International Mathematics (0607): Extended Curriculum

Number

Algebra

Functions

Coordinate Geometry

Geometry

Vectors and Transformations

Mensuration

Trigonometry

Sets

Probability

Statistics

Vocabulary and notation for different sets of numbers: natural numbers ℕ, primes, squares, cubes, integers ℤ, rational numbers ℚ, irrational numbers, real numbers ℝ, triangle numbers

Ratio and proportion

Calculation of powers and roots

Highest common factor (HCF), lowest common multiple (LCM)

Use of the four operations and brackets

Equivalences between decimals, fractions and percentages

Absolute value | x |

Meaning of exponents (powers, indices) in ℚ Standard Form, a × 10^n where 1 ⩽ a < 10 and n ∈ ℤRules for exponents

Percentages including applications such as interest and profit

Surds (radicals), simplification of square root expressions Rationalisation of the denominator

Estimating, rounding, decimal places and significant figures

Calculations involving time: seconds (s), minutes (min), hours (h), days, months, years including the relation between consecutive units

Problems involving speed, distance and time

Writing, showing and interpretation of inequalities, including those on the real number line

Solution of linear and quadratic inequalities Solution of inequalities using a graphic display calculato

Solution of linear equations including those with fractional expressions

Indices

Derivation, rearrangement and evaluation of formulae

Solution of simultaneous linear equations in two variables

Expansion of brackets, including the square of a binomial

Factorisation: common factor, difference of squares, trinomial, four term

Algebraic fractions: simplification, including use of factorisation,  addition or subtraction of fractions with linear denominators or single term,  multiplication or division and simplification of two fractions

Solution of quadratic equations: by factorisation, using a graphic display calculator, using the quadratic formula

Use of a graphic display calculator to solve equations, including those which may be unfamiliar

Continuation of a sequence of numbers or patterns Determination of the nth term Use of a difference method to find the formula for a linear sequence, a quadratic sequence or a cubic sequence Identification of a simple geometric sequence and determination of its formula

Direct variation (proportion)Inverse variationBest variation model for given data

Notation, Domain and range, Mapping diagrams

Recognition of the following function types from the shape of their graphs: Linear, Quadratic, Cubic, reciprocal, exponential, absolute value, trigonometric

Determination of at most two of a, b, c or d in simple cases of E3.2

Finding the quadratic function given vertex and another point, x-intercepts and a point, vertex or x-intercepts with a = 1

Understanding of the concept of asymptotes and graphical identification of simple examples parallel to the axes

Use of a graphic display calculator to: sketch the graph of a function, produce a table of values, find zeros, local maxima or minima,  find the intersection of the graphs of functions

Simplify expressions such as f(g(x)) where g(x) is a linear expression

Description and identification, using the language of transformations, of the changes to the graph of y = f(x) when y = f(x) + k, y = kf(x), y = f(x + k)

Inverse function

Logarithmic function as the inverse of the exponential function, y = a^x equivalent to x = loga y, Rules for logarithms corresponding to rules for exponents, Solution to a^x = b as x = loga/logb

Plotting of points and reading from a graph in the Cartesian plane

Distance between two points

Mid-point of a line segment

Gradient of a line segment

Gradient of parallel lines

Equation of a straight line as y = mx + c and ax + by = d (a, b and d integer)

Linear inequalities in the Cartesian plane

Symmetry of diagrams or graphs in the Cartesian plane

Use and interpret the geometrical terms: acute, obtuse, right angle, reflex, parallel, perpendicular, congruent, similar Use and interpret vocabulary of triangles, quadrilaterals, polygons and simple solid figures

Line and rotational symmetry

Angle measurement in degrees

Angles round a point Angles on a straight line and intersecting straight lines Vertically opposite angles Alternate and corresponding angles on parallel lines Angle sum of a triangle, quadrilateral and polygons Interior and exterior angles of a polygon Angles of regular polygons

Similarity Calculation of lengths of similar figures Use of area and volume scale factors

Pythagoras’ Theorem and its converse in two and three dimensions Including: chord length distance of a chord from the centre of a circle distances on a grid

Use and interpret vocabulary of circles Properties of circles: • tangent perpendicular to radius at the point of contact • tangents from a point • angle in a semicircle • angles at the centre and at the circumference on the same arc • cyclic quadrilateral • alternate segment

Notation: component form (vertical vector)

Addition and subtraction of vectors Negative of a vector Multiplication of a vector by a scalar

Find the magnitude of (Vertical Vector) 

Transformations on the Cartesian plane: • translation • reflection • rotation • enlargement (reduction) • stretchDescription of a transformation 

Inverse of a transformation

Combined transformations

Converting between units.

Perimeter and area of rectangle, triangle and compound shapes derived from these

Circumference and area of a circle Arc length and area of sector

Surface area and volume of prism and pyramid (in particular, cuboid, cylinder and cone) Surface area and volume of sphere and hemisphere

Areas and volumes of compound shapes

Right-angled triangle trigonometry

Exact values for the trigonometric ratios of 0°, 30°, 45°, 60°, 90° 

Extension to the four quadrants, i.e. 0°–360°

Sine rule

Cosine rule

Area of triangle

Applications: three-figure bearings and North, East, South, West problems in two and three dimensions

Properties of the graphs of y = sin x, y = cos x, y = tan x

Notation and meaning for: • number of elements in A (n(A)) • is an element of (∈) • is not an element of (∉) • complement of A (A′) • empty set (∅ or { }) • universal set (U) • is a subset of (⊆) • is a proper subset of (⊂)

Sets in descriptive form { x |      } or as a list

Venn diagrams with at most three sets

Intersection and union of sets

Probability P(A) as a fraction, decimal or percentage Significance of its value

Relative frequency as an estimate of probability

Expected frequency of occurrences

Combining events: the addition rule P(A or B) = P(A) + P(B) the multiplication rule P(A and B) = P(A) × P(B)

Tree diagrams including successive selection with or without replacement

Probabilities from Venn diagrams and tables

Reading and interpretation of graphs or tables of data

Discrete and continuous data

(Compound) bar chart, line graph, pie chart, pictograms, stem-and-leaf diagram, scatter diagram

Mean, mode, median, quartiles and range from lists of discrete data Mean, mode, median and range from grouped discrete data

Mean from continuous data

Cumulative frequency table and curve Median, quartiles, percentiles and interquartile range

Use of a graphic display calculator to calculate mean, median, and quartiles for discrete data and mean for grouped data

Understanding and description of correlation (positive, negative or zero) with reference to a scatter diagram Straight line of best fit (by eye) through the mean on a scatter diagram Use a graphic display calculator to find equation of linear regression