Kilroy's College

Kilroy's College

Online & Home Study Courses

Leaving Certificate Maths course

Course Contents

Remember, you can complete this Leaving Certificate Maths course within 6 to 24 Months of enrolling. So take your first step by contacting us today !

Please note the content shown below is 2023 syllabus. This course is also available for 2024 syllabus. Please contact college for details.

Higher Level

See Ordinary level >>

Algebra

Probability

Arithmetics

Statistics

Number Systems

Trigonometry


Detailed Content

Algebra

  • Algebraic operations on polynomials and rational functions.
  • Addition, subtraction, multiplication and division and the use of brackets and surds
  • Laws of indices and logarithms
  • The Factor Theorem for polynomials of degree two or three.
  • Factorisation of such polynomials (the linear and quadratic factors having integer coefficients).
  • Solution of cubic equations with at least one integer root.
  • Solution of equations e.g. f(x) = g(x)
  • Sums and products of roots of quadratic equations.
  • Unique solution of simultaneous linear equations with two or more unknowns.
  • Inequalities: solution of inequalities of the form g(x) < k, where g(x) = ax2+bx+c
  • Use of the notation |x|; solution of |x-a| < b, |x – a| >b and combinations of these

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Euclidean geometry

  • Geometrical constructions
  • Proof of theorems
  • Enlargements

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Probability

  • Fundamental principle of counting
  • Discrete probability – simple cases – tossing coins, dice throwing, birthday distribution etc.
  • Outcome space, events
  • Addition of probabilities, conditional probability, independent events
  • Binomial and normal distributions
  • Populations and samples

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Coordinate geometry of the straight line and circle

  • General equation of the line in form ax+by+c = 0
  • Length of perpendicular from (x1, y1) to ax+by+c = 0
  • Angle between two lines with slopes m1 and m2
  • Equation of line through the intersection of two lines a1x+b1y+c1 = 0 and a2x+b2y+c2 = 0 {form L(a1x+b1y+c1)+M(a2x+b2y+c2) = 0, L, M constant}
  • Division of a line segment in ratio m:n
  • Addition, substraction of vectors, multiplication by a scalar. Unit vectors i and j
  • Equation of circle centre (0,0) and radius r (x2 + y2 = r2)
  • General equation of circle centre (- g, - f) and radius r (x2 + y2 + 2gx + 2fy + c = 0)
  • Equation of tangent at (x1, y1) to x2 + y2 = r2
  • Intersection of line and specific circle

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Arithmetics

  • Percentage error and tolerance
  • Rates, income tax, PRSI and USC
  • Value Added Tax (VAT)
  • Costing (materials, labour and wastage)
  • Area and perimeter of 2D shapes
  • Area and circumference of circles and sectors of circles
  • Problems involving area
  • The nets of rectangular solids
  • Surface area and volume of various 3D shapes
  • Problems involving surface area and volume
  • Trapezoid rule to approximate area

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Functions and Differential Calculus

  • Finding the period and range of a continuous periodic function, given its graph on scaled and labelled axis
  • Informal treatment of limits of functions: Rules for sums, products and quotients
  • Derivations from first principles of x2, x3, sin x, cos x, 1/x
  • First derivatives of polynomials, rational, power and trigonometric functions
  • First derivatives of sums
  • First derivatives of differences
  • First derivatives of products
  • First derivatives of quotients
  • Application to finding tangents to curves
  • Simple second derivatives
  • First derivatives of implicit and parametric functions
  • Rates of change
  • Maxima and minima
  • Curve sketching

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Statistics

  • Calculation of mean and standard deviation
  • Centres of measure – mean, median and mode
  • Line of best fit
  • Make predictions based on the line of best fit
  • Percentiles
  • Interquartile range

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Number Systems

  • Review of numbers systems
  • Complex numbers: Argand diagram; addition, subtraction, multiplication, division; modulus; conjugate; conjugates of sums and products; conjugate root theorem
  • De Moivre’s theorem: proof by induction, applications such as nth roots of unity and identities

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Series and Induction

  • Geometric sequences and series
  • Sum of finite and infinite geometric series
  • Sum to infinity of geometric series
  • Applications of above e.g. derive the formula for a mortgage repayment
  • Recurring decimals as infinite GPs
  • Induction

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Trigonometry

  • Use the radian measure of angles
  • Calculate the area of a sector of a circle and the length of an arc and solve problems involving these calculations
  • Use trigonometry to calculate the area of a triangle
  • Use the sine and cosine rules to solve problems 2D and 3D
  • Define sine A, cos A and tan A for all values of A
  • Graph the trigonometric function sine, cosine and tangent
  • Graph trigonometric functions of type a sinnA, a cosnA for an n ε N
  • Solve trigonometric equations such as sinnA = 0 and cosnA = ½ giving all solutions
  • Calculate the area of a sector of a circle and the length of an arc and solve problems involving these calculations
  • Derive the trigonometric formulae 1, 2, 3, 4, 5, 6, 7, 9
  • Apply the trigonometric formulae 1 - 24

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Integral Calculus

  • Integration techniques (integrals of sums, multiplying constants, and substitution)
  • Definite integrals with applications to areas and volumes of revolution (confined to cones and spheres)

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