- further mathematical topics and techniques such as integration, coordinate geom-
etry, Laplace transforms - solving systems of linear equations occurring in electrical circuits, chemical reac-
tions, etc. - solving differential equations
- numerical methods and statistics
2.1 Review
2.1.1 Multiplication of linear expressions ➤^4073 ➤➤
Expand the brackets in the following expressions
(i) −(x− 3 ) (ii) 2x(x− 1 ) (iii) (a− 3 )( 2 a− 4 )
(iv) (t− 3 )(t+ 3 ) (v) (u− 2 )^22.1.2 Polynomials ➤^4374 ➤➤
Expand and simplify into polynomial form
(i) x^3 − 2 x+ 1 + 3 (x^4 + 2 x^3 − 4 x^2 −x− 1 )
(ii) (x− 2 )(x+ 3 )
(iii) (x− 1 )^2 (x+ 1 )
(iv) ( 2 x− 1 )(x^2 +x+ 1 )2.1.3 Factorisation of polynomials by inspection ➤^4575 ➤➤
A. Factorise (i) 3x^2 + 6 x (ii) u^2 − 16
B. Factorise (i) x^2 −x− 2 (ii) x^3 − 2 x^2 −x+ 2
(iii) 3x^2 + 5 x− 22.1.4 Simultaneous equations ➤^4875 ➤➤
Solve the simultaneous equations
2 x−y= 1
x+ 2 y= 22.1.5 Equalities and identities ➤^5076 ➤➤
DetermineAandBif
A(x− 3 )+B(x+ 2 )≡ 4