Download Grade 9 Syllabus

Grade 9 Syllabus
TOPIC
H&H MYP 3 pages
site Mymaths.co.uk
ADVANCED CLASSES
follow H&H MYP4.
REQUIRED SKILLS
SEMESTER I
DIFFERENT STRATEGIES IN PROBLEM SOLVING
CALCULATOR INSTRUCTIONS
EXACT AND ESTIMATED VALUES, SCIENTIFIC
NOTATION, SIGNIFICANT FIGURES
183
1 NUMBER REVISION
A
Natural numbers
B
Divisibility tests
C
Integers
D
Order of operations
E
Fractions and rational numbers
F
Decimal numbers
G
Ratio
H
Prime numbers and index notation
27
28
30
32
34
37
41
46
50
2
A
B
C
D
E
F
G
ALGEBRAIC OPERATIONS REVISION
Algebraic notation
The language of mathematics
Changing words to symbols
Generalising arithmetic
Algebraic substitution
Collecting like terms
Product and quotient simplification
55
56
59
60
63
64
67
69
3
A
B
C
D
E
F
PERCENTAGE REVISION
Percentage
The unitary method in percentage
Finding a percentage of a quantity
Percentage increase and decrease
Percentage change using a multiplier
Finding the original amount
73
74
78
80
81
85
89
4
A
B
C
ALGEBRAIC EXPANSION
The distributive law
The expansion of (a + b ) (c + d )
The expansion rules
99
100
105
106
5
A
B
C
D
E
F
G
SOLVING EQUATIONS
The solution of an equation
Maintaining balance
Isolating the unknown
Formal solution of linear equations
Equations with a repeated unknown
Fractional equations
Unknown in the denominator
133
134
136
137
138
141
143
146
Ex: Prove the irrationality of 2 .
Binary system.
Illustration of the main principles: If A = B, then
A-B=0, An = Bn (for natural n), 1/A = 1/B.
If A=B and C=D, then A+C=B+D, AC=BD.
If A>B, B>C then A>C, -A< - B.
Expansion of radical expressions
Principal cases for linear equation:
unique solution, infinite number
of solutions and absence of solution.
6
A
B
C
D
E
F
ALGEBRA
Converting into algebraic form
Forming equations
Problem solving using equations
Finding an unknown from a formula
Linear inequations
Solving linear inequations
243
244
246
248
251
253
255
Solve: 1/x < 1; 2/(x-1) > 2
_________________________________________________________________________________________
SEMESTER II
7
A
B
8
A
ALGEBRAIC FACTORISATION
Common factors
Factorising with common factors
353
354
356
359
361
( x  y)n  4 x( x  y)n1  y( x  y) n2  ?
Difference of two squares factorising
Perfect square factorisation
(e.g.9x6 +256y18 – 96y9x3 ),
Miscellaneous factorisation
B
C
D
INDICES
Algebraic products and quotients in index
notation
Index laws
Expansion laws
Zero and negative indices
173
174
176
178
180
9
A
RADICALS AND PYTHAGORAS
Square roots
189
191
Three and more terms; conjugated radicals:
B
Rules for square roots
192
simplify: 2  3 2
C
D
E
F
G
H
Solving equations of the form xz =k
The theorem of Pythagoras
The converse of Pythagoras' theorem
Pythagorean triples
Problem solving using Pythagoras
Three dimensional problems (not Core)
194
196
202
203
205
208
Prove the Pythagoras theorem from the
identity (a+b)2
10
A
B
C
D
E
F
G
H
I
COORDINATE GEOMETRY
Plotting points
Linear relationships
Plotting linear graphs
The equation of a line
Gradient or slope
Graphing lines from equations
Other line forms
Finding equations from graphs
Points on lines
277
279
281
284
286
287
291
294
298
299
11
A
B
C
D
E
SIMULTANEOUS EQUATIONS
Trial and error solution
Graphical solution
Solution by substitution (not Core)
Solution by elimination (not Core)
Problem solving with simultaneous equations
303
304
305
306
308
311
1 4 3
Divide a segment in a given ratio
Parallel and perpendicular lines.
Find the equation of the line perpendicular
to the line 3x+4y =1 and intersecting it on
the x-axis.
Simple problems for three equations with
three unknowns
12 TRANSFORMATIONS, SIMILARITY AND CONGRUENCE 329
A
Translations
330
B
Reflections and line symmetry
331
Simple composite transformations
C
Rotations and rotational symmetry
334
D
Enlargements and reductions
337
E
Similar figures
338
F
Similar triangles
340
G
Areas and volumes of similar objects
341
H
Congruence of triangles
346
13
A
B
C
D
TRIGONOMETRY (optional)
Using scale diagrams in geometry
Trigonometry
The trigonometric ratios
Problem solving with trigonometry
453
454
455
460
464
Harder 2D and 3D problems. Example:
Deduce exact values for sin, cos and tan
of 30, 45 and 60o