Essentials!
Question
1 Volumes and Area
(a)
(i) Must be able to find the length of an arc and the
area of a segment of a circle (a) (ii)Must be able to
find the area of a rectangle ,cube ,triangle.
(b)Must
be able to use Simpsons role in all situations . (c) Must
be able to find the volume of a figure which may contain
a ,cylinder,cone ,sphere ,hemisphere (formula for the
hemisphere is not in the tables )
Question
2 : The Line :
(a)(i)You
must know all the formulae (ii)Must be able to find the
slope of the line ax + by + c = 0 (b)Must be able to find
where a line cuts the axes . (c)Must be able to find the
equation of a line perpendicular to a given line .(d)You
must be able to find where two lines intersect (e)Must
be able to use Symmetry and translations . (f)Must be
able to find the area of a triangle,parallelogram.
Question 3: The Circle:
(a)Must be able to find the
centre and radius of 
.
(b) Must be able to find the points of intersection of
ax + by + c = 0 and 
.
(c) Must be able to find the equation of a tangent at
(
) on 
.
(d)Must be able to find the centre and radius of 
.
(e) Must be able to find the image of this circle by a
translation or a central symmetry .
Question 4 : Geometry
(a) Must know you theorems (b) Must be able to find the
image of a triangle by an enlargement . I do not recommend
this question .
Question 5 Trigonometry :
(a)Must know how to find the length of an arc and to
find the lengths of the sides of a right angled triangle
.
and be able to use thses results in
tne expressions Sin(A+B), Cos(A+B) as given in page 9
of the maths tables (b) Must be able to use the Sine Rule
and the Cosine Rules to solve a triangle . (c) Must be
able to use your calculator to solve trigonometric equations
ex If Cos X = - .5 find two values of X between 0 and
360 degrees .
Question 6 Probability /Permutations
/Combinations .
(a) Must know to find the number of
arrangements of n things (i) all at a time (ii) r at a
time . (b) Must Know how to find the number of selections
of n things r at a time (ncr) . (c) Must know the rules
for probability (the and or rules ).
Question 7: Statistics ;
(a) Must be able to find ,the mean and
mode of a frequency table . (b) Must be able to find a
weighted mean . (c) Must be able to draw a Histogram from
a frequency table where the class intervals are unequal
. (d) Must be able to complete a partially completed frequency
table given a Histogram .(e) Must be able to construct
a cumulative frequency table ,draw an Ogive find the median
and inter quartile range . (f) Must be able to answer
questions on the ogive .
The Options :
Question 8 Further Geometry :
Questions based on the extra geometry
theorems (only 5) best advice is to avoid this question
unless you have done higher junior cert maths! .
Question 9 : Vectors :
(a)Must be able to add vectors using the triangle rule
. (b) Must be able to write vectors in terms of two given
vectors. (c) Must be able to deal with vectors written
in terms of i and j . (the easiest option if explained
well)
Question 10 : The Binomial theorem /Further Sequences
and Series .
(a)Must be able to write out the Binomial expansion of
( 1 + x ) ,(1 - x) , n < = 7. n E N . (b)Must
know the formula for the sum to infinity of a GP . (c)
Must be able to find the Amount of an investment when
successive instalments are made .(First two bits are easy
the part c can be tricky)
Question 11: Linear Programming :
(a) Must be able to sketch inequalities of the form
3x + 4y < 12 . (b) Must be able to solve problems on
Linear programming . The good news is that the problem
can only involve two lines and the two axes .Easy question
but tends to take a long time
Ordinary
Level Paper 2
