ALGEBRA
LINEAR SIMULTANEOUS EQUATIONS.
2005 I 1a,
2004 I 2a, 2002 I 2a, 2000 I 2a, 1998 I 1a, 1996 I 2a, 1994 I 1b
NON-LINEAR SIMULTANEOUS EQUATIONS
EXAMPLE
Solve the simultaneous equations:
SOLUTION
2003 I 2a, 2001 I 2a, 1999 I 2a, 1997 I 2a, 1995 I 2a, 1994 I 2a.
FACTORS
2004 I 1c, 2000 I 2c.
SURDS
EXAMPLE
SOLUTION
2004 I 1a, 1999 I 1a, 1996 I 1a.
INDICES
2005 I 1 b(i).
ALGEBRAIC FRACTIONS
EXAMPLE
Express the following as a single fraction in its simplest form
SOLUTION
2004 I 1b(ii) (includes indices), 2003 I 1a, 2000 I
1a.
FACTOR THEOREM
Know the
proof of this for cubics and quadratics.
Group like powers together and use the difference of two cubes and the
difference of two squares to get a common factor of (x-a) for each term.
2005 I b(ii), 2004 I 1b(i), 2003 I 1b(i), 2001 I 1b, 2000 I 1b, 1998 I 1b, 1997 I 1b,
1996 I 1b(i), 1995 I 1b.
ALGEBRAIC MULTIPLICATION
2000 I 2b(ii).
ALGEBRAIC DIVISION
2005 I 1c,
2003 I 1b(ii), 2003 I 2b(ii), 2001 I 1c, 2000 I 1c, 1999 I 1c, 1997 I 1c, 1996
I 1b(i), 1994 I 1c.
UNDETERMINED COEFFICIENTS
2001 I 1a, 1995
I 1a.
INEQUALITIES
Modulus
Inequalities
EXAMPLE
SOLUTION
2005 I 2a, 2003 I 2b(i),
2001 I 2b(i), 1998 I 2a.
Quadratic Inequalities
2002 I 2b(i).
Fraction Inequalities
EXAMPLE
SOLUTION
Multiply both
sides of the inequality by the square
of the denominator.
This kind of quadratic is positive outside
the roots i.e. when
2004 I 2b(i), 1999 I 1b, 1996 I 2b(i), 1995 I 1c(i).
Graphing Inequalities
1996 I 1c(i), 1995 I 1c(ii).
Other
2000 I 2c, 1999 I 2c, 1998 I 2c, 1995 I 2c.
SUBSTITUTION
2005 I 2c,
2004 I 2c, 2002 I 2b(ii), 1999 I 2b, 1997 I 1a, 1997 I 2c, 1996 I 1b(ii)
1996 2b(ii) 1995 I 2b(ii), 1994 I 2c.
SOLVING CUBIC EQUATIONS
METHOD:
Find one solution, x = a by guessing and substituting.
Divide by x – a and solve the resulting
quadratic.
2005 I 2b, 2002 I 1b.
QUADRATICS
NB: The coefficient of x2 must be 1 for the above to apply.
2004 I 2b(ii) 2003 I 2c(ii), 2001 I 2c, 1995 I 2b(i),
1994 I 2b.
Minus B Formula
2004 I 2c(ii), 2003 I 1c, 2002 I 1c, 2002 I 2c.
Equations Which Transform Into a Quadratic
2003 I 2c(i), 2002 I 1a,
2000 I 2b, 1998 I 1c, 1997 I 2b, 1994 I 1a.