# 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 >>

## 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

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

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

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

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)

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

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)

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

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

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

Final Test 1