BGS - 04. Formulae and Equations Flashcards
Changing the Subject of Formula
The golden rule in rearranging a forumla is that what you do to one side, you do to the other.
We know that the circumference of a circle equation is,
C = 2πr
How do we make r the subject
To leave r on its own, we need to divide both sites by 2π
c/2π = 2πr/2π
2π / 2π is the same as 1, so this cancels it out, leaving us with the formula
c/2π = r
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Working with Indicies and Roots in Formula
The opposite of a squared number is a square root. The opposite of a cubed number is a cubed root.
Make r the subject
A / π = r²
If r squared is the same as A / π this means the square root of A / π must be the same as r.
√(A / π ) = r
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Powers and Roots Formulae
When written in algebra format, a number infront of a letter followed by a superscript means
number x letter^n
i.e.
4c² ⋉ 4 x c x c x c
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Powers and Roots Formulae
Similar to when multiply or dividing numbers which are powered (i.e. 3² x 4²) you use the same method of adding powers when the sides are multipled, and subtracting the powers when they are divided
p^4 x p^2
4 + 2 = 6
Becomes..
p^6
p^4 / p^2
4 - 2 = 2
Becomes..
p^2
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Powers and Roots Formulae
If variables are multipled by numbers, the numbers in the equation follow normal multiuplication and division rules.
4s^3 x 3s^2
3 + 2 = 5
4s x 3s = 12s
Becomes..
12s^5
8t^7 / 2t^3
7 - 3 = 4
8t / 2t = 4t
Becomes..
4t^4
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Powers and Roots Formulae
Where a variable has no index, this is the same as being the power of 1
For example, what is y x y^2
y x y^2
⋉
y^1 x y^2
We know when multiplying variables that have powers, we add the powers
So..
1 + 2 = 3
Becomes..
y^3
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Mixed Term Expressions
It is possible in algebra to group like terms and simplify.
What is the simplifed term of
3p^2 + 2p +4 - 2p^2 + 5
Start by grouping like terms;
3p^2 + 2p +4 - 2p^2 + 5
Becomes..
(3p^2 - 2p^2) + 2p + (4 + 5)
Becomes..
p^2 + 2p + 9
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Mixed Term Expressions
Where you are given a value for a variable, this can be used in an equation to provide a numerical answer.
Simplify
3p^2 + 2p +4 - 2p^2 + 5
where p = 3
3p^2 + 2p +4 - 2p^2 + 5
(3p^2 - 2p^2) + 2p + (4 + 5)
p^2 + 2p + 9
Replace p with 3
Becomes…
3^2 + (2 x 3) + 9
(3 x 3) + 6 + 9
9 + 6 + 9
= 24
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Equations with Brackets
In an equation with brackets and variables, it is easiest to multiply out the bracket first.
Make C the subject;
5(c + 2) = 35
Multiply out the brackets first;
5(c + 2) = 35
Becomes..
(5 x c) + (5 x 2) = 35
⋉
5c + 5 x 2 = 35
5c + 10 = 35
5c + 10 - 10 = 35 - 10
5c = 25
5c / 5 = 25 / 5
c = 5
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Simultaneous Equations
Where you are given 2 equations with two unknown variables, you need to try and eliminate one of the unknowns to get a value for the variables.
Find the values of x and y for;
equation 1: 2x + y = 7
equation 2: 3x - y = 8
First eliminate the y’s by adding the 2 equations together
(2x + y = 7) + (3x - y = 8)
Remember to group similiar variables.
In this example, y cancels itself out
Becomes…
2x + 3x = 7 + 8
5x = 15
Get x on its own, divide both sides by 5
x = 3
Now we have value for x, this can be substituted in either of the equations to work out y
2x + y = 7
(2 x 3) + y = 7
6 + y = 7
6 + y - 6 = 7 - 6
y = 1
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