IB-12-Syllabus-Maths

                     IB 12 SYLLABUS  MATHS

Topic 1

Algebra

 Topic 2

 Functions and equations

 Topic 3

Circular functions and trigonometry

 Topic 4

Vectors

Topic 5

Statistics and probability

 Topic 6

Calculus

 Mathematical exploration

Internal assessment in mathematics SL is an individual exploration. This is a piece of written work that involves investigating an area of mathematics.

Topic

 Number

Content

 Routine use of addition, subtraction, multiplication and division, using integers, decimals and fractions, including order of operations. Simple positive exponents. Simplification of expressions involving roots (surds or radicals). Prime numbers and factors, including greatest common divisors and least common multiples. Simple applications of ratio, percentage and proportion, linked to similarity. Definition and elementary treatment of absolute value (modulus), a . Rounding, decimal approximations and significant figures, including appreciation of errors. Expression of numbers in standard form (scientific notation), that is, 10k a × , 1 10 ≤ < .¢a , k ∈

Sets and numbers

 Concept and notation of sets, elements, universal (reference) set, empty (null) set, complement, subset, equality of sets, disjoint sets. Operations on sets: union and intersection. Commutative, associative and distributive properties. Venn diagrams. .¡, and irrationals; real numbers, ¤; rationals, ¢Number systems: natural numbers; integers,  Intervals on the real number line using set notation and using inequalities. Expressing the solution set of a linear inequality on the number line and in set notation. Mappings of the elements of one set to another. Illustration by means of sets of ordered pairs, tables, diagrams and graphs.

 Algebra

Manipulation of simple algebraic expressions involving factorization and expansion, including quadratic expressions. Rearrangement, evaluation and combination of simple formulae. Examples from other subject areas, particularly the sciences, should be included. The linear function and its graph, gradient and y-intercept. Addition and subtraction of algebraic fractions. The properties of order relations: <≤>≥ ,,, . Solution of equations and inequalities in one variable, including cases with rational coefficients. Solution of simultaneous equations in two variables. 16 Mathematics SL guide Prior learning topics Topic Content.

Trigonometry

Angle measurement in degrees. Compass directions and three figure bearings. Right-angle trigonometry. Simple applications for solving triangles. Pythagoras’ theorem and its converse.

 Geometry

 Simple geometric transformations: translation, reflection, rotation, enlargement. Congruence and similarity, including the concept of scale factor of an enlargement. The circle, its centre and radius, area and circumference. The terms “arc”, “sector”, “chord”, “tangent” and “segment”. Perimeter and area of plane figures. Properties of triangles and quadrilaterals, including parallelograms, rhombuses, rectangles, squares, kites and trapeziums (trapezoids); compound shapes. Volumes of prisms, pyramids, spheres, cylinders and cones. Coordinate geometry Elementary geometry of the plane, including the concepts of dimension for point, line, plane and space. The equation of a line in the form y mx c = + . Parallel and perpendicular lines, including m m 1 2 = and 1 2 m m = −1. Geometry of simple plane figures. The Cartesian plane: ordered pairs (, ) x y , origin, axes. Mid-point of a line segment and distance between two points in the Cartesian plane and in three dimensions.

 Statistics and probability

 Descriptive statistics: collection of raw data; display of data in pictorial and diagrammatic forms, including pie charts, pictograms, stem and leaf diagrams, bar graphs and line graphs. Obtaining simple statistics from discrete and continuous data, including mean, median, mode, quartiles, range, interquartile range. Calculating probabilities of simple events. Mathematics SL guide 17 Syllabus Syllabus content Syllabus content