Kilroy's College

Kilroy's College

Online & Home Study Courses

Junior Certificate Mathematics course

Course Contents

Remember, you can complete this Junior Certificate Mathematics course within 12 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 >>

Functions

Final Test 1

Final Test 2


Detailed Content

Sets and Number Patterns (Strand 3)

  • Listing of elements of a set. Membership of a set defined by a rule. Universe, subsets. Null set (empty set). Equality of sets
  • Venn diagrams
  • Set operations: intersection, union, difference, complement. Set operations extended to three sets
  • Commutative property and associative property for intersection and union; failure of commutativity and associativity for difference; necessity of brackets
  • Number Patterns: linear sequences/patterns; quadratic sequences; exponential sequences

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Number Systems (Strand 3)

  • The set N of natural numbers. Place value. Sets of divisors. Pairs of factors. Prime numbers. Sets of multiples. Lowest common multiple
  • Highest common factor. Cardinal number of a set. The operations of addition, subtraction, multiplication and division in N
  • The set Z of integers. The operations of addition, subtraction, multiplication and division in Z. Use of the number line in addition and subtraction
  • The set Q of rational numbers. Decimals and fractions plotted on the number line
  • Rules for indices. Square roots, reciprocals: understanding and computation.
  • The set R of real numbers. Addition, subtraction and multiplication applied to a where a ε Q, b ε Q. The set of irrational numbers RQ
  • Commutative and associative properties for addition and multiplication; failure of commutativity and associativity for division; distributive property

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Applied Arithmetic and Measure

  • Bills. Profit and loss. Percentage discount. Tax. Annual interest. Compound interest. Value added tax (VAT)
  • SI units of length, area, mass and time. Multiples and submultiples. Twenty four clock transport timetables. Relationship between average speed and distance
  • Perimeter and area: square, rectangle, triangle. Surface area and volume of rectangular solids. Use of formulae for circle etc.
  • Application to problems including the calculation of the area/volume of compound figures. Length of circumference of circle = 2πr. Length of diameter
  • Application to problems including use of the theorem of Pythagoras

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Algebra (Strand 4)

  • Meaning of variable, constant, term, expression, coefficient. Evaluation of expressions
  • Addition and subtraction of simple algebraic expressions of form
  • Addition, subtraction, multiplication and division of expressions of the form
  • Use of the distributive law in the factorising of expressions
  • Factorisation of quadratic expressions of the for assignment

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Statistics (Strand 1)

  • Collecting and recording data. Tabulating data. Drawing and interpreting bar charts, pie charts, and trend graphs. Mean, median and mode
  • Discrete array as a frequency table. Drawing and interpreting histograms. Mean of a grouped frequency distribution, median, interquartile range. (HL)

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Geometry (Strand 2)

  • Preliminary concepts: the plane, points on the plane, lines, line segments and half-lines (rays)
  • Length of line segments, collinear points, angle notation, identify different types of angles, estimation and measurement of angles
  • Recognise perpendicular, parallel, vertical and horizontal lines, use axioms to solve problems
  • Theorems (Proofs necessary for Higher Level)
  • Vertically opposite angles, alternate and corresponding angles in parallel lines
  • Triangles – isosceles, equilateral and scalene, sum of angles in a triangle
  • Quadrilaterals, parallelograms, rectangles and squares
  • Properties of the circle

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Transformation Geometry, Co-ordinate Geometry and Trigonometry (Strand 2)

  • Transformation geometry: axis of symmetry, translation, central symmetry, centre of symmetry axial symmetry
  • Coordinate geometry: coordinating the plane; coordinates of images of points under translation, axial symmetry in the x or y axis and central symmetry
  • Using two points to get the midpoint, distance, and slope, slope intercept. Parallel and perpendicular lines (HL)
  • Trigonometry: cosine, sine and tangent of angles less than 90. Values of these ratios for integer values of angle. Value of angle, given value of sin, cos, tan
  • Functions of 30 o 45 o and 60 o in surd form, derived from suitable triangles Solution of right-angled triangle problems of a simple nature
  • Mariner’s compass (HL)

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Algebra continued (Strand 4)

  • Formation and interpretation of number sentences leading to the solution of first degree equations in one variable. First degree equations in two variables
  • Quadratic equations of the form ax2 + bx + c = 0. Solution using factors and/or the formula for real roots only. Problems and their solutions
  • Solution of equations. Problems and their solutions
  • Solution of linear inequalities in one variable

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Probability (Strand 1)

  • Outcomes, listing outcomes: systematic listing, two-way tables, tree diagrams
  • The fundamental principle of counting: introduction to probability, the language of probability, the likelihood scale, the probability scale
  • Relative frequency, relative frequency and fairness, probability, expected frequency
  • Using counting methods to solve probability questions: two- way tables, tree diagrams, using Venn diagrams

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Functions

  • Concept of a function. Couples, domain, codomain and range
  • Drawing graphs of functions f:x->f(x), where f(x) is of the form ax+b or ax2+ bx + c
  • Using the graphs to estimate the (range of) value(s) of x for which f(x)=k
  • Maximum and minimum values of quadratic functions estimated from graphs (Higher Level only)
  • Graphing solution sets on the number line for linear inequalities in one variable
  • Graphical treatment of solution of first degree simultaneous equations in two variables

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Final Test 1

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Final Test 2

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