Leaving Certificate Mathematics
Two papers of 2 1/2 hours each. There are 300 marks for each paper. Paper One: 9.30 - 12p.m., Thursday, June 8th.
Paper Two: 9.30 - 12p.m, Friday, June 9th. Students may use their own calculators. Calculators are not provided at the examination. Mathematical tables and graph paper will be provided.
Higher Course
Paper One
There are eight questions. Students should attempt at least six. If more than six questions are attempted, the best six marks are used to calculate the total mark.
In general terms: Question 1, Question 2, Question 3, and Question 5 seem to examine key algebra skills.
The application or proof of the Factor Theorem seems to turn up in Question One.
A question testing the ability to manipulate powers (indices) in nth terms of expressions seems to turn up in Question Two.
Question Three seems also to test operations with matrices (, -, x) and the calculation of the inverse of a matrix. Also the solution of simultaneous equations using matrix methods. The theory of complex numbers seems to be examined here.
Question Five also seems to test knowledge of the Binomial Theorem.
Question Four seems to examine the theory of sequences and series, including the binomial series and the properties of binomial coefficients.
Question Six and Question Seven seem to examine the theory of differentiation and applications to such topics as max/ min, curve sketching.
Question Eight seems to examine the theory of integration and its application to calculating the area bounded by a curve and the volume of revolution of a simple curve.
Paper Two
There are seven questions in Section A and four questions in Section B.
Students should attempt at least five from Section A and at least one question from Section B. If more than five questions are attempted from Section A, the best five marks are used in calculating the total mark. If more than one question is attempted from Section B the best mark is used in calculating the total mark.
Section A - Question One seems to test knowledge of the co-ordinate geometry of the circle.
Question Two seems to test knowledge of vectors.
Question Three seems to test knowledge of the co-ordinate geometry of the line and also transformational geometry.
Question Four and Question Five seem to test knowledge of trigonometry, the solution of trigonometric equations, applications of the Sine and Cosine Rules, and the proof of trigonometric identities.
Question Six and Question Seven seem to test knowledge of permutations and combinations and problems involving probability, the ability to solve a difference equation and also knowledge of mean, weighted mean, mode, median, and standard deviation.
Section B - Question Eight seems to test knowledge of integration by parts, applications of Maclaurin's Theorem, applications of the ratio test for the convergence of series, and the solution of a max/min problem.
Question Nine seems to test knowledge of further probability and statistics, involving binomial and normal distributions and tests of significance.
Question Ten seems to test knowledge of group theory and its basic concepts, and the proof of one of a specified list of results.
Question Eleven seems to test knowledge of further transformational geometry, involving basic properties of the ellipse, and the proof of (possibly) two theorems from the specified list of results.
Ordinary Course
Paper One
There are eight questions. Students should attempt at least six. If more than six questions are attempted, the best six marks are used to calculate the total mark.
In general terms:
Question One seems to test knowledge of arithmetic (ratio, proportion, compound interest and depreciation, speed, time, etc).
Questions Two and Three seem to test knowledge of key algebra skills (equations, factors, roots, powers etc).
Question Four seems to test knowledge of complex numbers.
Question Five seems to test knowledge of sequences and series.
Questions Six, Seven, and Eight seem to test knowledge of differentiation (from first principles and by rule), and applications to speed and acceleration, max/min problems, the slope of tangents to curves and curve sketching.
Paper Two
There are seven questions in Section A and four questions in Section B. Students should attempt at least five from Section A and at least one question from Section B. If more than five questions are attempted from Section A, the best five marks are used in calculating the total mark. If more than one question is attempted from Section B, the best mark is used in calculating the total mark.
Section A
In general terms:
Question One seems to test the calculation of areas and volumes, and the use of Simpson's Rule.
Question Two seems to test knowledge of the co-ordinate geometry of the straight line.
Question Three seems to test knowledge of the co-ordinate geometry of the circle.
Question Four seems to test knowledge of the geometry of the plane, involving the proof of one of the theorems specified for this section, and the application of theorem results to problems, and enlargements and reductions of plane figures.
Question Five seems to test knowledge of trigonometry (application of Pythagoras's Theorem, Sine Rule, Cosine Rule, etc).
Question Six seems to test knowledge of permutations, combinations and probability.
Question Seven seems to test knowledge of statistics (mean, mode, median, standard deviation, use of cumulative frequency curve, interquartile range etc.)
Section B
Question Eight seems to test knowledge of the geometry of the plane, involving the proof of one of the theorems specified for Section B, and the application of theorem results to problems.
Question Nine seems to test knowledge of vectors.
Question Ten seems to test knowledge of the Binomial Theorem and the expansion of series, the infinite sum of convergent geometric series and applications of compound interest and depreciation.
Question Eleven seems to test knowledge of inequalities and the graphing of regions of the plane which satisfy several inequalities. A problem involving linear programming is given.
Foundation Course
Paper One
There are seven questions. Students should attempt Question One (100 marks) and at least four others (50 marks each). If more than four other questions are attempted, the mark for Question One and the best four other marks are used to calculate the total mark.
Formulae required for this paper are printed at the end of the examination paper.
In general terms:
Question One seems to test the accurate and efficient use of the calculator to solve 10 short problems.
Question Two seems to test knowledge of the metric system, pay and tax problems, and buying and selling problems involving profit and loss.
Question Three seems to test knowledge of error and percentage error in estimation, compound interest and depreciation. Question Four seems to test knowledge of the solution of single equations and simultaneous equations. A problem is given which requires the formation of an equation or equations, and the solution of such.
Question Five seems to test knowledge of prime numbers and prime factors, the solution of a quadratic equation by factoring or by formula (which is given), and the solution of inequalities.
Question Six seems to test the ability to extract information from graphs and tables.
Question Seven seems to test knowledge of the ability to graph quadratic and linear functions on the same axes, and the use of these graphs to obtain approximate solutions to equations.
Paper Two
There are eight questions. Students should attempt at least six. If more than six questions are attempted, the best six marks are used to calculate the total mark. Students should receive a standard booklet containing the formulae required for the questions on length, area, volume, including Simpson's Rule; and the question on co-ordinate geometry.
In general terms:
Question One seems to test the calculation of lengths, perimeters and areas of plane figures and the use of Simpson's Rule.
Question Two seems to test the calculation of lengths, surface areas and volumes of three-dimensional objects. Problems involving melting and recasting may be asked.
Question Three seems to test the application of results from the specified list of theorems to geometrical problems.
Question Four seems to test knowledge of the co-ordinate geometry of points in the plane and of the line.
Question Five seems to test knowledge of trigonometry, the definitions of sin, cos, and tan, and the solution of a problem based on a right-angled triangle.
Question Six seems to test knowledge of the principle of counting and the calculation of probabilities involving AND/OR statements.
Question Seven seems to test knowledge of the mean, mode, median and standard deviation of statistical data. The use of the cumulative frequency curve to estimate the median and the construction of histograms with unequal groupings may be examined.
Question Eight seems to test the ability to carry out one of the specified geometrical constructions and the solution of problems involving the enlargement and reduction of plane figures.