Maths

GCSE Maths revision cards

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  • Created by: catherine
  • Created on: 31-10-08 12:32

1.Simplifying.

Expanding brackets
use the 'beak' method
Remember:
RxR=Rsquared, TYsquared means TxYxY BUT (TY)Squared means TxTxYxY
if theres a minus outside the bracket, it REVERSES ALL SIGNS when you multiply.

If the brackets are squared,write out the two brackets, and then use beak method.

Factorising into brackets
putting brackets in
EG.
Xsquared+8x+15
What add together to make 8?
but times together to make 15?

answer=
(x+5)(x+3)

If it =0 dont forget the x=? or ?

Rearranging,changing the subject
remember, if you swp the sides, the sign changes
and if theres brackets, work them out first using beak method

EG.
make X the subject:
Y=5(X+7)
Y=5X+35
[-35]
Y-35=5X
[/5]
Y=-35
------- = X
5

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2. SOLVING.

Linear Equations
finding the unkown value.
1)
6x + 4 = 22

2) 22x + 6 = 16x - 30

3) 2 + x - 89 = 75

To solve number 1 you need to get rid of the 4 on the left-hand side (LHS) of the equation by subtracting it BUT...you need to subtract 4 on the right-hand side (RHS). When you've done this, you should end up with this:
6x = 18
To get x =(what you want), you need to divide the LHS and the RHS by 6. This reads:
6x/6 = 18/6
(Note: If you had 6x/6 = 18, you would just multiply both sides by 6) 6x/6 equals x (the two sixes cancel). 18/6 = 3. Therefore x = 3.

Right then, onto number 2.
22x + 6 = 16x - 30
Subtract 16x from both sides.
22x (- 16x) + 6 = 16x (- 16x) - 30
6x + 6 = - 30
Subtract 6 from both sides.
6x + 6 (- 6) = -30 (- 6)
6x = -36
Divide both sides by 6.
6x (/6) = -36 (/6)
x = - 6.

And finally... Number 3!
2 + x - 89 = 75
Add 89 to both sides.
2 + x - 89 (+ 89) = 75 (+ 89)
2 + x = 164
Subtract 2 from both sides
2 (- 2) + x = 164 (- 2)
x = 162

Simultaneous Eqautions
Simultaneous equations are two equations with two unknowns. They are called simultaneous because they must both be solved at the same time.

The first step is to try to eliminate one of the unknowns.

EG.
Solve these simultaneous equations and find the values of x and y.

  • Equation 1: 2x + y = 7
  • Equation 2: 3x - y = 8

Add the two equations to eliminate the ys:

  • 2x + y = 7
  • 3x - y = 8
  • ------------
  • 5x = 15
  • x = 3
  • Now you can put x = 3 in either of the equations.
  • Substitute x = 3 into the equation 2x + y = 7:
  • 6 + y = 7
  • y = 1

So the answers are x = 3 and y = 1

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3. Graphs

Quadratic Graphs
The general form of a quadratic is "y = ax2 + bx + c". For graphing, the leading coefficient "a" indicates how "fat" or "skinny" the parabola will be.

For | a | > 1 (such as a = 3 or a = –4), the parabola will be "skinny", because it grows more quickly (three times as fast or four times as fast, respectively, in the case of our sample values of a). For
| a | < 1 (such as a = 1/3 or a = –1/4 ), the parabola will be "fat", because it grows more slowly (one-third as fast or one-fourth as fast, respectively, in the examples). Also, if a
is negative, then the parabola is upside-down.

Straight line graphs
horizontal and vertical lines: "x=a" and "y=a"
x=a is a vertical line through "a" on the x-axis
y=a isa horizontal line through "a" on the y-axis
Remember:
the y-axis is also the line x=0, the x-axis is also the line y=0

the main diagonals: "y=x" and "y=-x"
y=x is the main diagonal that goes UPHILL from left to right.
y=-x is the main diagonal that goes DOWNHILL from left to right.

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