#### G1. ANGLES, TRIANGLES & POLYGONS

- right, acute, obtuse and reflex angles
- vertically opposite angles, angles on a straight line and angles at a point
- angles formed by two parallel lines and a transversal: corresponding angles, alternate angles, interior angles
- properties of triangles, special quadrilaterals and regular polygons (pentagon, hexagon, octagon and decagon), including symmetry properties
- classifying special quadrilaterals on the basis of their properties
- angle sum of interior and exterior angles of any convex polygon
- properties of perpendicular bisectors of line segments and angle bisectors
- construction of simple geometrical figures from given data (including perpendicular bisectors and angle bisectors) using compasses, ruler, set squares and protractors, where appropriate

#### G2. CONGRUENCE & SIMILARITY

- congruent figures and similar figures
- properties of similar triangles and polygons:
- corresponding angles are equal
- corresponding sides are proportionaL
- enlargement and reduction of a plane figure
- scale drawings
- determining whether two triangles are
- congruent
- similar
- ratio of areas of similar plane figures
- ratio of volumes of similar solids
- solving simple problems involving similarity and congruence

#### G3. PROPERTIES OF CIRCLES

- symmetry properties of circles:
- equal chords are equidistant from the centre
- the perpendicular bisector of a chord passes through the centre
- tangents from an external point are equal in length
- the line joining an external point to the centre of the circle bisects the angle between the tangents
- angle properties of circles:
- angle in a semicircle is a right angle
- angle between tangent and radius of a circle is a right angle
- angle at the centre is twice the angle at the circumference
- angles in the same segment are equal
- angles in opposite segments are supplementary

#### G4. PYTHAGORAS' THEOREM & TRIGONOMETRY

- use of Pythagoras’ theorem
- determining whether a triangle is right-angled given the lengths of three sides
- use of trigonometric ratios (sine, cosine and tangent) of acute angles to calculate unknown sides and angles in right-angled triangles
- extending sine and cosine to obtuse angles
- use of the formula \( \frac{1}{2} \)ab sin C for the area of a triangle
- use of sine rule and cosine rule for any triangle
- problems in two and three dimensions including those involving angles of
elevation and depression and bearings

#### G5. MENSURATION

- area of parallelogram and trapezium
- problems involving perimeter and area of composite plane figures
- volume and surface area of cube, cuboid, prism, cylinder, pyramid, cone and sphere
- conversion between cm
^{2}and m^{2}, and between cm^{3}and m^{3} - problems involving volume and surface area of composite solids
- arc length, sector area and area of a segment of a circle
- use of radian measure of angle (including conversion between radians and degrees)

#### G6. COORDINATE GEOMETRY

- finding the gradient of a straight line given the coordinates of two points on it
- finding the length of a line segment given the coordinates of its end points
- interpreting and finding the equation of a straight line graph in the form y = mx + c
- geometric problems involving the use of coordinates

#### G7. VECTORS IN 2 DIMENSIONS

- use of notations:\( \binom {x} {y} , \vec{AB} \),
**a**, \( \left| \begin{matrix} \vec{AB} \end{matrix} \right| \) and \( \left| \begin{matrix}**b**\end{matrix} \right| \) - representing a vector as a directed line segment
- translation by a vector
- position vectors
- magnitude of a vector \( \binom {x} {y} \) as \( \sqrt{x^2+y^2} \)
- use of sum and difference of two vectors to express given vectors in terms of two coplanar vectors
- multiplication of a vector by a scalar
- geometric problems involving the use of vectors

#### G8. PROBLEMS IN REAL-WORLD CONTEXTS

- solving problems in real-world contexts (including floor plans, surveying, navigation, etc.) using geometry
- interpreting the solution in the context of the problem

#### N1. NUMBERS & THEIR OPERATIONS

- primes and prime factorisation
- finding highest common factor (HCF) and lowest common multiple (LCM), squares, cubes, square roots and cube roots by prime factorisation
- negative numbers, integers, rational numbers, real numbers, and their four operations
- calculations with calculator • representation and ordering of numbers on the number line
- use of the symbols <, >, ⩽, ⩾
- approximation and estimation (including rounding off numbers to a required number of decimal places or significant figures and estimating the results of computation)
- use of standard form A × 10
^{n}, where n is an integer, and 1 ⩽ A < 10 - positive, negative, zero and fractional indices
- laws of indices

#### N2. RATIO & PROPORTION

- ratios involving rational numbers
- writing a ratio in its simplest form
- map scales (distance and area)
- direct and inverse proportion

#### N3. PERCENTAGE

- expressing one quantity as a percentage of another
- comparing two quantities by percentage
- percentages greater than 100%
- increasing/decreasing a quantity by a given percentage
- reverse percentages

#### N4. RATE & SPEED

- average rate and average speed
- conversion of units (e.g. km/h to m/s)

#### N5. ALGEBRAIC EXPRESSIONS & FORMULAE

- using letters to represent numberS
- interpreting notations:
- ab as a × b
- \( \frac{a}{b} \) as a ÷ b or a × \( \frac{1}{b} \)
- a
^{2}as a × a, a^{3}as a × a × a, a^{2}b as a × a × b, ... - 3y as y + y + y or 3 × y
- 3(x + y) as 3 × (x + y)
- \( \frac{3+y}{5} \) as (3 + y) ÷ 5 or \( \frac{1}{5} \) × (3 + y)
- evaluation of algebraic expressions and formulae
- translation of simple real-world situations into algebraic expressions
- recognising and representing patterns/relationships by finding an algebraic expression for the nth term
- addition and subtraction of linear expressions
- simplification of linear expressions such as:
- −2(3x − 5) + 4x
- \( \frac{2x}{3}- \frac{3(x-5)}{2} \)
- use brackets and extract common factors
- factorisation of linear expressions of the form ax + bx + kay + kby
- expansion of the product of algebraic expressions
- changing the subject of a formula
- finding the value of an unknown quantity in a given formula
- use of:
- (a + b)
^{2}= a^{2}+ 2ab + b^{2} - (a − b)
^{2}= a^{2}− 2ab + b^{2} - a
^{2}− b^{2}= (a + b)(a − b) - factorisation of quadratic expressions ax
^{2}+ bx + c - multiplication and division of simple algebraic fractions such as:
- \( ( \frac{3a}{4b^2})( \frac{5ab}{3}) \)
- \( \frac{3a}{4} \div \frac{9a^2}{10} \)
- addition and subtraction of algebraic fractions with linear or quadratic denominator such as:
- \( \frac{1}{x-2} + \frac{2}{x-3} \)
- \( \frac{1}{x^2-9} + \frac{2}{x-3} \)
- \( \frac{1}{x-3} + \frac{2}{(x-3)^2} \)

#### N6. FUNCTIONS & GRAPHS

- Cartesian coordinates in two dimensions
- graph of a set of ordered pairs as a representation of a relationship between two variables
- linear functions (y = ax + b) and quadratic functions (y = ax
^{2}+ bx + c) - graphs of linear functions
- the gradient of a linear graph as the ratio of the vertical change to the horizontal change (positive and negative gradients)
- graphs of quadratic functions and their properties:
- positive or negative coefficient of x
^{2} - maximum and minimum points
- symmetry
- sketching the graphs of quadratic functions given in the form:
- y = – (x − p)
^{2}+ q - y = − (x − p)
^{2}+ q - y = – (x − a)(x − b)
- y = − (x − a)(x − b)
- graphs of power functions of the form y = ax
^{n}, where n = −2, −1, 0, 1, 2, 3, and simple sums of not more than three of these - graphs of exponential functions y = ka
^{x}, where a is a positive integer - estimation of the gradient of a curve by drawing a tangent

#### N7. EQUATIONS & INEQUALITIES

- solving linear equations in one variable
- solving simple fractional equations that can be reduced to linear equations
such as:
- \( \frac{x}{3} + \frac{x-2}{4} =3 \)
- \(\frac{3}{x-2} =6 \)
- solving simultaneous linear equations in two variables by
- substitution and elimination methods
- graphical method
- solving quadratic equations in one unknown by
- factorisation
- use of formula
- completing the square for y = x
^{2}+ px + q - graphical methods
- solving fractional equations that can be reduced to quadratic equations such as:
- \( \frac{6}{x+4} \)=x+3
- \( \frac{1}{x-2}+ \frac{2}{x-3}=5 \)
- formulating equations to solve problems
- solving linear inequalities in one variable, and representing the solution on
the number line

#### N8. SET LANGUAGE & NOTATION

- use of set language and the following notation:
- Union of A and B A ∪ B
- Intersection of A and B A ∩ B
- ‘... is an element of ...’ ∈
- ‘... is not an element of ...’ ∉
- Complement of set A A′
- The empty set ∅
- Universal set \( \xi \)
- A is a (proper) subset of B A ⊂ B
- A is not a (proper) subset of B A ⊄ B
- union and intersection of two sets
- Venn diagrams

#### N9. MATRICES

- display of information in the form of a matrix of any order
- interpreting the data in a given matrix
- product of a scalar quantity and a matrix
- problems involving the calculation of the sum and product (where appropriate) of two matrices

#### N10. PROBLEMS IN REAL-WORLD CONTEXTS

- solving problems based on real-world contexts:
- in everyday life (including travel plans, transport schedules, sports and games, recipes, etc.)
- involving personal and household finance (including simple and compound interest, taxation, instalments, utilities bills, money exchange, etc.)
- interpreting and analysing data from tables and graphs, including distance– time and speed–time graphS
- interpreting the solution in the context of the problem

#### S1. DATA ANALYSIS

- analysis and interpretation of:
- tables
- bar graphs
- pictograms
- line graphs
- pie charts
- dot diagrams
- histograms with equal class intervals
- stem-and-leaf diagrams
- cumulative frequency diagrams
- box-and-whisker plots
- purposes and uses, advantages and disadvantages of the different forms of statistical representations
- explaining why a given statistical diagram leads to misinterpretation of data
- mean, mode and median as measures of central tendency for a set of data
- purposes and use of mean, mode and median
- calculation of the mean for grouped data
- quartiles and percentiles
- range, interquartile range and standard deviation as measures of spread for a set of data
- calculation of the standard deviation for a set of data (grouped and ungrouped)
- using the mean and standard deviation to compare two sets of data

#### S2. PROBABILITY

- probability as a measure of chance
- probability of single events (including listing all the possible outcomes in a simple chance situation to calculate the probability)
- probability of simple combined events (including using possibility diagrams and tree diagrams, where appropriate)
- addition and multiplication of probabilities (mutually exclusive events and independent events)