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Leaving Cert Pass Paper 2

Must Know File .

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 (ii)Must be able to find the area of a rectangle , surface area of a cube , area of a triangle .(b)Must be able to use Simpsons rule 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.This Question is often dived into Questions based on points , Questions based on lines .

Question 3: The Circle:

(a)Must be able to find the centre and radius of , show a point is on /not on the circle , find where this circle cuts the axes . (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 ( The Quick way is to use the formula . (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 .(by the way thecircle in the formis not on the course !)

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 a question based on the right angled triangle has been asked every year since 1995!(b) Must be able to use the Sine Rule and the Cosine Rules to solve a triangle (find the length of the sides and the measure of the angles) . (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 . (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 , ,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 and name the inequalities in a given Diagram. (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

(b) Best preparation for 2001, (1) Pick your questions! (2) practice 99,98,97 ,96.