Mathematics (0607): Extended/Core

NUMBER

ALGEBRA

FUNCTIONS

COORDINATE GEOMETRY

GEOMETRY

VECTORS & TRANSFORMATIONS

MENSURATION

TRIGONOMETRY

SETS

PROBABILITY

STATISTICS

Vocabulary and notation for different sets of numbers: 1. natural numbers ℕ, 2. primes, 3. squares, 4. cubes, 5. integers ℤ, 6. rational numbers ℚ, 7. irrational numbers, 8. real numbers ℝ, 9. triangle numbers

Use of the four operations and brackets

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

Calculation of powers and roots

Ratio and proportion

Absolute value | x |

Equivalences between decimals, fractions and percentages

Percentages including applications such as interest and profit

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

Rules for exponents

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 simple linear inequalities

Solution of linear equations

Simple indices – multiplying and dividing

Derivation, rearrangement and evaluation of simple formulae

Solution of simultaneous linear equations in two variables

Expansion of brackets

Factorisation: common factor only

Algebraic fractions: 1. Simplification addition or subtraction of fractions with integer denominators 2. Multiplication or division of two simple fractions

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

Continuation of a sequence of numbers or patterns 1. Determination of the nth term 2. Use of a difference method to find the formula for a linear sequence or a simple quadratic sequence

Notation, Domain and range and Mapping diagrams

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

Use of a graphic display calculator to: 1. Sketch the graph of a function 2. Produce a table of values 3. Find zeros, local maxima or minima 4. Find the intersection of the graphs of functions

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

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 or x = k

Symmetry of diagrams or graphs in the Cartesian plane

Use and interpret the geometrical terms: 1. acute, obtuse, right angle, reflex, parallel, perpendicular, congruent, similar 2. Use and interpret vocabulary of triangles, quadrilaterals, polygons and simple solid figures

Line and rotational symmetry

Angle measurement in degrees

1. Angles round a point 2. Angles on a straight line and intersecting straight lines 3. Vertically opposite angles 4. Alternate and corresponding angles on parallel lines 5. Angle sum of a triangle, quadrilateral and polygons 6. Interior and exterior angles of a polygon 7. Angles of regular polygons

Similarity and the calculation of lengths of similar figures

Pythagoras’ Theorem in two dimensions, including: chord length, distance of a chord from the centre of a circle and 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

Notation: component form (vertical matrix 2x1)

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

Units of distance, area, volume, capacity and weight (Metric system)

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

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

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

Areas and volumes of compound shapes

Right-angled triangle trigonometry

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

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 two 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 (Simple cases only)

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 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

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

Solution of linear equations including those with fractional expressions

Indices

Expansion of brackets, including the square of a binomial

Factorisation:

Algebraic fractions:

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

Continuation of a sequence of numbers or patterns

Variation

Recognition of the following function types from the shape of their graphs:1. Linear2. Quadratic3. Cubic4. Reciprocal5. Exponential6. Absolute Value7. Trigonometric

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

Finding the quadratic function given:

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

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 = (logb)/(loga)

Linear inequalities in the Cartesian plane

Use of area and volume scale factors

Use and interpret vocabulary of circles Properties of circles:

Vectors

Find the magnitude of (vertical matrix 2x1)

Transformations on the cartesian plane and description of a transformation

Inverse of a transformation

Combined transformations

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 & three dimensions

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

Venn diagrams with at most three sets

Combining events

Scatter Graphs

common factor

difference of squares

trinomial

four term

simplification, including use of factorisation addition or subtraction of fractions with linear denominators or single term

multiplication or division and simplification of two fractions

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 (propotion) with linear, quadratic, cubic and square root functions

Inverse Variation with linear, quadratic and square root functions

Best variation for given data.

Vertex and another point

X-intercepts and a point

Vertex or x-intercepts with a = 1

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 

Addition and subtraction of vectors

Negative of a vector

Multiplication of a vector by a scalar

translation

reflection

rotation

enlargement (reduction)

stretch

the addition rule P(A or B) = P(A) + P(B)

the multiplication rule P(A and B) = P(A) × P(B)

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