise is that when you cross multiply they will be equivalent. So you get 3x4 = 2x6. Getting an A grade in maths is easily achievable
What I have just shown you is how these simple arithmetical rules can be applied to solving algebra, trigonometry, formula and even percentage questions. Now I will give you examples of GCSE questions that apply to these simple arithmetical rules. Before doing this I will state a more basic arithmetical rule. Numbers that are involved in adding or subtracting turn into their opposites when they jump over the = sign. So 6+ 4 = 10 becomes 6 = 10-4 when the 4 jumps over and 6 - 2 = 4 becomes 6 = 4 +2 when the -2 jumps over. Only multiplying numbers become dividers when they jump over the = sign.
Let's try some algebra
a) X/3 = 2 so x = 3x2 ....x = 6
3x = 12 so x = 12/3.....x=4
b) (3x +8)/5 = 4 so 3x+8 = 20
3x = 20 - 8
3x = 12
c)(3x+2)/5 = (2x+8)/4
Simplest way to solve this is to cross multiply both sides because they are equivalent.
12x +8 = 10x + 40
12x- 10x = 40 - 8
2x = 32
x = 32/2
x = 16
Re- arranging formula
a) v = u +at make a the subject
u +at = v (no mathematical change)
at = v - u
a = (v- u) /t
b) this one is a bit trickier
a = 1/p + 1/q make p the subject
This is in the same form as 7 = 1/0.2 + 1/0.5
You can see that if you remove the numerators i.e the 1's then they need to be multiplied by the number 7
So 7x 0.2 x 0.5 = 0.2 + 0.5 Now we have it on a straight line so it is easy to continue.
Going back to the problem
apq = p+q
apq - p = q
now we need to factorise
p(aq -1) =q
p = q/ (aq-1)
Ok this was trickier because we had two numerators and had to factorise but if you want an A* you must know how to do this. If you are happy with an A don't let it worry you.
A grade the sine rule
This is for non right angled triangles when you need to find the length of a side or an angle.
the rule is a/sinA = b/sin B
This is not an explanation of the rule just an example of how it is just based on knowing how to manipulate 2/3 = 4/6
a/ sin 50 =6/ sin 48 We know 3 out of 4 numbers. The sin 48 and sin 50 are stored in the calculator.
So a = (sin 50 x 6) /sin48
All we had to do was cross multiply and use the other number as a divider.
You may be interested in a hub I wrote about "How to get a grade C in GCSE maths. "
I always forget how to do that bluey link thing.