# 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

## Detailed Content

- 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

- 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

- 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

- 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

- 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)

- 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: 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)

- 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

- 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

- 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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