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Algebra





 DAYTOPIC NOTES 
  ALGEBRA 

 



 LEARNING OUTCOMES  WORK  RESOURCES
 EXPANDING BRACKETS

5(x+3),-5x(2x-1)


 EX.24.1
EX.24.2
PPP24.1 BRILLIANT INTRODUCING THE CONCEPT OF EXPANDING 

PPP24.1 EXPAND A BRACKET
 EXPAND AND SIMPLIFY

4(x+3) + 5(x-2)
decimal 0.5(x+2) + 0.25(x+8)


 
EX.24.3
EX.24.4
 
JIGSAW EXPAND A LETTER AND A BRACKET
 FINDING THE NTH TERM
IN A SEQUENCE

2, 5, 8, ..., 3n-1
 
PHOTOCOPY
 
POWER POINTS
 FACTORISING
A number as a common factor
6a + 9b + 21c
 

EX.24.5
EX.24.6
 
 FACTORISING
A letter as a common factor
pq + pr, 2pqr - qr

 

EX.24.7
 

 A power as a common factor
3x2 + 5x, x3 + x2 - x

 EX.24.8

 
 SOLVING EQUATIONS

Simple equations
x + 5 = 61, x - 5 = -6



Simple eq's involving mult/div
11x = -132, -8x=-48

Mixed simple eq's
x/4 = -2, 0.2x=3
 


EX.25.1



EX.25.2, EX.25.3


EX.25.4
EX.25.5(NUMBER MACHINES)


 


PPP25.1 INTRODUCING EQS
PPP25.1 SOLVING EQS INV SUM AND MINUS
PPP25.1 SIMPLE EQS TEST

PPP25.2 SOLVING EQS INV MULT AND DIV

PPP25.4 SOLVING EQS INV SUM,MINUS,MULT AND DIV

WORD25.4 SOLVING EQS USING NUMBER LINE
 USING EQ'S TO SOLVE PROBLEMS

Perimeter problems, etc

 
EX.25.6

 
 SOLVING EQUATIONS (II)

Eq's with x on both sides
4x+2=x-7,15-2x=17-3x

 

EX.25.7
 
WORKSHEET
BALANCE METHOD

PPP25.7 EQS INVOLVING X BOTH SIDES
WORD.25.7 REVISION
 USING EQ'S TO SOLVE PROBLEMS (II)

Rectangle problems 2x+1=x+5
 

EX.25.8
 
 SOLVING EQUATIONS (III)


Eq's with brackets
3(x-8)=9,


 5(4-3x)-2(10-x)=5x

Eq's that link fractions
x/10=4/5
(X+2)/2=(2X-5)/3

Eq's add/subt alg fractions
x/2+x/3=5,x-4=x/4+20
x/2+(x-3)/3=4

 


EX.25.11


EX.25.12
EX.24.13


EX.25.14
EX.25.15
 


PPP25.11 EQS INVOLVING BRACKETS
PPP25.11 BINGO SOLVING EQS
NOT THIS YEAR
 INEQUATIONS
2x<6,2(x+5)<x+8
 
EX.25.16
 
PPP25.16 INEQUALITIES ON NUMBER LINE
EXPANDING A PAIR OF BRACKETS

Revision expand one bracket
-10(x+2) 
Revision collecting like terms
x2-10x-2x+20
Revision expand and simplify
x(x+4)+2(x+4)


Expand and simplify
(x+3)(x+2), (x+8)(x-11)


(x+2)2,(x-15)2


(x+2)(x-2),(x+0.1)(x-0.1)

(2x-3)(x+1),(4x-3)(3x-1)

 


EX.26.1

EX.26.2

EX.26.3



EX.26.4


EX.26.5


EX.26.6

EX.26.7

 









PPP26.4 EXPAND BRACKETS
PPP26.4 EXPAND USING BOX

PPP26.5 EXPAND (a+b)2 (geometric demo)


EXCEL26.7 EXPAND QUADRATICS
 FACTORISING QUADRATICS WITH a=1

Both positive
x2+7x+12, x2+6x+9

A negative and a positive
x2-5x-14,x2-16x+39

Only two terms
x2+2x,x2-81

A mixture of all types

 


EX.26.8


EX.26.9


EX.26.10

EX.26.11
 

PPP26.8 FACTORISE QUADRATICS

WORD26.8 INVESTIGATION FACTORISING QUADRATICS


 FACTORISING QUADR WITH ANY a

a common factor
2x2+14x+20,4x2+28x-72
 


EX.26.12

 

JIGSAW FACTORISE DOMINO
 2D GRAPHS

Reading information from a graph

Distance-time graphs



A reminder on Plotting points






Complete table to fit the rule y=2x
(Connect the idea of M=3T)

Using EXCEL to plot y=3x-5


 

EX.27.1

EX.27.2



EX.27.3






EX.27.4

EX.27.5
(ICT ROOM)


 

WORD27.1

PPP27.2 MATCHING SITUATION AND GRAPH


PPP27.3.A FIRST QUADRANT

PPP27.3.B FOUR QUADRANTS

PPP27.4 DRAW LINES
(1ST PART)
POSITIVE  GRADIENTS

Find grad from a line and vice versa.

Find grad from an eq

NEGATIVE GRADIENTS

Find grad from a line and vice versa.

Find grad from an eq and draw them
 

EX.27.6

EX.27.7



EX.27.8

EX.27.9
 

PPP27.6 INTRODUCE LINES MEANING OF M AND C
 INTERCEPTS

Find the y-intercept AND draw lines

Generalise the method to draw any line
y=4x-1, y=-5/3x+4



EX.27.10 


EX.27.11

 




PPP27.11 LINES 
USING M AND C

 HORIZONTAL AND VERTICAL LINES

y=1, x=-2
 

EX.27.12
 

PPP27.4 DRAW LINES
(2ND PART)
 USING STRAIGHT-LINE RULES

Applications in real life


 EX.27.13
 

PPP27.13 TRAVEL GRAPHS
 PARABOLAS

Trajectory of a rugby ball
y=x2+1,x2+5x,(x-3)2+2,x2-x-6
 


EX.27.14
 


PPP27.14 DRAW QUADRATIC
                       
                 

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