Essentials!
Question
1 : Algebra :
(a)
Linear Algebra : You must be able to solve linear equations
in ,one ,two and three variables (Simultaneous equations)(b)You
must be able to solve inequalities . (c)You must be able
to prove and use the factor theorem . (d) You must be
able to use the remainder theorem .
Question 2: Algebra :
Quadratic
Equations :(a) You must be able to solve a quadratic equation
.(b)You must know the rules which connect the roots to
the coefficients of a quadratic equation . (c) You must
know the conditions for which a quadratic equation has
(i)Real,(ii)Unreal,(iii)equal roots .(d)You must be able
to solve a difference equation . (e)You must be able to
solve an inequality involving indices .
Question 3:Matrices /Complex Numbers :
(a)You
must be able to add,subtract,multiply,2x2 matrices . (b)You
must be able to find the inverse of a 2x2 matrix and be
able to solve a matrix equation . (c)You must be able
to deal with complex numbers both in Cartesian (x + iy)
form and in Polar form (Cosx + i Sinx). (d)You must be
able to solve equations of the form 
.Conjugate
roots theorem appeared in ,99 might be worth a look at
Question 4 :Sequences and Series :
(a)Must
know the formulae for Un and Sn of an AP and a GP . (b)
Must know Sáof a GP . (b)To do this question you must
be very familiar with all aspects of the properties
of AP's,and GP's.Question 4 is the main sequences
and series question it often contains an equation in 
see
99.98,997,96 this can be very easy
Question 5: Series /Induction/Logs :
(a)You
must be able to prove all of the following by Induction
(i)Sums of Series (ii)Inequalities (iii)That a given number
is a factor of a given expression ,(b)Must be able to
solve equations involving Logs .(c)You must be able to
use the Binomial expansion,you must be able to use the
general term to find specific terms ,you must know the
properties of Binomial Coefficients .(d)You must be able
to find Un ,Sn and S of a telescopic type series ,You
must be able to find Un,Sn,S of an APGP .
Question 6 :Differential Calculus :
(a)You
must be able to differentiate functions using the product,quotient,and
chain rules (b)You must be able to differentiate implicit
functions . (c)You must be able to use calculus to find
the turning points on a curve .(d)You must be able to
find the Asymptotes of a curve .
Question 7 : Differential Calculus :
(a)You
must be able to differentiate specific functions from
first principals (can appear in Q6orQ7) ;(b)You must be
able to use calculus to solve problems involving distance,speed
,time and rate of change problems in general,(c)You must
be able to differentiate functions in parametric form
.Newton Raphson has been a particular favorite
in this question in recent years.
Question 8 : Integral Calculus :
(a)You
must be able to integrate standard integrals (b)You must
be able to use substitutions in particular the udu substitution
. (c)You must be able to use integration to find (i)the
Area under a curve (ii)the volume formed by rotating
a function about an axis (objects formed can only be cones
or spheres) .(d)The last part of this question may be
quite difficult be well prepared .
General Comments :
(a)The
marking scheme is as follows (i)Each question is broken
into three parts a = 10 marks,b = 20 marks,c = 20 marks
.(ii) Attempt marks will be awarded for any step in the
right direction (iii)Errors are marked as follows, - 1
for a slip a small arithmetical error ,-3 for a blunder
a technical error . (iv) The same mistake is never punished
more than once ie you cannot lose marks more that once
for a repeated error . (v)The order in which the questions
are attempted is not important . For some students the
best advice is to do all the part a and b's first then
come back and do the more difficult part c's.
Proofs on this paper (1)Factor theorem(2)Induction(3)The
Calculus proofs from first principals
,
makes proving the product rules and quotient rule in calculus
a lot easier 
Higher
Level Paper 1
