(:title Singapore Mathematics - Secondary Two :)
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[! width=270]Topic/Sub-topic
[!]Content
[!]Learning Outcomes
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[ colspan=3]%c12 exa%1 Numbers and Algebra%%
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[]%c11 pra%1.1 Numbers and the four operations%%
[]Include: none
[]
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[]%c11 pra%1.2 Ratio, rate and proportion
[]Include:
*map scales (distance and area)
*direct and inverse proportion
[]
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[]%c11 pra%1.3 Percentage
[]Include: none
[]
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[]%c11 pra%1.4 Speed
[]Include: none
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[]%c11 pra%1.5 Algebraic representation and formulae
[]Include: none
[]
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[]%c11 pra%1.6 Algebraic manipulation
[]Include:
*expansion of the product of algebraic expressions
*changing the subject of a formula
*finding the value of an unknown quantity in a given formula
*recognising and applying the special products
** {$ (a \pm b)^2=a^2 \pm 2ab+b^2 $} [[http://www.mathcasts.org/gg/student/formulas/aplusbSQ.html|%exa b%InterActivity%%]]
** {$ a^2-b^2=(a+b)(a-b) $}
* factorisation of linear algebraic expressions of the form
** {$ a^2x^2 - b^2y^2 $} (where {$ a $} is a constant)
** {$ a^2 \pm 2ab+b^2 $}
** {$ ax^2+bx+c $} [[GlossaryT/Factoring|%b exa%Whole number factorisation of {$ x^2+bx+c $}%%]]
*multiplication and division of simple algebraic fractions, e.g.
** {$ \left( {{{3a} \over {4b^2 }}} \right)\left( {{{5ab} \over 3}} \right) $}
**{$ \left( {{{3a} \over 4}} \right) \div \left( {{{9a^2 } \over {10}}} \right) $}
*addition and subtraction of algebraic fractions with linear or quadratic denominator, e.g
**{$ {1 \over {x - 2}} + {2 \over {x - 3}} $}
**{$ {1 \over {x^2 - 9}} + {2 \over {x - 3}} $}
**{$ {1 \over {x - 3}} + {2 \over {(x - 3)^2 }} $}
[]
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[]%c11 pra%1.7 Functions and graphs
[]Include:
* [[GlossaryT/LinearFunction|%exa%graphs of linear equations in two unknowns%%]]
* [[GlossaryT/QuadraticFunction|%exa%graphs of quadratic functions and their properties%%]]
**positive or negative coefficient of {$ x^2 $}
**maximum and minimum points
**symmetry
[]
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[]%c11 pra%1.8 Solutions of equations and inequalities
[]Include:
* solving simultaneous linear equations in two unknowns by
**[[Glossary/Systems2mc|%exa%substitution and elimination methods%%]]
**graphical method
*solving quadratic equations in one unknown by factorisation
*formulating a pair of linear equations in two unknowns or a quadratic equation in one unknown to solve problems >>&<<[[InterA/BoatCurrent|%exa%Complete InterActivity for the "Boat in the River Current - 2x2 Linear System%%]]
[]
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[]%c11 pra%1.9 Set language and notation
[]Include:
*use of set language and the following notation:
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[]Union of A and B
[] {$ A \cup B$}
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[]Intersection of A and B
[]{$ A \cap B$}
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[]Number of elements in set A
[]{$ n(A) $}
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[]“… is an element of …”
[]{$ \in $}
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[]“… is not an element of …”
[]{$ \notin $}
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[]Complement of set A
[]{$ A’ $}
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[]The empty set
[]{$ \emptyset $}
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[]Universal set
[]
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[]A is a subset of B
[]{$A \subseteq B$}
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[]A is a proper subset of B
[]{$A \subset B$}
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[]A is a not a subset of B
[]{$ A \not\subseteq B $}
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[]A is a not a proper subset of B
[]{$ A \not\subset B $}
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*union and intersection of two sets
*Venn diagrams
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