(:title Singapore Mathematics - Secondary Two :) >>&<< [table border=1 width=100% cellpadding=3] [row] [! width=270]Topic/Sub-topic [!]Content [!]Learning Outcomes [row] [ colspan=3]%c12 exa%1 Numbers and Algebra%% [row] []%c11 pra%1.1 Numbers and the four operations%% []Include: none [] [row] []%c11 pra%1.2 Ratio, rate and proportion []Include: *map scales (distance and area) *direct and inverse proportion [] [row] []%c11 pra%1.3 Percentage []Include: none [] [row] []%c11 pra%1.4 Speed []Include: none [] [row] []%c11 pra%1.5 Algebraic representation and formulae []Include: none [] [row] []%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 **{${1 \over {x - 2}} + {2 \over {x - 3}}$} **{${1 \over {x^2 - 9}} + {2 \over {x - 3}}$} **{${1 \over {x - 3}} + {2 \over {(x - 3)^2 }}$} [] [row] []%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 [] [row] []%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%%]] [] [row] []%c11 pra%1.9 Set language and notation []Include: *use of set language and the following notation: (:div1121 class="s8" style="margin-left:20px":) [table border=0 ] [row] []Union of A and B [] {$A \cup B$} [row] []Intersection of A and B []{$A \cap B$} [row] []Number of elements in set A []{$n(A)$} [row] []“… is an element of …” []{$\in$} [row] []“… is not an element of …” []{$\notin$} [row] []Complement of set A []{$A’$} [row] []The empty set []{$\emptyset$} [row] []Universal set [] [row] []A is a subset of B []{$A \subseteq B$} [row] []A is a proper subset of B []{$A \subset B$} [row] []A is a not a subset of B []{$A \not\subseteq B$} [row] []A is a not a proper subset of B []{$A \not\subset B$} [tableend] (:div1121end:) >>&<< *union and intersection of two sets *Venn diagrams >>&<>&<< ---- >>&<< [table width=100% border=0] [row] [][[Sg/| Attach:main/tri_purple_up_a.gif ]] [[Sg/| Up one level]] [r](:html:) (:htmlend:) [tableend]