Download Class notes - Nayland Maths

Starter
Expand
1) -4m2(m + 3)2 =
2)
(2 – 5x)3 =
8x y  
2xy 
4
3) Simplify
4) (extension)
2
3 2
6n1 xm1

n n 2 m1
32 x
Factorise fully
5) 11m2 – m =
6) 4x2 + 5x –21 =
7) 27px2 – 3py2 =
HW Theta pg 23 Done?
. Rearranging Formula: What do you notice? .
Make ‘x’ the subject of these equations:
1)
x= y 4
4xz2
y=
5
5y = 4xz2
5y
5y
x=
2 = x
so
4z
4z2
x+4
y=
2x 5
3x + 5
y=
2x + 3
y = x2 + 4
2)
y 4 = x2
3)
y(2x
2xy
2xy
x(2y
5) = x + 4
5y = x + 4
x = 4 + 5y
1) = 4 + 5y
4 + 5y
x=
2y 1
4)
y(2x + 3) = 3x + 5
2xy + 3y = 3x + 5
2 xy  3 x  5  3y
x2y  3  5  3y
5  3y
x 
2y  3
Rearrange formula
A formula (or equation) links numbers and variables.
4
eg V = 3 πr3
In this formula ‘V’ is the subject (the formula has V=)
eg E =
1
mv2
2
In this formula ‘E’ is the subject
We often want to change the subject of a formula.
To do this we rearrange the formula
Make ‘x’ the subject of
eg E =
1
2
mv
2
eg V =
4
3
πr3
Theta
Ex 4.01
Applications
Ex 4.02
y = 4x + 7
1) Make ‘m’ the subject
3) Make ‘r’ the subject
2) Make ‘v’ the subject
Rearranging Rational Expressions
A rational expression is a fraction with polynomials on the top and bottom.
Polynomial is a function which is the sum of terms of the form axn and n is a whole
number (Whole numbers: 0, 1, 2, 3…)
3x + 5
2
Polynomials: x2 + 4x +3
Rational
expression:
2x 3
x 2 + 3x
3
2x
+ 6x
5
NOT Polynomials:
x
3
 4x  3
2
 6x
3
5x
2x
x
5
The highest power of x is the degree of the polynomial
Theta
Ex 4.03
Make x the subject of…
1)
4y 
3
x5
2)
y
2x  1
x4
HW Theta pg 15 & 16
3)
y2
2x  3
x4