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

Unit 2: 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

Unit 3: 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

Unit 4: 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

Unit 5: 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)

Unit 6: 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

Unit 7: 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)

Unit 8: 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

Unit 9: 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

Unit 10: 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

Unit 11: Final Test 1

Unit 12: Final Test 2